Communications in Information and Systems

Volume 13 (2013)

Number 4

Special Issue in Honor of Marshall Slemrod: Part 4 of 4

Corrections to the standard model of cosmology

Pages: 445 – 468



Joel Smoller (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)

Blake Temple (Department of Mathematics, University of California at Davis)

Zeke Vogler (Department of Mathematics, University of California at Davis)


In this note, which is a first step in authors’ longer calculation, we present a system of equations for computing the $p = 0$ evolution of corrections to the Standard Model of Cosmology consistent with corrections produced by spherical self-similar perturbations of the Standard Model known to exist during the radiation phase of the Big Bang. We record here that the asymptotic equations close at leading order, creating a subsystem which contains a stable rest point which does not correspond to the unperturbed critical zero pressure Friedmann spacetime. Corrections to the Standard Model lying within the domain of attraction of this stable rest point would produce, time-asymptotically, quadratic corrections to redshift vs luminosity, i.e., quadratic corrections to the Hubble constant going out from the center, that would be independent of initial conditions, and different from the predictions of the Standard Model. In future investigations authors will characterize the parameter values associated with self-similar waves from the radiation era that would give rise to corrections that lie within this domain of attraction. The results in this paper arose as a step in the authors’ program to compute the corrections to redshift vs luminosity produced by self-similar waves from the radiation epoch, interpreting this as a baseline mechanism for the creation of anomalous accelerations that does not require extraneous fields like Dark Energy. Details will appear in their forthcoming paper.

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