The use of luminous red galaxies as cosmic chronometers provides us with an in-dispensable method of measuring the universal expansion rate H(z) in a model-independent way. Unlike many probes of the cosmological history, this approachdoes not rely on integrated quantities, such as the luminosity distance, and thereforedoes not require the pre-assumption of any particular model, which may bias sub-sequent interpretations of the data. We employ three statistical tools – the Akaike,Kullback, and Bayes Information Criteria (AIC, KIC and BIC) – to compare theΛCDM model and the R h = ct Universe with the currently available measurementsof H(z), and show that the R h = ct Universe is favored by these model selectioncriteria. The parameters in each model are individually optimized by maximum like-lihood estimation. The R h = ct Universe ﬁts the data with a reduced χ 2dof = 0.745 fora Hubble constant H 0 = 63.2±2.5km s −1 Mpc −1 , and H 0 is the sole parameterin thismodel. By comparison, the optimal ΛCDM model, which has three free parameters(including H

Cosmic chronometers in the Rh = ct Universe

In this paper, we continue to build support for the proposal to use gamma-ray bursts (GRBs) as standard candles in constructing the Hubble diagram at redshifts beyond the current reach of Type Ia supernova observations. We confirm that correlations among certain spectral and light-curve features can indeed be used as luminosity indicators, and demonstrate from the most up-to-date GRB sample appropriate for this work that the Lambda CDM model optimized with these data is characterized by parameter values consistent with those in the concordance model. Specifically, we find that (Omega(m), Omega(Lambda)) approximate to (0.25(-0.06)(+0.05), 0.75(-0.05)(+0.06)), which are consistent, to within 1 sigma, with (0.29, 0.71) obtained from the 9 yr Wilkinson Microwave Anisotropy Probe data. We also carry out a comparative analysis between Lambda CDM and the R-h = ct universe and find that the optimal Lambda CDM model fits the GRB Hubble diagram with a reduced chi(2)(dof) approximate to 2.26, whereas the fit using R-h = ct results in a chi(2)(dof) approximate to 2.14. In both cases, about 20% of the events lie at least 2 sigma away from the best-fit curves, suggesting that either some contamination by non-standard GRB luminosities is unavoidable or that the errors and intrinsic scatter associated with the data are being underestimated. With these optimized fits, we use three statistical tools-the Akaike information criterion, the Kullback information criterion, and the Bayes information criterion-to show that, based on the GRB Hubble diagram, the likelihood of R-h = ct being closer to the correct model is similar to 85%-96%, compared to similar to 4%-15% for Lambda CDM.

http://iopscience.iop.org/article/10.1088/0004-637X/772/1/43/pdf

The gamma-ray burst hubble diagram and its implications for cosmology

In this paper, we continue to build support for the proposal to use gamma-ray bursts (GRBs) as standard candles in constructing the Hubble Diagram at redshifts beyond the current reach of Type Ia supernova observations. We confirm that correlations among certain spectral and lightcurve features can indeed be used as luminosity indicators, and demonstrate from the most up-to-date GRB sample appropriate for this work that the $\Lambda$CDM model optimized with these data is characterized by parameter values consistent with those in the concordance model. Specifically, we find that $(\Omega_m,\Omega_\Lambda)\approx (0.25_{-0.06}^{+0.05}, 0.75_{-0.05}^{+0.06})$, which are consistent, to within $1\sigma$, with $(0.29,0.71)$ obtained from the 9-yr WMAP data. We also carry out a comparative analysis between $\Lambda$CDM and the $R_{\rm h}=ct$ Universe and find that the optimal $\Lambda$CDM model fits the GRB Hubble Diagram with a reduced $\chi^2_{\rm dof}\approx 2.26$, whereas the fit using $R_{\rm h}=ct$ results in a $\chi^2_{\rm dof}\approx 2.14$. In both cases, about 20% of the events lie at least $2\sigma$ away from the best-fit curves, suggesting that either some contamination by non-standard GRB luminosities is unavoidable, or that the errors and intrinsic scatter associated with the data are being underestimated. With these optimized fits, we use three statistical tools---the Akaike Information Criterion (AIC), the Kullback Information Criterion (KIC), and the Bayes Information Criterion (BIC)---to show that, based on the GRB Hubble Diagram, the likelihood of $R_{\rm h}=ct$ being closer to the correct model is $\sim 85-96%$, compared to $\sim 4-15%$ for $\Lambda$CDM.

The Gamma-Ray Burst Hubble Diagram and Its Cosmological Implications

One cannot understand the early appearance of 10^9 solar-mass black holes without invoking anomalously high accretion rates or the creation of exotically massive seeds, neither of which is seen in the local Universe. Recent observations have compounded this problem by demonstrating that most, if not all, of the high-z quasars appear to be accreting at the Eddington limit. In the context of LCDM, the only viable alternative now appears to be the assemblage of supermassive black holes via mergers, as long as the seeds started forming at redshifts >40, but ceased being created by z~20-30. In this paper, we show that, whereas the high-z quasars may be difficult to explain within the framework of the standard model, they can instead be interpreted much more sensibly in the context of the R_h=ct Universe. In this cosmology, 5-20 solar-mass seeds produced after the onset of re-ionization (at z 10^9 solar masses by z> 6, merely by accreting at the standard Eddington rate.

High-z Quasars in the R_h=ct Universe

The horizon problem in the standard model of cosmology (LDCM) arises from the observed uniformity of the cosmic microwave background radiation, which has the same temperature everywhere (except for tiny, stochastic fluctuations), even in regions on opposite sides of the sky, which appear to lie outside of each other's causal horizon. Since no physical process propagating at or below lightspeed could have brought them into thermal equilibrium, it appears that the universe in its infancy required highly improbable initial conditions. In this paper, we examine this well-known problem by considering photon propagation through a Friedmann-Robertson-Walker (FRW) spacetime at a more fundamental level than has been attempted before, demonstrating that the horizon problem only emerges for a subset of FRW cosmologies, such as LCDM, that include an early phase of rapid deceleration. We show that the horizon problem is nonexistent for the recently introduced R_h=ct universe, obviating the principal motivation for the inclusion of inflation. We demonstrate through direct calculation that, in the R_h=ct universe, even opposite sides of the cosmos have remained causally connected to us - and to each other - from the very first moments in the universe's expansion. Therefore, within the context of the R_h=ct universe, the hypothesized inflationary epoch from t=10^{-35} seconds to 10^{-32} seconds was not needed to fix this particular "problem", though it may still provide benefits to cosmology for other reasons.

/pdf/the-r-h-ct-universe-without-inflation-16g9ds2ej8.pdf

The R_h=ct Universe Without Inflation

The backbone of standard cosmology is the Friedmann-Robertson-Walker solution to Einstein's equations of general relativity (GR). In recent years, observations have largely confirmed many of the properties of this model, which is based on a partitioning of the universe's energy density into three primary constituents: matter, radiation, and a hypothesized dark energy which, in LambdaCDM, is assumed to be a cosmological constant Lambda. Yet with this progress, several unpalatable coincidences (perhaps even inconsistencies) have emerged along with the successful confirmation of expected features. One of these is the observed equality of our gravitational horizon R_h(t_0) with the distance ct_0 light has traveled since the big bang, in terms of the current age t_0 of the universe. This equality is very peculiar because it need not have occurred at all and, if it did, should only have happened once (right now) in the context of LambdaCDM. In this paper, we propose an explanation for why this equality may actually be required by GR, through the application of Birkhoff's theorem and the Weyl postulate, at least in the case of a flat spacetime. If this proposal is correct, R_h(t) should be equal to ct for all cosmic time t, not just its present value t_0. Therefore models such as LambdaCDM would be incomplete because they ascribe the cosmic expansion to variable conditions not consistent with this relativistic constraint. We show that this may be the reason why the observed galaxy correlation function is not consistent with the predictions of the standard model. We suggest that an R_h=ct universe is easily distinguishable from all other models at large redshift (i.e., in the early universe), where the latter all predict a rapid deceleration.

The Rh=ct universe

The R_h = ct Universe

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 WMAP, and ground-based and HST 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 traveled 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 FRW cosmologies, to show—at least in the specific cases we consider here, including 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 0.5ct0.

http://inspirehep.net/record/1082304/files/arXiv:1112.4774.pdf

Photon geodesics in Friedmann–Robertson–Walker cosmologies

The Hubble radius is a particular manifestation of the Universe's gravitational horizon, R_h(t_0)=c/H_0, 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 WMAP, and ground-based and HST searches for Type Ia supernovae, we now know that R_h(t_0)~13.5 Glyr. This coincides with the maximum distance (ct_0~13.7 Glyr) light could have traveled since the big bang. However, the physical meaning of R_h 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 R_h, the claim being that R_h 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 FRW cosmologies, to show---at least in the specific cases we consider here, including LCDM---that no photon trajectories reaching us today could have ever crossed R_h(t_0). 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 LCDM, measured as a proper distance, is approximately 0.45ct_0.

Andrew Shevchuk

Papers

The Rh=ct universe

The R_h = ct Universe

Photon geodesics in Friedmann–Robertson–Walker cosmologies

Photon Geodesics in FRW Cosmologies