Single Field Inflation models allowed and ruled out by the three years WMAP data

Abstract

We study the single field slow-roll inflation models that better fit the available CMB and LSS data including the three years WMAP data: new inflation and hybrid inflation. We study them as effective field theories in the Ginsburg-Landau context: a trinomial potential turns out to be a simple and well motivated model. The compute the spectral index n_s of the adiabatic fluctuations, the ratio r of tensor to scalar fluctuations and the running index d n_s/dln k, derive explicit formulae and provide relevant plots. In new inflation, and for the three years WMAP central value n_s = 0.95, we predict 0.03<r<0.04 and -0.00070<d n_s/d ln k<-0.00055. In hybrid inflation, and for n_s = 0.95, we predict r = 0.2 and dn_s/dln k=-0.001.We find in new inflation n_s bounded from above by n_{smax} = 0.9615 and that r is a two valued function of n_s in the interval 0.96<n_s<0.9615. In the first branch we find r<r_{max} = 0.1148.In hybrid inflation we find a critical value mu_{0 crit}^2 for the mass parameter mu_0^2 of the field sigma coupled to the inflaton.For mu_0^2< Lambda_0 M_{Pl}^2/192, hybrid inflation is ruled out by the WMAP three years data since it yields n_s>1. Hybrid inflation for mu_0^2>Lambda_0 M_{Pl}^2/192 can fullfill all the present CMB+LSS data. Even if chaotic inflation predicts n_s values compatible with the data, chaotic inflation is disfavoured since it predicts a too high value for the ratio r=0.27. The model which best fits the current data and which best prepares the way to the expected data r < 0.1, is the trinomial potential with negative mass term: new inflation.