Aim. The lack of large-angle correlations in the fluctuations of the cosmic microwave background (CMB) conflicts with predictions of slow-roll inflation. But while probabilities (≲0.24%) for the missing correlations disfavour the conventional picture at ≳3σ, factors not associated with the model itself may be contributing to the tension. Here we aim to show that the absence of large-angle correlations is best explained with the introduction of a non-zero minimum wave number kmin for the fluctuation power spectrum P(k). Methods. We assumed that quantum fluctuations were generated in the early Universe with a well-defined power spectrum P(k), although with a cut-off kmin ≠ 0. We then re-calculated the angular correlation function of the CMB and compared it with Planck observations. Results. The Planck 2013 data rule out a zero kmin at a confidence level exceeding 8σ. Whereas purely slow-roll inflation would have stretched all fluctuations beyond the horizon, producing a P(k) with kmin = 0 – and therefore strong correlations at all angles – a kmin ≠ 0 would signal the presence of a maximum wavelength at the time (tdec) of decoupling. This argues against the basic inflationary paradigm, and perhaps even suggests non-inflationary alternatives, for the origin and growth of perturbations in the early Universe. In at least one competing cosmology, the Rh = ct universe, the inferred kmin corresponds to the gravitational radius at tdec.

In general relativity, a gravitational horizon (more commonly known as the "apparent horizon") 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. (C) 2018 American Association of Physics Teachers.

Aims. The discovery of quasar J1342+0928 (z = 7.54) reinforces the time compression problem associated with the premature formation of structure in A cold dark matter (ACDM). Adopting the Planck parameters, we see this quasar barely 690 Myr after the big bang, no more than several hundred Myr after the transition from Pop III to Pop II star formation. Yet conventional astrophysics would tell us that a 10 M-circle dot seed, created by a Pop II/III supernova, should have taken at least 820 Myr to grow via Eddington-limited accretion. This failure by ACDM constitutes one of its most serious challenges, requiring exotic "fixes", such as anomalously high accretion rates, or the creation of enormously massive (similar to 10(5) M-circle dot) seeds, neither of which is ever seen in the local Universe, or anywhere else for that matter. Indeed, to emphasize this point, J1342+0928 is seen to be accreting at about the Eddington rate, negating any attempt at explaining its unusually high mass due to such exotic means. In this paper, we aim to demonstrate that the discovery of this quasar instead strongly confirms the cosmological timeline predicted by the R-h = Ct Universe. Methods. We assume conventional Eddington-limited accretion and the time versus redshift relation in this model to calculate when a seed needed to start growing as a function of its mass in order to reach the observed mass of J1342+0928 at z = 7.54. Results. Contrary to the tension created in the standard model by the appearance of this massive quasar so early in its history, we find that in the R-h = Ct cosmology, a 10 M-circle dot seed at z similar to 15 (the start of the Epoch of Reionization at t similar to 878 Myr) would have easily grown into an 8 x 10(8) M-circle dot black hole at z = 7.54 (t similar to 1.65 Gyr) via conventional Eddington-limited accretion.

Unlike other observational signatures in cosmology, the angular-diameter distance dA(z) uniquely reaches a maximum (at zmax) 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 zmax 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 zmax can effectively discriminate between them. We find that zmax = 1.70 ± 0.20 – an important new probe of the Universe’s geometry. The most strongly favoured model is Rh = ct, followed by PlanckΛCDM. Several others, including Milne, Einstein-de Sitter, and Static tired light are strongly rejected. According to these results, the Rh = ct universe, which predicts zmax = 1.718, has a ∼92.8 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 Rh = ct and PlanckΛCDM are among the few models that account for angular-size data better than those that are disfavoured by zmax. The dA(z) comparison, however, is less discerning than that with zmax, due to the additional free parameter, H0. We find that H0 = 63.4 ± 1.2 km s−1 Mpc−1 for Rh = 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 zmax is independent of H0.

We examine whether a comparison between wCDM and $R_{\textrm{h}}=ct$ using merged Type-Ia SN catalogs produces results consistent with those based on a single homogeneous sample. Using the Betoule et al. (Astron. Astrophys., 568 (2014) 22). Joint Lightcurve Analysis (JLA) of a combined sample of 613 events from SNLS and SDSS-II, we estimate the parameters of the two models and compare them. We find that the improved statistics can alter the model selection in some cases, but not others. In addition, based on the model fits, we find that there appears to be a lingering systematic offset of ~0.04–0.08 mag between the SNLS and SDSS-II sources, in spite of the cross-calibration in the JLA. Treating wCDM, ΛCDM and $R_{\textrm{h}}=ct$ as separate models, we find in an unbiased pairwise statistical comparison that the Bayes Information Criterion (BIC) favors the $R_{\textrm{h}}=ct$ Universe with a likelihood of $82.8\%$ vs. $17.2\%$ for wCDM, but the ratio of likelihoods is reversed ($16.2\%$ vs. $83.8\%$ ) when $w_{\textrm{de}}=-1$ (i.e., ΛCDM) and strongly reversed ($1.0\%$ vs. $99.0\%$ ) if in addition k = 0 (i.e., flat ΛCDM). We point out, however, that the value of k is a measure of the net energy (kinetic plus gravitational) in the Universe and is not constrained theoretically, though some models of inflation would drive $k\rightarrow 0$ due to an expansion-enforced dilution. Since we here consider only the basic ΛCDM model, the value of k needs to be measured and, therefore, the pre-assumption of flatness introduces a significant bias into the BIC.

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-Lemaitre-Robertson-Walker space-time, we see it retreating at proper speed c, giving rise to the eponymously named cosmological model R-h = ct. As of today, this cosmology has passed over 20 observational tests, often better than Lambda 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 mc(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.

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 cold dark matter (CDM) 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 CDM. 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 CDM. 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.

A validation of the cosmic distance duality (CDD) relation, h() ( ) () () z zdz dz º+ = 1 A L 1 2 , coupling the luminosity (dL) and angular-diameter (dA) distances, is crucial because its violation would require exotic new physics. We present a model-independent test of the CDD, based on strong lensing and a reconstruction of the H II galaxy Hubble diagram using Gaussian processes, to confirm the validity of the CDD at a very high level of confidence. Using parameterizations h( )z z = +1 h0 and h( )z zz =+ + 1 h h 1 2 2, our best-fit results are h = - + 0.0147 0 0.066 0.056, and h = - + 0.1091 1 0.1568 0.1680 and h = - - + 0.0603 2 0.0988 0.0999, respectively. In spite of these strong constraints, however, we also point out that the analysis of strong lensing using a simplified single isothermal sphere (SIS) model for the lens produces some irreducible scatter in the inferred CDD data. The use of an extended SIS approximation, with a power-law density structure, yields very similar results, but does not lessen the scatter due to its larger number of free parameters, which weakens the best-fit constraints. Future work with these strong lenses should therefore be based on more detailed ray-tracing calculations to determine the mass distribution more precisely

In general relativity, a gravitational horizon (more commonly known as the "apparent horizon") 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. (C) 2018 American Association of Physics Teachers.

To understand the formation and evolution of galaxies at redshifts 0 less than or similar to z less than or similar to 10, one must invariably introduce specific models (e.g., for the star formation) in order to fully interpret the data. Unfortunately, this tends to render the analysis compliant to the theory and its assumptions, so consensus is still some-what elusive. Nonetheless, the surprisingly early appearance of massive galaxies challenges the standard model, and the halo mass function estimated from galaxy surveys at z greater than or similar to 4 appears to be inconsistent with the predictions of Lambda CDM, giving rise to what has been termed "The Impossibly Early Galaxy Problem" by some workers in the field. A simple resolution to this question may not be forthcoming. The situation with the halos themselves, however, is more straightforward and, in this paper, we use linear perturbation theory to derive the halo mass function over the redshift range 0 less than or similar to z less than or similar to 10 for the R-h = ct universe. We use this predicted halo distribution to demonstrate that both its dependence on mass and its very weak dependence on redshift are compatible with the data. The difficulties with Lambda CDM may eventually be overcome with refinements to the underlying theory of star formation and galaxy evolution within the halos. For now, however, we demonstrate that the unexpected early formation of structure may also simply be due to an incorrect choice of the cosmology, rather than to yet unknown astrophysical issues associated with the condensation of mass fluctuations and subsequent galaxy formation.