Inflation and nonequilibrium renormalization group

We study de spectrum of primordial fluctuations and the scale dependence of the inflaton spectral index due to self-interactions of the field. We compute the spectrum of fluctuations by applying nonequilibrium renormalization group techniques. PACS numbers: 98.80.Cq, 11.10.Hi, 11.10.Jj Submitted to: J. Phys. A: Math. Gen. In this paper we explore a mechanism to explain departures of the primordial fluctuations from the spectrum of a free inflaton field. This is important, because the spectrum of the inflaton field at the exit of the horizon is directly related with the level of inhomogeneity of the observed universe. The question we want to address is how the nonlinearities for an interacting field affect the predicted spectrum [1, 2, 3, 4]. To this end we will use a nonequilibrium renormalization group (RG). If the inflaton field were a free field, its spectrum would be of Harrison-Zel’dovich type. At the horizon exit (HE) of the mode with wave number k it would be 〈Φ(k, t)Φ(k, t)〉HE ∝ 1 k3 . (1) The spectral index n(k) measures deviations from this law. It is defined by 〈Φ(k, t)Φ(k, t)〉HE ∝ 1 k3 k. (2) Hence, the Harrison-Zel’dovich spectrum (1) has n(k) = 1. Present experiments show that the spectral index is close to one and that presumably it runs with the scale, n(k) = 1 + ∆(k), (3) just at the edge of the experimental precision [5]. We will compute the spectrum of the inflaton field for a toy model of inflation. The goal is to show how a RG defined for nonequilibrium problems can be used to predict the spectrum of an interacting inflaton field. We will assume a spatially flat Robertson-Walker metric with constant expansion rate H , ds = dt − a(t) (