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