Search

Recent attempts at measuring the variation of c using an assortment of standard candles and the redshift-dependent Hubble expansion rate inferred from the currently available catalogue of cosmic chronometers have tended to show that the speed of light appears to be constant, at least up to z ∼ 2. A notable exception is the use of high-redshift ultraviolet + X-ray quasars, whose Hubble diagram seems to indicate an ∼2.7σ deviation of c from its value c 0 (≡ 2.99792458 × 1010 cm s−1) on Earth. We show in this paper, however, that this anomaly is due to an error in the derived relation between the luminosity distance, D L, and H (z) when c is allowed to vary with redshift, and an imprecise calibration of the quasar catalogue. When these deficiencies are addressed correctly, one finds that c / c 0 = 0.95 ± 0.14 in the redshift range 0 ≲ z ≲ 2, fully consistent with zero variation within the measurement errors. [ABSTRACT FROM AUTHOR]

Momentum is characterized in terms of inertial mass for particles moving at less than the speed of light, but entirely in terms of their energy for those lacking inertia. Does this difference suggest a physically distinct origin of momentum in the two cases and, if so, what is actually being conserved in interactions involving both types of particle? In this paper, we consider a recently proposed gravitational origin for rest-mass energy to demonstrate that a single definition of momentum applies to all particles, massless or otherwise. When introduced into this description, inertial mass is merely a surrogate for the particle's 'free' energy, but does not imply an origin of momentum different from that of particles without mass. [ABSTRACT FROM AUTHOR]

Studies of the Universe's transition to smoothness in the context of Lambda cold dark matter (ΛCDM) have all pointed to a transition radius no larger than ∼300 Mpc. These are based on a broad array of tracers for the matter power spectrum, including galaxies, clusters, quasars, the Ly-α forest, and anisotropies in the cosmic microwave background. It is therefore surprising, if not anomalous, to find many structures extending out over scales as large as ∼2 Gpc, roughly an order of magnitude greater than expected. Such a disparity suggests that new physics may be contributing to the formation of large-scale structure, warranting a consideration of the alternative Friedmann–Lemaître–Robertson–Walker cosmology known as the R h = ct universe. This model has successfully eliminated many other problems in ΛCDM. In this paper, we calculate the fractal (or Hausdorff) dimension in this cosmology as a function of distance, showing a transition to smoothness at ∼2.2 Gpc, fully accommodating all of the giant structures seen thus far. This outcome adds further observational support for R h = ct over the standard model. [ABSTRACT FROM AUTHOR]

The energy conditions in general relativity are introduced to establish powerful theorems without having to restrict their applicability to specific choices of the stress‐energy tensor. They are famously invoked, e.g., to prove the singularity theorems of Penrose and Hawking, but have also been applied elsewhere, including various tests of certain cosmological theories. These conditions have become somewhat controversial, however, because they appear to be violated by commonly accepted scenarios, such as inflation shortly after the Big Bang and late‐time acceleration of the cosmic expansion. But accommodating these processes by abandoning all of the energy conditions will promote other disquieting possibilities, including the breakdown of causality with traversable wormholes and closed timeloops. This paper advocates for the opposite viewpoint, demonstrating that the 'numen' scalar field, derived from the zero active mass condition in general relativity, satisfies all of the energy conditions in the early Universe. This unique feature among scalar fields adds to its success in accounting for the observed properties of the cosmic microwave background better than its inflationary counterpart. Specifically, numen's complete consistency with all of the energy conditions, and inflation's violation of at least one of them, provides additional justification for theoretically favoring the former over the latter. [ABSTRACT FROM AUTHOR]

The evidence in favor of a Universe expanding at a constant rate, in contrast to the various episodes of deceleration and acceleration expected in the standard model, has been accumulating for over a decade now. In recent years, this inference has been strengthened by a study of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric in relation to Einstein's principle of equivalence. This earlier work concluded that the choice of lapse function gtt = 1 characterizing the FLRW solution to Einstein's equations is inconsistent with any kind of accelerated cosmic expansion. In this paper, we demonstrate and confirm this important result by directly testing the self-consistency of four well-known FLRW cosmologies. These include the Milne universe, de Sitter space, the Lanczos universe, and the Rh = ct model. We show that only the constantly expanding models (Milne and Rh = ct) are consistent with the principle of equivalence, while de Sitter and Lanczos fail the test. We discuss some of the many consequences of this conclusion. [ABSTRACT FROM AUTHOR]

The so-called impossibly early galaxy problem, first identified via the Hubble Space Telescope 's observation of galaxies at redshifts z > 10, appears to have been exacerbated by the more recent JWST discovery of galaxy candidates at even higher redshifts (z ∼ 17) which, however, are yet to be confirmed spectroscopically. These candidates would have emerged only ∼230 Myr after the big bang in the context of Lambda cold dark matter (ΛCDM), requiring a more rapid star formation in the earliest galaxies than appears to be permitted by simulations adopting the concordance model parameters. This time-compression problem would therefore be inconsistent with the age–redshift relation predicted by ΛCDM. Instead, the sequence of star formation and galaxy assembly would confirm the timeline predicted by the R h = ct universe, a theoretically advanced version of ΛCDM that incorporates the 'zero active mass' condition from general relativity. This model has accounted for many cosmological data better than ΛCDM, and eliminates all of its inconsistencies, including the horizon and initial entropy problems. The latest JWST discoveries at z ≳ 14, if confirmed, would add further support to the idea that the R h = ct universe is favoured by the observations over the current standard model. [ABSTRACT FROM AUTHOR]

The sample of time-delay gravitational lenses appropriate for studying the geometry of the Universe continues to grow as dedicated campaigns, such as the Dark Energy Survey, the (Very Large Telescope) VLT Survey Telescope (VST) ATLAS survey, and the Large Synoptic Survey Telescope, complete their census of high-redshift sources. This catalogue now includes hundreds of strong lensing systems, at least 31 of which have reasonably accurate time-delay measurements. In this paper, we use them to compare the predictions of two competing Friedmann–Lemaître–Robertson–Walker models: flat Lambda cold dark matter (ΛCDM), characterized by two adjustable parameters (H 0 and Ωm), and the R h = ct universe (with H 0 as the single free variable). Over the past decade, the latter has accounted for the data better than the standard model, most recently the emergence of well-formed galaxies discovered by JWST at cosmic dawn. Here, we show that the current sample of time-delay lenses favours R h = ct with a likelihood of ∼ |$84{{\ \rm per\ cent}}$| versus ∼ |$16{{\ \rm per\ cent}}$| for the standard model. This level of accuracy will greatly improve as the ongoing surveys uncover many thousands of additional lens systems over the next several years. [ABSTRACT FROM AUTHOR]

Modern cosmology is broadly based on the Cosmological principle, which assumes homogeneity and isotropy as its foundational pillars. Thus, there is not much debate about the metric (i.e., Friedmann-Lemaître-Robertson-Walker; FLRW) one should use to describe the cosmic spacetime. But Einstein's equations do not unilaterally constrain the constituents in the cosmic fluid, which directly determine the expansion factor appearing in the metric coefficients. As its name suggests, ΛCDM posits that the energy density is dominated by a blend of dark energy (typically a cosmological constant, Λ), cold dark matter (and a "contamination" of baryonic matter) and radiation. Many would assert that we have now reached the age of "precision" cosmology, in which measurements are made merely to refine the excessively large number of free parameters characterizing its empirical underpinnings. But this mantra glosses over a growing body of embarrassingly significant failings, not just "tension" as is sometimes described, as if to somehow imply that a resolution will eventually be found. In this paper, we take a candid look at some of the most glaring conflicts between the standard model, the observations, and several foundational principles in quantum mechanics, general relativity and particle physics. One cannot avoid the conclusion that the standard model needs a complete overhaul in order to survive. [ABSTRACT FROM AUTHOR]

The absence of large-angle correlations in the temperature of the cosmic microwave background (CMB), confirmed by three independent satellite missions, creates significant tension with the standard model of cosmology. Previous work has shown, however, that a truncation, k min , of the primordial power spectrum comprehensively resolves the anomaly and the missing power at ℓ ≲ 5 (the low multipoles). Since this cutoff is consistent with the hypothesized delay of inflation well beyond the Planck time, we are strongly motivated to consider its possible impact on other observational signatures. In this Letter , we analyze and predict its influence on the most revealing probe awaiting measurement by upcoming missions—the B-mode polarization of the CMB, whose accurate determination should greatly impact the inflationary picture. We highlight the quantitative power of this discriminant by specifically considering the LiteBIRD mission, predicting the effect of k min on both the angular power spectrum and the angular correlation function of the B-mode, for a range of tensor-to-scalar ratios, r. While its impact on the latter appears to be negligible, k min should have a very pronounced effect on the former. We show that for r = 0.036 , k min 's impact on C ℓ B B at low ℓ 's should be easily detectable by LiteBIRD, but will be largely hidden by the total uncertainty of the measurement if r ≲ 0.02. [ABSTRACT FROM AUTHOR]

We use the age measurements of 114 old astrophysical objects (OAO) in the redshift range 0 ≲ z ≲ 8 to explore the Hubble tension. The age of the universe at any z is inversely proportional to the Hubble constant, H 0, so requiring the universe to be older than the OAO it contains at any z will lead to an upper limit on H 0. Assuming flat ΛCDM and setting a Gaussian prior on the matter density parameter Ωm = 0.315 ± 0.007 informed by Planck, we obtain a 95% confidence level upper limit of H 0 < 70.6 km sâˆ'1 Mpcâˆ'1, representing a 2 σ tension with the measurement using the local distance ladder. We find, however, that the inferred upper limit on H 0 depends quite sensitively on the prior for Ωm, and the Hubble tension between early-time and local measurements of H 0 may be due in part to the inference of both Ωm and H 0 in Planck, while the local measurement uses only H 0. The age-redshift data may also be used for cosmological model comparisons. We find that the R h = ct universe accounts well for the data, with a reasonable upper limit on H 0, while Einsteinâ€"de Sitter fails to pass the cosmic-age test. Finally, we present a model-independent estimate of the spatial curvature using the ages of 61 galaxies and the luminosity distances of 1048 Pantheon Type Ia supernovae. This analysis suggests that the geometry of the universe is marginally consistent with spatial flatness at a confidence level of 1.6 σ, characterized as Ω k = 0.43 âˆ' 0.27 + 0.27 . [ABSTRACT FROM AUTHOR]

The Friedmann–Lemaître–Robertson–Walker (FLRW) metric used to describe the cosmic spacetime is based on the cosmological principle, which assumes homogeneity and isotropy throughout the Universe. It also adopts free-fall conditions via the selection of a constant lapse function, g t t = 1 , regardless of whether or not the chosen energy–momentum tensor T α β produces an accelerated expansion. This is sometimes justified by arguing that one may shift the gauge, if necessary, transforming the time d t to a new coordinate d t ′ ≡ g t t d t , thereby re-establishing a unitary value for g t ′ t ′ . Previously, we have demonstrated that this approach is inconsistent with the Friedmann equations derived using comoving coordinates. In this paper, we advance this discussion significantly by using the Local Flatness Theorem in general relativity to prove that g t t in FLRW is inextricably dependent on the expansion dynamics via the expansion factor a (t) , which itself depends on the equation-of-state in T α β . One is therefore not free to choose g t t arbitrarily without ensuring its consistency with the energy–momentum tensor. We prove that the use of FLRW in cosmology is valid only for zero active mass, i.e. ρ + 3 p = 0 , where ρ and p are, respectively, the total energy density and pressure in the cosmic fluid. [ABSTRACT FROM AUTHOR]

The cosmic distance duality relation (CDDR), η(z) = (1 + z)2 dA (z)/ dL (z) = 1, is one of the most fundamental and crucial formulae in cosmology. This relation couples the luminosity and angular diameter distances, two of the most often used measures of structure in the Universe. We here propose a new model-independent method to test this relation, using strong gravitational lensing (SGL) and the high-redshift quasar Hubble diagram reconstructed with a Bézier parametric fit. We carry out this test without pre-assuming a zero spatial curvature, adopting instead the value Ω K  = 0.001 ± 0.002 optimized by Planck in order to improve the reliability of our result. We parametrize the CDDR using η(z) = 1 + η0 z , 1 + η1 z + η2 z 2, and 1 + η3 z /(1 + z), and consider both the SIS and non-SIS lens models for the strong lensing. Our best-fitting results are: |$\eta _0=-0.021^{+0.068}_{-0.048}$|⁠ , |$\eta _1=-0.404^{+0.123}_{-0.090}$|⁠ , |$\eta _2=0.106^{+0.028}_{-0.034}$|⁠ , and |$\eta _3=-0.507^{+0.193}_{-0.133}$| for the SIS model, and |$\eta _0=-0.109^{+0.044}_{-0.031}$| for the non-SIS model. The measured η(z), based on the Planck parameter Ω K , is essentially consistent with the value (=1) expected if the CDDR were fully respected. For the sake of comparison, we also carry out the test for other values of Ω K , but find that deviations of spatial flatness beyond the Planck optimization are in even greater tension with the CDDR. Future measurements of SGL may improve the statistics and alter this result but, as of now, we conclude that the CDDR favours a flat Universe. [ABSTRACT FROM AUTHOR]

The EDGES collaboration has reported the detection of a global 21-cm signal with a plateau centered at 76 MHz (i.e., redshift 17.2), with an amplitude of 500 - 500 + 200 mK. This anomalous measurement does not comport with standard cosmology, which can only accommodate an amplitude ≲ 230 mK. Nevertheless, the line profile's redshift range ( 15 ≲ z ≲ 20 ) suggests a possible link to Pop III star formation and an implied evolution out of the 'dark ages.' Given this tension with the standard model, we here examine whether the observed 21-cm signal is instead consistent with the results of recent modeling based on the alternative Friedmann–Lemaître–Robertson–Walker cosmology known as the R h = c t universe, showing that – in this model – the CMB radiation might have been rethermalized by dust ejected into the IGM by the first-generation stars at redshift z ∼ 16 . We find that the requirements for this process to have occurred would have self-consistently established an equilibrium spin temperature T s ≈ 3.4 K in the neutral hydrogen, via the irradiation of the IGM by deep penetrating X-rays emitted at the termination shocks of Pop III supernova remnants. Such a dust scenario has been strongly ruled out for the standard model, so the spin temperature ( ∼ 3.3 K) inferred from the 21-cm absorption feature appears to be much more consistent with the R h = c t profile than that implied by Λ CDM, for which adiabatic cooling would have established a spin temperature T s (z = 17.2) ∼ 6 K. [ABSTRACT FROM AUTHOR]

In the standard model of cosmology, the Universe began its expansion with an anomalously low entropy, which then grew dramatically to much larger values consistent with the physical conditions at decoupling, roughly 380,000 years after the Big Bang. There does not appear to be a viable explanation for this 'unnatural' history, other than via the generalized second law of thermodynamics (GSL), in which the entropy of the bulk, S bulk , is combined with the entropy of the apparent (or gravitational) horizon, S h . This is not completely satisfactory either, however, since this approach seems to require an inexplicable equilibrium between the bulk and horizon temperatures. In this paper, we explore the thermodynamics of an alternative cosmology known as the R h = c t universe, which has thus far been highly successful in resolving many other problems or inconsistencies in Λ CDM. We find that S bulk is constant in this model, eliminating the so-called initial entropy problem simply and elegantly. The GSL may still be relevant, however, principally in selecting the arrow of time, given that S h ∝ t 2 in this model. [ABSTRACT FROM AUTHOR]

The geometry of the Universe may be probed using the Alcock–Paczyński (AP) effect, in which the observed redshift size of a spherical distribution of sources relative to its angular size varies according to the assumed cosmological model. Past applications of this effect have been limited, however, by a paucity of suitable sources and mitigating astrophysical factors, such as internal redshift-space distortions and poorly known source evolution. In this Letter , we introduce a new test based on the AP effect that avoids the use of spatially bound systems, relying instead on sub-samples of quasars at redshifts z  ≲ 1.5 in the Sloan Digital Sky Survey IV, with a possible extension to higher redshifts and improved precision when this catalogue is expanded by upcoming surveys. We here use this method to probe the redshift-dependent expansion rate in three pertinent Friedmann–Lemaître–Robertson–Walker cosmologies: Λ cold dark matter (ΛCDM), which predicts a transition from deceleration to acceleration at z  ∼ 0.7; Einstein–de Sitter, in which the Universe is always decelerating; and the R h = ct universe, which expands at a constant rate. ΛCDM is consistent with these data, but R h = ct is favoured overall. [ABSTRACT FROM AUTHOR]

The recent measurement of a cutoff kmin in the fluctuation power spectrum P(k) of the cosmic microwave background may vitiate the possibility that slow‐roll inflation can simultaneously solve the horizon problem and account for the formation of structure via the growth of quantum fluctuations in the inflaton field. Instead, we show that kmin may be interpreted more successfully in the Rh = ct cosmology as the first mode exiting from the Planck scale into the semiclassical universe shortly after the Big Bang. In so doing, we demonstrate that such a scenario completely avoids the well‐known trans‐Planckian problem plaguing standard inflationary cosmology. [ABSTRACT FROM AUTHOR]

With the distance sum rule in the Friedmann–Lemaître–Robertson–Walker metric, model-independent constraints on both the Hubble constant H0 and spatial curvature can be obtained using strong lensing time-delay data and Type Ia supernovae (SNe Ia) luminosity distances. This method is limited by the relatively low redshifts of SNe Ia, however. Here, we propose using quasars as distance indicators, extending the coverage to encompass the redshift range of strong lensing systems. We provide a novel and improved method of determining H0 and simultaneously. By applying this technique to the time-delay measurements of seven strong lensing systems and the known ultraviolet versus X-ray luminosity correlation of quasars, we constrain the possible values of both H0 and , and find that km and. The measured is consistent with zero spatial curvature, indicating that there is no significant deviation from a flat universe. If we use flatness as a prior, we infer that km , representing a precision of 2.5%. If we further combine these data with the 1048 current Pantheon SNe Ia, our model-independent constraints can be further improved to km and. In every case, we find that the Hubble constant measured with this technique is strongly consistent with the value (∼74 km) measured using the local distance ladder, as opposed to the value optimized by Planck. [ABSTRACT FROM AUTHOR]

Slow-roll inflation may simultaneously solve the horizon problem and generate a near scale-free fluctuation spectrum P(ĸ). These two processes are intimately connected via the initiation and duration of the inflationary phase. But a recent study based on the latest Planck release suggests that P(ĸ) has a hard cut-off, ĸmin ≠0, inconsistent with this conventional picture. Here, we demonstrate quantitatively that most--perhaps all-slow-roll inflationary models fail to accommodate this minimum cut-off. We show that the small parameter ∈ must be ... 0.9 throughout the inflationary period to comply with the data, seriously violating the slow-roll approximation. Models with such an ∈ predict extremely red spectral indices, at odds with the measured value. We also consider extensions to the basic picture (suggested by several earlier workers) by adding a kinetic-dominated or radiation-dominated phase preceding the slow-roll expansion. Our approach differs from previously published treatments principally because we require these modifications not only to fit the measured fluctuation spectrum but also simultaneously to fix the horizon problem. We show, however, that even such measures preclude a joint resolution of the horizon problem and the missing correlations at large angles. [ABSTRACT FROM AUTHOR]

It has been known for over three decades that the monochromatic X-ray and UV luminosities in quasars are correlated, though non-linearly. This offers the possibility of using high- z quasars as standard candles for cosmological testing. In this paper, we use a recently assembled, high-quality catalogue of 1598 quasars extending all the way to redshift ∼6, to compare the predictions of the R h = ct and Lambda cold dark matter (ΛCDM) cosmologies. In so doing, we affirm that the parameters characterizing the correlation depend only weakly on the chosen cosmology, and that both models account very well for the data. Unlike ΛCDM, however, the R h = ct model has no free parameters for this work, so the Bayesian Information Criterion favours it over ΛCDM with a relative likelihood of |$\sim 88{{\ \rm per\ cent}}$| versus |$\sim 10{{\ \rm per\ cent}}$|⁠. This result is consistent with the outcome of other comparative tests, many of which have shown that R h = ct is favoured over the standard model based on a diverse range of observations. [ABSTRACT FROM AUTHOR]

The emergence of a highly improbable coincidence in cosmological observations speaks of a remarkably simple cosmic expansion. Compelling evidence now suggests that the Universe's gravitational horizon, coincident with the better known Hubble sphere, has a radius improbably equal to the distance light could have traveled since the Big Bang. The confirmation of this unexpected result would undoubtedly herald the influence of new physics, yet appears to be unavoidable after a recent demonstration that the Friedmann–Lemaître–Robertson–Walker metric is valid only for the so-called zero active mass equation of state. As it turns out, a cosmic fluid with this property automatically produces the aforementioned equality, leaving little room for a cosmological constant. The alternative — a dynamical dark energy — would suggest an extension to the Standard Model of particle physics and a serious re-evaluation of the Universe's early history. [ABSTRACT FROM AUTHOR]

We present a phenomenological method for predicting the number of flat-spectrum radio quasars (FSRQs) that should be detected by upcoming Square Kilometre Array (SKA) SKA1-MID Wide Band 1 and Medium-Deep Band 2 surveys. We use the Fermi blazar sequence and mass estimates of Fermi FSRQs, and γ-ray emitting narrow-line Seyfert 1 galaxies, to model the radio emission of FSRQs as a function of mass alone, assuming a near-Eddington accretion rate, which is suggested by current quasar surveys at z  ≳ 6. This is used to determine the smallest visible black hole mass as a function of redshift in two competing cosmologies we compare in this paper: the standard Λ cold dark matter (ΛCDM) model and the R h =  ct universe. We then apply lockstep growth to the observed black hole mass function at z  = 6 in order to devolve that population to higher redshifts and determine the number of FSRQs detectable by the SKA surveys as a function of z. We find that at the redshifts for which this method is most valid, ΛCDM predicts ∼30 times more FSRQs than R h =  ct for the Wide survey, and ∼100 times more in the Medium-Deep survey. These stark differences will allow the SKA surveys to strongly differentiate between these two models, possibly rejecting one in comparison with the other at a high level of confidence. [ABSTRACT FROM AUTHOR]

The Universe has a gravitational horizon with a radius R h = c / H coincident with that of the Hubble sphere. This surface separates null geodesics approaching us from those receding, and as free-falling observers within the Friedmann–Lemaître–Robertson–Walker space–time, we see it retreating at proper speed c , giving rise to the eponymously named cosmological model R h = c t. As of today, this cosmology has passed over 20 observational tests, often better than Λ CDM. The gravitational radius R h therefore appears to be highly relevant to cosmological theory, and in this paper we begin to explore its impact on fundamental physics. We calculate the binding energy of a mass m within the horizon and demonstrate that it is equal to m c 2 . This energy is stored when the particle is at rest near the observer, transitioning to a purely kinetic form equal to the particle's escape energy when it approaches R h . In other words, a particle's gravitational coupling to that portion of the Universe with which it is causally connected appears to be the origin of rest-mass energy. [ABSTRACT FROM AUTHOR]

The cosmic distance duality (CDD) relation (based on the Etherington reciprocity theorem) plays a crucial role in a wide assortment of cosmological measurements. Attempts at confirming it observationally have met with mixed results, though the general consensus appears to be that the data do support its existence in nature. A common limitation with past approaches has been their reliance on a specific cosmological model, or on measurements of the luminosity distance to Type Ia SNe, which introduces a dependence on the presumed cosmology in spite of beliefs to the contrary. Confirming that the CDD is actually realized in nature is crucial because its violation would require exotic new physics. In this paper, we study the CDD using the observed angular size of compact quasar cores and a Gaussian Process reconstruction of the H ii galaxy Hubble diagram – without pre-assuming any particular background cosmology. In so doing, we confirm at a very high level of confidence that the angular-diameter and luminosity distances do indeed satisfy the CDD. We then demonstrate the potential power of this result by utilizing it in a comparative test of two competing cosmological models – the R h= ct universe and ΛCDM – and show that R h= ct is favoured by the CDD data with a likelihood |${\sim } 82.3{{\ \rm per\ cent}}$| compared with |${\sim } 17.7{{\ \rm per\ cent}}$| for the standard model. [ABSTRACT FROM AUTHOR]

Unlike other observational signatures in cosmology, the angular-diameter distance dA (z) uniquely reaches a maximum (at z max) and then shrinks to zero towards the big bang. The location of this turning point depends sensitively on the model, but has been difficult to measure. In this paper, we estimate and use z max inferred from quasar cores: (1) by employing a sample of 140 objects yielding a much reduced dispersion due to pre-constrained limits on their spectral index and luminosity, (2) by reconstructing dA (z) using Gaussian processes, and (3) comparing the predictions of seven different cosmologies and showing that the measured value of z max can effectively discriminate between them. We find that z max = 1.70 ± 0.20 – an important new probe of the Universe's geometry. The most strongly favoured model is R h = ct, followed by Planck ΛCDM. Several others, including Milne, Einstein-de Sitter, and Static tired light are strongly rejected. According to these results, the R h = ct universe, which predicts z max = 1.718, has a $${\sim } 92.8{{\ \rm per\ cent}}$$ probability of being the correct cosmology. For consistency, we also carry out model selection based on dA (z) itself. This test confirms that R h = ct and Planck ΛCDM are among the few models that account for angular-size data better than those that are disfavoured by z max. The dA (z) comparison, however, is less discerning than that with z max, due to the additional free parameter, H 0. We find that H 0 = 63.4 ± 1.2 km s−1 Mpc−1 for R h = ct, and 69.9 ± 1.5 km s−1 Mpc−1 for ΛCDM. Both are consistent with previously measured values in each model, though they differ from each other by over 4σ. In contrast, model selection based on z max is independent of H 0. [ABSTRACT FROM AUTHOR]

In general relativity, a gravitational horizon (more commonly known as the “apparent horizon”) is an imaginary surface beyond which all null geodesics recede from the observer. The Universe has an apparent (gravitational) horizon, but unlike its counterpart in the Schwarzschild and Kerr metrics, it is not static. It may eventually turn into an event horizon—an asymptotically defined membrane that forever separates causally connected events from those that are not—depending on the equation of state of the cosmic fluid. In this paper, we examine how and why an apparent (gravitational) horizon is manifested in the Friedmann–Robertson–Walker metric, and why it is becoming so pivotal to our correct interpretation of the cosmological data. We discuss its observational signature and demonstrate how it alone defines the proper size of our visible Universe. In so doing, we affirm its physical reality and its impact on cosmological models. [ABSTRACT FROM AUTHOR]

A previous analysis of starburst-dominated H ii galaxies and H ii regions has demonstrated a statistically significant preference for the Friedmann–Robertson–Walker cosmology with zero active mass, known as the Rh = ct universe, over Λcold dark matter (ΛCDM) and its related dark-matter parametrizations. In this paper, we employ a two-point diagnostic with these data to present a complementary statistical comparison of Rh = ct with Planck ΛCDM. Our two-point diagnostic compares, in a pairwise fashion, the difference between the distance modulus measured at two redshifts with that predicted by each cosmology. Our results support the conclusion drawn by a previous comparative analysis demonstrating that Rh = ct is statistically preferred over Planck ΛCDM. But we also find that the reported errors in the H ii measurements may not be purely Gaussian, perhaps due to a partial contamination by non-Gaussian systematic effects. The use of H ii galaxies and H ii regions as standard candles may be improved even further with a better handling of the systematics in these sources. [ABSTRACT FROM AUTHOR]

Measurements of the Hubble constantH(z) are increasingly being used to test the expansion rate predicted by various cosmological models. But the recent application of two-point diagnostics, such as Om(zi, zj) and Omh²(zi, zj), has produced considerable tension between CDM's predictions and several observations, with other models faring even worse. Part of this problem is attributable to the continued mixing of truly model-independent measurements using the cosmic-chronometer approach, and model-dependent data extracted from baryon acoustic oscillations. In this paper, we advance the use of two-point diagnostics beyond their current status, and introduce new variations, which we call Δh(zi, zj), that are more useful for model comparisons. But we restrict our analysis exclusively to cosmic-chronometer data, which are truly model independent. Even for these measurements, however, we confirm the conclusions drawn by earlier workers that the data have strongly non-Gaussian uncertainties, requiring the use of both 'median' and 'mean' statistical approaches. Our results reveal that previous analyses using two-point diagnostics greatly underestimated the errors, thereby misinterpreting the level of tension between theoretical predictions and H(z) data. Instead, we demonstrate that as of today, only Einstein-de Sitter is ruled out by the two-point diagnostics at a level of significance exceeding ~3σ. The Rh = ct universe is slightly favoured over the remaining models, including Lambda cold dark matter and Chevalier-Polarski-Linder, though all of them (other than Einstein-de Sitter) are consistent to within 1s with the measured mean of the Δh(zi, zj) diagnostics. [ABSTRACT FROM AUTHOR]

We use recently published redshift space distortion measurements of the cosmological growth rate, fσ8(z), to examine whether the linear evolution of perturbations in the Rh = ct cosmology is consistent with the observed development of large-scale structure. We find that these observations favour Rh = ct over the version of Λ cold dark matter (ΛCDM) optimized with the joint analysis of Planck and linear growth rate data, particularly in the redshift range 0 < z < 1, where a significant curvature in the functional form of fσ8(z) predicted by the standard model--but not by Rh = ct--is absent in the data. When ΛCDM is optimized using solely the growth rate measurements; however, the two models fit the observations equally well though, in this case, the low-redshift measurements find a lower value for the fluctuation amplitude than is expected in Planck ΛCDM. Our results strongly affirm the need for more precise measurements of fσ8(z) at all redshifts, but especially at z < 1. [ABSTRACT FROM AUTHOR]

The extensive catalogue of gamma-ray selected flat-spectrum radio quasars (FSRQs) produced by Fermi during a four-year survey has generated considerable interest in determining their gamma-ray luminosity function (GLF) and its evolution with cosmic time. In this paper, we introduce the novel idea of using this extensive database to test the differential volume expansion rate predicted by two specific models, the concordance Λ cold dark matter (_CDM) and Rh = ct cosmologies. For this purpose, we use two well-studied formulations of the GLF, one based on pure luminosity evolution (PLE) and the other on a luminosity-dependent density evolution (LDDE). Using a Kolmogorov-Smirnov test on one-parameter cumulative distributions (in luminosity, redshift, photon index and source count), we confirm the results of earlier works showing that these data somewhat favour LDDE over PLE; we show that this is the case for both ΛCDM and Rh = ct. Regardless of which GLF one chooses, however, we also show that model selection tools very strongly favour Rh = ct over ΛCDM. We suggest that such population studies, though featuring a strong evolution in redshift, may none the less be used as a valuable independent check of other model comparisons based solely on geometric considerations. [ABSTRACT FROM AUTHOR]

The measured properties of the epoch of reionization (EoR) show that reionization probably began around z ∼ 12-15 and ended by z = 6. In addition, a careful analysis of the fluctuations in the cosmic microwave background indicate a scattering optical depth t ∼ 0.066 ± 0.012 through the EoR. In the context of Λ cold dark matter, galaxies at intermediate redshifts and dwarf galaxies at higher redshifts now appear to be the principal sources of UV ionizing radiation, but only for an inferred (ionizing) escape fraction fion ∼ 0.2, which is in tension with other observations that suggest a value as small as ∼0.05. In this paper, we examine how reionization might have progressed in the alternative Friedmann-RobertsonWalker cosmology known as the Rh = ct universe, and determine the value of fion required with this different rate of expansion. We find that Rh=ct accounts quite well for the currently known properties of the EoR, as long as its fractional baryon density falls within the reasonable range 0.026 ≲ Ωb ≲ 0.037. This model can also fit the EoR data with fion ∼ 0.05, but only if the Lyman continuum photon production is highly efficient and Ωb ∼ 0.037. These results are still preliminary, however, given their reliance on a particular form of the star formation rate density, which is still uncertain at very high redshifts. It will also be helpful to reconsider the EoR in Rh = ct when complete structure formation models become available. [ABSTRACT FROM AUTHOR]

The Rh = ct universe is a Friedmann-Robertson-Walker (FRW) cosmology which, like Λ cold dark matter (ΛCDM), assumes the presence of dark energy in addition to (baryonic and non-luminous) matter and radiation. Unlike ΛCDM, however, it is also constrained by the equation of state (EOS) p=-ρ/3, in terms of the total pressure p and energy density ρ. Oneon-one comparative tests between Rh = ct and ΛCDM have been carried out using over 14 different cosmological measurements and observations. In every case, the data have favoured Rh = ct over the standard model, with model selection tools yielding a likelihood ∼90-95 per cent that the former is correct, versus only ∼5-10 per cent for the latter. In other words, the standard model without the EOS p=-ρ/3 does not appear to be the optimal description of nature. Yet in spite of these successes - or perhaps because of them - several concerns have been published recently regarding the fundamental basis of the theory itself. The latest paper on this subject even claims - quite remarkably - that Rh = ct is a vacuum solution, though quite evidently ρ ρ= 0. Here, we address these concerns and demonstrate that all criticisms levelled thus far against Rh = ct, including the supposed vacuum condition, are unwarranted. They all appear to be based on incorrect assumptions or basic theoretical errors. Nevertheless, continued scrutiny such as this will be critical to establishing Rh = ct as the correct description of nature. [ABSTRACT FROM AUTHOR]

In this paper, we continue to examine the fundamental basis for the Friedmann- Robertson-Walker (FRW) metric and its application to cosmology, specifically addressing the question: What is the proper size of the visible universe? There are several ways of answering the question of size, though often with an incomplete understanding of how far light has actually traveled in reaching us today from the most remote sources. The difficulty usually arises from an inconsistent use of the coordinates or an over-interpretation of the physical meaning of quantities such as the so-called proper distance R(t ) = a(t )r, written in terms of the (unchanging) co-moving radius r and the universal expansion factor a(t ). In this paper, we prove for the five non-trivial FRW metrics with a constant spacetime curvature that, when the expansion began from an initial singularity, the visible universe today has a proper size equal to Rh(t0/2), i.e., the gravitational horizon at half its current age. The exceptions are de Sitter and Lanczos, whose contents had pre-existing positions away from the origin. In so doing, we confirm earlier results showing the same phenomenon in a broad range of cosmologies, including CDM, based on the numerical integration of null geodesic equations through an FRW metric. [ABSTRACT FROM AUTHOR]

ABSTRACT Cosmological redshift z grows as the Universe expands and is conventionally viewed as a third form of redshift, beyond the more traditional Doppler and gravitational effects seen in other applications of general relativity. In this paper, we examine the origin of redshift in the Friedmann-Robertson-Walker (FRW) metrics with constant space-time curvature, and show that - at least for the static space-times - the interpretation of z as due to the 'stretching' of space is coordinate dependent. Namely, we prove that redshift may also be calculated solely from the effects of kinematics and gravitational acceleration. This suggests that its dependence on the expansion factor is simply a manifestation of the high degree of symmetry in FRW, and ought not be viewed as evidence in support of the idea that space itself is expanding. [ABSTRACT FROM AUTHOR]

ABSTRACT The Hubble radius is a particular manifestation of the Universe's gravitational horizon, Rh( t0) ≡ c/ H0, the distance beyond which physical processes remain unobservable to us at the present epoch. Based on recent observations of the cosmic microwave background (CMB) with Wilkinson Microwave Anisotropy Probe, and ground-based and Hubble Space Telescope searches for Type Ia supernovae, we now know that Rh( t0) ∼13.5 Glyr. This coincides with the maximum distance ( ct0≈ 13.7 Glyr) light could have travelled since the big bang. However, the physical meaning of Rh is still not universally understood or accepted, though the minimalist view holds that it is merely the proper distance at which the rate of cosmic recession reaches the speed of light c. Even so, it is sometimes argued that we can see light from sources beyond Rh, the claim being that Rh lies at a redshift of only ∼2, whereas the CMB was produced at a much greater redshift (∼1100). In this paper, we build on recent developments with the gravitational radius by actually calculating null geodesics for a broad range of Friedmann-Robertson-Walker cosmologies, to show - at least in the specific cases we consider here, including Λ cold dark matter (ΛCDM) - that no photon trajectories reaching us today could have ever crossed Rh( t0). We therefore confirm that the current Hubble radius, contrary to a commonly held misconception, is indeed the limit to our observability. We find that the size of the visible universe in ΛCDM, measured as a proper distance, is approximately 0.5 ct0. [ABSTRACT FROM AUTHOR]

ABSTRACT The Galaxy's supermassive black hole, Sgr A*, produces an outburst of infrared (IR) radiation about once every 6 h, sometimes accompanied by an even more energetic flurry of X-rays. It is rather clear now that the near-IR (NIR) photons are produced by non-thermal synchrotron processes, but we still do not completely understand where or why these flares originate, nor exactly how the X-rays are emitted. Circumstantial evidence suggests that the power-law electrons radiating the IR light may be partially cooled, allowing for the possibility that their distribution should be more accurately described by a broken power law with a ('cooling break') transition frequency. In addition, the emission region (energized by an as yet unidentified instability) appears to be rather compact, possibly restricted to the inner edge of the accretion disc. In that case, the X-ray outburst may itself be due to synchrotron processes by the most energetic particles in this population. In this paper, we examine several key features of this proposal, producing relativistically correct polarimetric images of Sgr A*'s NIR and X-ray flare emission, in order to determine (1) whether the measured NIR polarization fraction is consistent with this geometry and (2) whether the predicted X-ray to NIR peak fluxes are confirmed by the currently available multiwavelength observations. We also calculate the X-ray polarization fraction and position angle (relative to that of the NIR photons) in anticipation of such measurements in the coming years. We show that whereas the polarization fraction and position angle of the X-rays are similar to those of the NIR component for synchrotron-cooled emission, these quantities are measurably different when the X-rays emerge from a scattering medium. It is clear, therefore, that the development of X-ray polarimetry will represent a major new tool for studying the space-time near supermassive black holes. [ABSTRACT FROM AUTHOR]

We present here the transformations required to recast the Robertson–Walker metric and Friedmann–Robertson–Walker equations in terms of observer-dependent coordinates for several commonly assumed cosmologies. The overriding motivation is the derivation of explicit expressions for the radius Rh of our cosmic horizon in terms of measurable quantities for each of the cases we consider. We show that the cosmological time dt diverges for any finite interval ds associated with a process at R → Rh, which therefore represents a physical limit to our observations. This is a key component required for a complete interpretation of the data, particularly as they pertain to the nature of dark energy. With these results, we affirm the conclusion drawn in our earlier work that the identification of dark energy as a cosmological constant does not appear to be consistent with the data. [ABSTRACT FROM AUTHOR]

Within the context of standard cosmology, an accelerating universe requires the presence of a third "dark" component of energy, beyond matter and radiation. The available data, however, are still deemed insufficient to distinguish between an evolving dark energy component and the simplest model of a time-independent cosmological constant. In this paper, we examine the cosmological expansion in terms of observer-dependent coordinates, in addition to the more conventional comoving coordinates. This procedure explicitly reveals the role played by the radius Rh of our cosmic horizon in the interrogation of the data. (In Rindler's notation, Rh coincides with the "event horizon" in the case of de Sitter, but changes in time for other cosmologies that also contain matter and/or radiation.) With this approach, we show that the interpretation of dark energy as a cosmological constant is clearly disfavored by the observations. Within the framework of standard Friedmann–Robertson–Walker cosmology, we derive an equation describing the evolution of Rh, and solve it using the WMAP and Type Ia supernova data. In particular, we consider the meaning of the observed equality (or near-equality) Rh(t0) ≅ ct0, where t0 is the age of the universe. This empirical result is far from trivial, for a cosmological constant would drive Rh(t) toward ct (t is the cosmic time) only once — and that would have to occur right now. Though we are not here espousing any particular alternative model of dark energy, for comparison we also consider scenarios in which dark energy is given by scaling solutions, which simultaneously eliminate several conundrums in the standard model, including the "coincidence" and "flatness" problems, and account very well for the fact that Rh(t0) ≈ ct0. [ABSTRACT FROM AUTHOR]

The hierarchical clustering inherent in Λcold dark matter cosmology seems to produce many of the observed characteristics of large-scale structure. But some glaring problems still remain, including the overprediction (by a factor of 10) of the number of dwarf galaxies within the virialized population of the local group. Several secondary effects have already been proposed to resolve this problem. It is still not clear, however, whether the principal solution rests with astrophysical processes, such as early feedback from supernovae, or possibly with as yet undetermined properties of the dark matter itself. In this paper, we carry out a detailed calculation of the dwarf halo evolution incorporating the effects of a hypothesized dark matter decay, D→ D′+ l, where D is the unstable particle, D′ is the more massive daughter particle and l is the other, lighter (or possibly massless) daughter particle. This process preferentially heats the smaller haloes, expanding them during their evolution and reducing their present-day circular velocity. We find that this mechanism can account very well for the factor of 4 deficit in the observed number of systems with velocity compared to those predicted by the numerical simulations, if , where Δ m is the mass difference between the initial and final states. The corresponding lifetime τ cannot be longer than ∼30 Gyr, but may be as short as just a few Gyr. [ABSTRACT FROM AUTHOR]

The High-Energy Stereoscopic System (HESS) has detected intense diffuse TeV emission correlated with the distribution of molecular gas along the Galactic ridge at the centre of our Galaxy. Earlier HESS observations of this region had already revealed the presence of several point sources at these energies, one of them (HESS J1745−290) coincident with the supermassive black hole Sagittarius A*. It is still not entirely clear what the origin of the TeV emission is, nor even whether it is due to hadronic or leptonic interactions. It is reasonable to suppose, however, that at least for the diffuse emission, the tight correlation of the intensity distribution with the molecular gas indicates a pionic-decay process involving relativistic protons. In this paper, we explore the possible source(s) of energetic hadrons at the Galactic Centre, and their propagation through a turbulent medium. We conclude that though Sagittarius A* itself may be the source of cosmic rays producing the emission in HESS J1745−290, it cannot be responsible for the diffuse emission farther out. A distribution of point sources, such as pulsar wind nebulae dispersed along the Galactic plane, similarly do not produce a TeV emission profile consistent with the HESS map. We conclude that only a relativistic proton distribution accelerated throughout the intercloud medium can account for the TeV emission profile measured with HESS. [ABSTRACT FROM AUTHOR]

The cosmological principle, promoting the view that the Universe is homogeneous and isotropic, is embodied within the mathematical structure of the Robertson–Walker (RW) metric. The equations derived from an application of this metric to the Einstein Field Equations describe the expansion of the Universe in terms of comoving coordinates, from which physical distances may be derived using a time-dependent expansion factor. These coordinates, however, do not explicitly reveal the properties of the cosmic space–time manifested in Birkhoff's theorem and its corollary. In this paper, we compare two forms of the metric – written in (the traditional) comoving coordinates, and a set of observer-dependent coordinates – first for the well-known de Sitter universe containing only dark energy, and then for a newly derived form of the RW metric, for a universe with dark energy and matter. We show that Rindler's event horizon – evident in the comoving system – coincides with what one might call the ‘curvature horizon’ appearing in the observer-dependent frame. The advantage of this dual prescription of the cosmic space–time is that with the latest Wilkinson Microwave Anisotropy Probe results, we now have a much better determination of the Universe's mass-energy content, which permits us to calculate this curvature with unprecedented accuracy. We use it here to demonstrate that our observations have probed the limit beyond which the cosmic curvature prevents any signal from having ever reached us. In the case of de Sitter, where the mass-energy density is a constant, this limit is fixed for all time. For a universe with a changing density, this horizon expands until de Sitter is reached asymptotically, and then it too ceases to change. [ABSTRACT FROM AUTHOR]

Converging flows (e.g., gas accreting on to compact objects) are often ionized and magnetized. As the gas in these systems compresses towards smaller radii, flux conservation acts to intensify the magnetic field B, which can attain superequipartition values. (Throughout this paper, equipartition is meant to imply a comparison between the energy density in the field and that of the particles only, not including turbulence.) Since such a field probably cannot remain anchored in the gas, it is often assumed that the field intensity in excess of equipartition (i.e., B[sub eq]) is dissipated as heat, and that B therefore saturates at its B[sub eq] value – the so-called ‘equipartition assumption’. In this paper we make an attempt at developing a model for magnetic field dissipation based on resistive magnetic tearing, in order to provide a more realistic means of determining the evolution of B in cases where the contribution to the spectrum from magnetic bremsstrahlung is important. We find that the violation of equipartition can vary in degree from large to small radii, and in either direction. Thus the spectrum predicted on the basis of the equipartition assumption is not always an adequate representation of the actual state of the system. However, several major shortcomings remain in our formulation. For example, our approach in this paper is to consider the turbulence as being initiated primarily by hydrodynamic processes. Arguing that the magnetic field is frozen into the highly ionized plasma, we therefore adopt a magnetic field spatial distribution that mirrors that of the gas. This may be valid only when the field is subequipartition, for otherwise the turbulent cascade may be influenced primarily by magnetic dissipation, rather than the hydrodynamics. In the application of this work to systems such as Sgr A* at the Galactic Centre, our approach may therefore break down at small radii (i.e., several Schwarzschild radii) where the magnetic field can in fact become superequipartition, for which a complete treatment of magnetic turbulence would need to be considered. However, the dominant emission mechanism in sources such as this appears to be magnetic bremsstrahlung over the full extent of the accreting region, so that even with these limitations, the bulk of the spectrum is influenced significantly by the qualitative results presented here. [ABSTRACT FROM AUTHOR]

The inner few parsecs at the Galactic Center have come under intense scrutiny in recent years, in part due to the exciting broad-band observations of this region, but also because of the growing interest from theorists motivated to study the physics of black hole accretion, magnetized gas dynamics, and unusual star formation. The Galactic Center is now known to contain arguably the most compelling supermassive black hole candidate, weighing in at a little over 2.6 million suns. Its interaction with the nearby environment, comprised of clusters of evolved and young stars, a molecular dusty ring, ionized gas streamers, diffuse hot gas, and a hypernova remnant, is providing a wealth of accretion phenomenology and high-energy processes for detailed modeling. In this review, we summarize the latest observational results and focus on the physical interpretation of the most intriguing object in this region—the compact radio source Sgr A*, thought to be the radiative manifestation of the supermassive black hole. [ABSTRACT FROM AUTHOR]

The quantum to classical transition of fluctuations in the early universe is still not completely understood. Some headway has been made incorporating the effects of decoherence and the squeezing of states, though the methods and procedures continue to be challenged. But new developments in the analysis of the most recent Planck data suggest that the primordial power spectrum has a cutoff associated with the very first quantum fluctuation to have emerged into the semi-classical universe from the Planck domain at about the Planck time. In this paper, we examine the implications of this result on the question of classicalization, and demonstrate that the birth of quantum fluctuations at the Planck scale would have been a 'process' supplanting the need for a 'measurement' in quantum mechanics. Emerging with a single wavenumber, these fluctuations would have avoided the interference between different degrees of freedom in a superposed state. Moreover, the implied scalar-field potential had an equation-of-state consistent with the zero active mass condition in general relativity, allowing the quantum fluctuations to emerge in their ground state with a time-independent frequency. They were therefore effectively quantum harmonic oscillators with classical correlations in phase space from the very beginning. [ABSTRACT FROM AUTHOR]

We consider several well-known f (R) cosmological models and constrain their parameters, namely the deviation parameter b and the cosmological parameters Ωm and h. We first obtain analytical approximations for the Hubble rate H (z) and the luminosity distance dL (z) in terms of these parameters, and then test these against the observational expansion rate derived from cosmic chronometers (CCs) and the distance modulus in the H  ii galaxy Hubble diagram, obtained in a model-independent way using Gaussian processes. We first optimize the models based solely on the CCs and then repeat this process with a joint analysis using both the CCs and H  ii galaxies. [ABSTRACT FROM AUTHOR]

A model proposed by Melia & Ruffert to evaluate the spectrum and radiation flux for accretion on to a black hole makes use of the ‘equipartition assumption’ in which the magnetic, turbulent and gravitational energy densities are assumed to be in approximate equilibrium for distances below the accretion radius, where Bondi–Hoyle infall begins. As a consequence, the mechanism for the dissipation of the magnetic field and the resulting effect on the flow of the accreting gas have not been treated quantitatively. Here we examine alternative approaches for modelling the dissipation of magnetic fields and turbulent flow to see how these may be incorporated into the model. The results of our study should be immediately applicable to the ever-improving measurements of the spectrum and size of the massive black hole at our Galactic Centre, in particular producing a more accurate estimate of its mass. Combined with greatly refined kinematic studies of this region, our work may constrain the dark matter concentration in the nucleus of our Galaxy. [ABSTRACT FROM AUTHOR]

The growth of structure may be traced via the redshift-dependent halo mass function. This quantity probes the re-ionization history and quasar abundance in the Universe, constituting an important probe of the cosmological predictions. Halos are not directly observable, however, so their mass and evolution must be inferred indirectly. The most common approach is to presume a relationship with galaxies and halos. Studies based on the assumption of a constant halo to stellar mass ratio M h / M ∗ (extrapolated from z ≲ 4 ) reveal significant tension with Λ CDM – a failure known as "The Impossibly Early Galaxy Problem". But whether this ratio evolves or remains constant through redshift 4 ≲ z ≲ 10 is still being debated. To eliminate the tension with Λ CDM, it would have to change by about 0.8 dex over this range, an issue that may be settled by upcoming observations with the James Webb Space Telescope. In this paper, we explore the possibility that this major inconsistency may instead be an indication that the cosmological model is not completely correct. We study this problem in the context of another Friedmann–Lemaître–Robertson–Walker (FLRW) model known as the R h = c t universe, and use our previous measurement of σ 8 from the cosmological growth rate, together with new solutions to the Einstein–Boltzmann equations, to interpret these recent halo measurements. We demonstrate that the predicted mass and redshift dependence of the halo distribution in R h = c t is consistent with the data, even assuming a constant M h / M ∗ throughout the observed redshift range ( 4 ≲ z ≲ 10 ), contrasting sharply with the tension in Λ CDM. We conclude that – if M h / M ∗ turns out to be constant – the massive galaxies and their halos must have formed earlier than is possible in Λ CDM. [ABSTRACT FROM AUTHOR]