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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]

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 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]

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]

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]

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]

We continue to build support for the proposal to useHII galaxies (HIIGx) and giant extragalactic HII regions (GEHR) as standard candles to construct the Hubble diagram at redshifts beyond the current reach of Type Ia supernovae. Using a sample of 25 high-redshift HIIGx, 107 local HIIGx, and 24 GEHR, we confirm that the correlation between the emission-line luminosity and ionized-gas velocity dispersion is a viable luminosity indicator, and use it to test and compare the standard model ΛCDM and the Rh = ct universe by optimizing the parameters in each cosmology using a maximization of the likelihood function. For the flat ΛCDM model, the best fit is obtained with Ωm = 0.40+0.09-0.09. However, statistical tools, such as the Akaike (AIC), Kullback (KIC) and Bayes (BIC) Information Criteria favour Rh = ct over the standard model with a likelihood of ≈94.8-98.8 per cent versus only ≈1.2-5.2 per cent. For wCDM (the version of ΛCDM with a dark-energy equation of state wde = pde/de rather than wde = wΛ =-1), a statistically acceptable fit is realized with Λm = 0.22+0.16-0.14 and wde = -0.51+0.15-0.25 which, however, are not fully consistent with their concordance values. In this case, wCDM has two more free parameters than Rh = ct, and is penalized more heavily by these criteria. We find that Rh = ct is strongly favoured over wCDM with a likelihood of ≈92.9-99.6 per cent versus only 0.4-7.1 per cent. The current HIIGx sample is already large enough for the BIC to rule out ΛCDM/wCDM in favour of Rh = ct at a confidence level approaching 3σ. [ABSTRACT FROM AUTHOR]