# A Family of Expanding Wave Solutions of the Einstein Equations that Includes the Standard Model of Cosmology

## Computational and Applied Mathematics Colloquium

## Meeting Details

For more information about this meeting, contact Kris Jenssen, Hope Shaffer, Yuxi Zheng.

**Speaker:** Blake Temple, University of California, Davis

**Abstract:** In this talk I discuss recent joint work with Joel Smoller
in which we derive a new set of equations whose solutions describe
a two parameter family of expanding wave solutions of the Einstein
equations that includes the critical (flat space k = 0) Friedmann
universe in the standard model of cosmology. All of the spacetime
metrics associated with this family apply when the equation of state
is given by $p=(rho c^2)/3$, correct for early Big Bang physics, after
inflation. 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 correction to the redshift vs luminosity
relation for an observer at the center of the expanding spacetime.
Both of these entail an adjustable free parameter that introduces
an anomalous acceleration. Since exact non-interacting expansion
waves represent possible time-asymptotic wave patterns for conservation
laws, we wonder whether it is possible that these corrections
to the standard model might account for the anomalous acceleration
of the galaxies, without the introduction of the cosmological constant.
(Articles and commentaries can be found on author's website:
http://www.math.ucdavis.edu/ temple/articles/)

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 10/03/2008

**Time:** 3:35pm - 4:25pm