A plausible solution to the problem of initial conditions for inflation

Abstract

We propose yet another solution to the initial condition problem of inflation associated with homogeneity beyond the horizon at the onset of inflation, in cases where inflation is preceded by a radiation era. One may argue that causality will allow for smoothness over the causal horizon scale $H^{-1}$, but for thermal inflationary scenarios, the background inflaton field will only be correlated over the thermal correlation length $\zeta\sim T^{-1}$ which is much smaller than $H^{-1}$. We argue, with examples, that if the number of relativistic degrees of freedom in the pre-inflationary era is very large $(>10^4)$ then the thermal correlation length can be of the order of the causal horizon size alleviating the initial conditions problem of inflation.