Mathematics Colloquia and Seminars

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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 = c^2 ρ /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 space- times 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. 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. (Articles and commentaries can be found on author’s website: http://www.math.ucdavis.edu/~temple/articles/ )