Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0901.1639

A One Parameter Family of Expanding Wave Solutions of the Einstein Equations That Induces an Anomalous Acceleration Into the Standard Model of Cosmology

Joel Smoller·Blake Temple
View original source ↗Read source document ↗Export metadata ↓

Abstract

We derive a new set of equations which describe a continuous one parameter family of expanding wave solutions of the Einstein equations such that the Friedmann universe associated with the pure radiation phase of the Standard Model of Cosmology, is embedded as a single point in this family. All of the spacetime metrics associated with this family satisfy the equation of state $p=ρc^2/3$, correct for the pure radiation phase after inflation in the Standard Model of the Big Bang. By expanding solutions about the center to leading order in the Hubble length, the family reduces to a one-parameter family of expanding spacetimes that represent a perturbation of the Standard Model. We then derive a co-moving coordinate system in which the perturbed spacetimes can be compared with the Standard Model. In this coordinate system we calculate the correction to the Hubble constant, as well as the exact leading order quadratic correction to the redshift vs luminosity relation for an observer at the center of the expanding FRW spacetime. The leading order correction to the redshift vs luminosity relation entails an adjustable free parameter that introduces an anomalous acceleration. We conclude that any correction to the redshift vs luminosity relation observed after the radiation phase of the Big Bang can be accounted for, at the leading order quadratic level, by adjustment of this free parameter. Since exact non-interacting expanding waves represent possible time-asymptotic wave patterns for conservation laws, we propose to further investigate the possibility that these corrections to the Standard Model might account for the anomalous acceleration of the galaxies, without the introduction of the cosmological constant.

Explore related subjects

astro-ph.COgr-qcmath.AP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Joel Smoller, Blake Temple. 2009-01-12. A One Parameter Family of Expanding Wave Solutions of the Einstein Equations That Induces an Anomalous Acceleration Into the Standard Model of Cosmology. https://arxiv.org/abs/0901.1639

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Absorption effects in the expanding Universe: spectral transmittance functions of the intergalactic medium for distant sources

We construct two self-consistent analytic approximations to the neutral hydrogen fraction, $x_{\rm HI}(z)$, and the helium ionization fractions, $x_{\rm HeI}(z)$, $x_{\rm HeII}(z)$, and $x_{\rm HeIII}(z)$, that are consistent with current constraints inferred from quasar spectra, galaxy surveys, and CMB polarization measurements. These approximations describe observationally motivated early- and late-reionization scenarios. Using these histories, we analyse the formation of broad absorption troughs in the continuum spectra of high-redshift sources over $1\leq z_{\rm s}\leq15$. We assume that neutral hydrogen and helium in a homogeneous diffuse intergalactic medium reside predominantly in their ground states and absorb radiation through the Lyman-series lines and continua of HI, HeI, and HeII. We compute the wavelength-dependent optical depths for the first 39 Lyman-series lines of HI and HeII, the first 10 lines of HeI, and the corresponding continua, and use them to derive spectral transmittance functions, $T(λ;z_{\rm s})$. As illustrative applications, we apply them to toy-model continuum spectra of starless haloes and to model spectra of a low-metallicity dwarf galaxy at different redshifts. Spectral features in sources at $5\lesssim z_{\rm s}\lesssim7$ caused by intergalactic absorption are found to be particularly sensitive to the adopted hydrogen and helium ionization histories

astro-ph.CO↗
arXiv2026

Union3.1: Reducing Systematics in Supernova Cosmology with Self-consistent Measurements of Host Galaxy Properties for 2000 Type Ia Supernovae

Photometrically derived distances of Type Ia supernovae (SNe Ia) rely on a $\sim5\%$ empirical correction based on host galaxy properties, e.g., global stellar mass. Unbiased cosmology inference therefore requires the self-consistent determination of host properties across the full range of redshifts probed, which we undertake here for approximately 2000 SNe in the Union3 compilation (now Union3.1). We use homogeneous, optical-infrared photometry from the DESI Legacy Imaging Surveys to infer global galaxy properties using the stellar population synthesis and SED-fitting code Prospector. We find that the host masses of $z<0.1$ SNe in Union3 were on average overestimated, while the opposite was true for $z<0.15$ SNe in Pantheon+. After correction, the two studies' average distance modulus estimated for low-redshift SNe, previously $>0.03$ mag discrepant, come into 0.01 mag agreement. Updating the UNITY SN analysis, we find the uncertainties on all standardization parameters shrink to $0.6$-$0.9\times$ their previous sizes. For flat-$Λ$CDM, we find from SNe alone $Ω_m=0.344^{+0.026}_{-0.025}$ (a $-0.4σ$ shift from Union3). We then combine with measurements of Baryon Acoustic Oscillations and the Cosmic Microwave Background exactly as done by DESI DR2 and find for flat $w_0w_a$CDM, $w_0=-0.719\pm0.084$ and $w_a=-0.95^{+0.29}_{-0.26}$, corresponding to $3.4σ$ evidence against a cosmological constant (down from $3.8σ$ per DESI-DR2+Planck+Union3). Updating the DESI-DR2+Planck+SN combined probe analysis with the recent Dovekie recalibration of DES-SN5YR (B. Popovic et al. 2025) or the updated Pantheon+, we find $3.4σ$ (was $4.2σ$ before Dovekie) and $3.2σ$ (was $2.8σ$ before our correction to Pantheon+) evidence, respectively, against a cosmological constant--a significantly improved consistency between SN analyses.

astro-ph.CO↗
arXiv2026

Reconciling large-scale Lyman-$α$ correlations with the SCRIPT Semi-numerical Model

Recent analyses of high-redshift Lyman-$α$ forest observations have revealed strong correlations on scales exceeding 200 cMpc at redshift z = 6. Reproducing these large-scale correlations has proven challenging for current large-volume reionization simulations. In this work, we investigate these large-scale correlations using mock spectra generated from the extended SCRIPT semi-numerical reionization model. We find that while the fiducial model ensemble systematically predicts smaller correlation lengths than those inferred from the 67 sightlines in the extended XQR-30 sample, 17.5% of individual mock realizations can naturally reproduce the observed signal. Using a delete-2 jackknife analysis, we demonstrate that the observed large-scale correlation length is disproportionately driven by a rare pair of highly transmissive sightlines associated with high-redshift transmission spikes. By inserting two such highly transmissive sightlines into our mock realizations, the fraction of realizations consistent with the observed redshift evolution and correlation length increases significantly from 17.5% to 74.1%. Furthermore, we show that spatial fluctuations in the ionizing mean free path remain an essential physical ingredient for reproducing the observed correlation structure. Our results suggest that the unexpectedly large Lyman-$α$ correlations can be reconciled with existing reionization models when accounting for cosmic variance and the outsized statistical impact of highly transmissive sightlines that occur as prominent outliers within the observational sample.

astro-ph.CO↗