Cosmological Coincidence without Fine Tuning

Abstract

We present a simple cosmological model in which a single, non-minimally coupled scalar field with a quartic potential is responsible for both inflation at early times and acceleration at late times. Little or no fine tuning is needed to explain why the present density of dark energy is comparable to that of pressureless matter. Dark energy is identified with the potential of the scalar field, which is sourced by the trace of the energy-momentum tensor. This becomes significant when matter has decoupled from radiation and become fully non-relativistic, so that $\phi\propto\rho_m^{1/3}\propto\rho_{m,0}^{1/3}(a_0/a)\sim(10^{-120})^{1/3}(10^{10})\sim10^{-30}$ and $V\sim\phi^4\sim10^{-120}$ in Planck units, as observed.