Fluid Interpretation of Cardassian Expansion

Abstract

A fluid interpretation of Cardassian expansion is developed. Here, the Friedmann equation takes the form $H^2 = g(ρ_M)$ where $ρ_M$ contains only matter and radiation (no vacuum). The function $g(\rhom)$ returns to the usual $8π\rhom/(3 m_{pl}^2)$ during the early history of the universe, but takes a different form that drives an accelerated expansion after a redshift $z \sim 1$. One possible interpretation of this function (and of the right hand side of Einstein's equations) is that it describes a fluid with total energy density $ρ_{tot} = {3 m_{pl}^2 \over 8 π} g(\rhom) = \rhom + ρ_K$ containing not only matter density (mass times number density) but also interaction terms $ρ_K$. These interaction terms give rise to an effective negative pressure which drives cosmological acceleration. These interactions may be due to interacting dark matter, e.g. with a fifth force between particles $F \sim r^{α-1}$. Such interactions may be intrinsically four dimensional or may result from higher dimensional physics. A fully relativistic fluid model is developed here, with conservation of energy, momentum, and particle number. A modified Poisson's equation is derived. A study of fluctuations in the early universe is presented, although a fully relativistic treatment of the perturbations including gauge choice is as yet incomplete.