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

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Smoller, Joel

Temple, Blake

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##### Abstract

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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
$p=\rho c^2/3$, 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.

Comment: 16 pages

Comment: 16 pages

##### Keywords

Astrophysics - Cosmology and Nongalactic Astrophysics, General Relativity and Quantum Cosmology, Mathematics - Analysis of PDEs