Revisiting Ryskin's Model of Cosmic Acceleration

Abstract

Cosmic backreaction as an additional source of the expansion of the universe has been a debate topic since the discovery of cosmic acceleration. The major concern is whether the self interaction of small-scale nonlinear structures would source gravity on very large scales. Gregory Ryskin argued against the additional inclusion of gravitational interaction energy of astronomical objects, whose masses are mostly inferred from gravitational effects and hence should already contain all sources with long-range gravity forces. Ryskin proposed that the backreaction contribution to the energy momentum tensor is instead from the rest of the universe beyond the observable patch. Ryskin's model elegantly solves the fine-tuning problem and is in good agreement with the Hubble diagram of Type Ia supernovae. In this article we revisit Ryskin's model and show that it is {\it inconsistent} with at least one of the following statements: (i) the universe is matter-dominated at low redshift ($z\lesssim 2$); (ii) the universe is radiation-dominated at sufficiently high redshift; (iii) matter density fluctuations are tiny ($\lesssim 10^{-4}$) at the recombination epoch.