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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]

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 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]

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 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]

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]

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]