A plausible solution to the problem of initial conditions for inflation

It has been argued that inflation requires an initial patch that is smooth over distance scales a bit larger than the causal horizon at the onset of inflation. While one may argue that causality will allow for smoothness on the scale of the causal horizon $H^{-1}$, we reiterate that for thermal inflationary scenarios the background inflaton field will be correlated only over the thermal correlation length $\zeta\sim T^{-1}$ which will be much smaller than the causal horizon size. However, we then argue that if the number of relativistic degrees of freedom in the Universe is very large $(>10^4)$ then the thermal correlation length can be of the order of the causal horizon size. We also provide two examples of models in which one can have such a large number of relativistic degrees of freedom. Our proposal is of relevance to all inflationary models in which the initial value of the inflaton field is set by a thermal phase transition at the onset of inflation. It can similarly be pertinent for warm inflation scenarios.