Model Selection Using Cosmic Chronometers with Gaussian Processes

The use of Gaussian Processes with a measurement of the cosmic expansion rate based solely on the observation of cosmic chronometers provides a completely cosmology-independent reconstruction of the Hubble constant H(z) suitable for testing different models. The corresponding dispersion sigma_H is smaller than ~9% over the entire redshift range (0 < z < 2) of the observations, rivaling many kinds of cosmological measurements available today. We use the reconstructed H(z) function to test six different cosmologies, and show that it favours the R_h=ct universe, which has only one free parameter (i.e., H_0) over other models, including Planck LCDM. The parameters of the standard model may be re-optimized to improve the fits to the reconstructed H(z) function, but the results have smaller p-values than one finds with R_h=ct.Comment: 20 pages, 24 figures, 3 tables. Matches final published version in JCA

The Maximum Angular-Diameter Distance in Cosmology

Unlike other observational signatures in cosmology, the angular-diameter distance d_A(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 d_A(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 LCDM. 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 ~92.8% probability of being the correct cosmology. For consistency, we also carry out model selection based on d_A(z) itself. This test confirms that R_h=ct and Planck LCDM are among the few models that account for angular-size data better than those that are disfavoured by z_max. The d_A(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/Mpc for R_h=ct, and 69.9 +\- 1.5 km/s/Mpc for LCDM. Both are consistent with previously measured values in each model, though they differ from each other by over 4 sigma. In contrast, model selection based on z_max is independent of H_0.Comment: 10 pages, 5 figures, 2 tables. Matches final, published version in MNRA

A Cosmological Solution to the Impossibly Early Galaxy Problem

To understand the formation and evolution of galaxies at redshifts z < 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 somewhat elusive. Nonetheless, the surprisingly early appearance of massive galaxies challenges the standard model, and the halo mass function estimated from galaxy surveys at z > 4 appears to be inconsistent with the predictions of LCDM, 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 z < 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 LCDM 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.Comment: 23 pages, 2 figures. Accepted for publication in Physics of the Dark Univers

Reconstruction of the HII Galaxy Hubble Diagram using Gaussian Processes

The Hubble diagram constructed using HII galaxies (HIIGx) and Giant extragalactic HII regions (GEHR) as standard candles already extends beyond the current reach of Type Ia SNe. A sample of 156 HIIGx and GEHR sources has been used previously to compare the predictions of LCDM and R_h=ct, the results of which suggested that the HIIGx and GEHR sources strongly favour the latter over the former. But this analysis was based on the application of parametric fits to the data and the use of information criteria, which disfavour the less parsimonious models. In this paper, we advance the use of HII sources as standard candles by utilizing Gaussian processes (GP) to reconstruct the distance modulus representing these data without the need to pre-assume any particular model, none of which may in the end actually be the correct cosmology. In addition, this approach tightly constrains the 1 sigma confidence region of the reconstructed function, thus providing a better tool with which to differentiate between competing cosmologies. With this approach, we show that the Planck concordance model is in tension with the HII data at more than 2.5 sigma, while R_h=ct agrees with the GP reconstruction very well, particularly at redshifts > 10^{-3}.Comment: 11 pages, 4 figures. Accepted for publication in JCA

A comparison of the Rh=ct and Λ CDM cosmologies based on the observed halo mass function

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 Mh/M (extrapolated from z less than or similar to 4) reveal significant tension with Lambda CDM - a failure known as The Impossibly Early Galaxy Problem. But whether this ratio evolves or remains constant through redshift 4 less than or similar to z less than or similar to 10 is still being debated. To eliminate the tension with Lambda 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-Lemaitre-Robertson-Walker (FLRW) model known as the Rh=ct universe, and use our previous measurement of sigma 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 Rh=ct is consistent with the data, even assuming a constant Mh/M throughout the observed redshift range (4 less than or similar to z less than or similar to 10), contrasting sharply with the tension in Lambda CDM. We conclude that - if Mh/M turns out to be constant - the massive galaxies and their halos must have formed earlier than is possible in Lambda CDM.Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Cosmological tests with strong gravitational lenses using Gaussian processes

Strong gravitational lenses provide source/lens distance ratios D-obs useful in cosmological tests. Previously, a catalog of 69 such systems was used in a one-on-one comparison between the standard model, Lambda CDM, and the R-h = ct universe, which has thus far been favored by the application of model selection tools to many other kinds of data. But in that work, the use of model parametric fits to the observations could not easily distinguish between these two cosmologies, in part due to the limited measurement precision. Here, we instead use recently developed methods based on Gaussian Processes (GP), in which D-obs may be reconstructed directly from the data without assuming any parametric form. This approach not only smooths out the reconstructed function representing the data, but also reduces the size of the 1 sigma confidence regions, thereby providing greater power to discern between different models. With the current sample size, we show that analyzing strong lenses with a GP approach can definitely improve the model comparisons, producing probability differences in the range similar to 10-30%. These results are still marginal, however, given the relatively small sample. Nonetheless, we conclude that the probability of R-h = ct being the correct cosmology is somewhat higher than that of Lambda CDM, with a degree of significance that grows with the number of sources in the subsamples we consider. Future surveys will significantly grow the catalog of strong lenses and will therefore benefit considerably from the GP method we describe here. In addition, we point out that if the R-h = ct universe is eventually shown to be the correct cosmology, the lack of free parameters in the study of strong lenses should provide a remarkably powerful tool for uncovering the mass structure in lensing galaxies.Chinese Academy of Sciences Visiting Professorships for Senior International Scientists [2012T1J0011]; Chinese State Administration of Foreign Experts Affairs [GDJ20120491013]Open access journal.This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]