MCMC analysis of WMAP3 and SDSS data points to broken symmetry inflaton potentials and provides a lower bound on the tensor to scalar ratio

Abstract

We perform a MCMC (Monte Carlo Markov Chains) analysis of the available CMB and LSS data (including the three years WMAP data) with single field slow-roll new inflation and chaotic inflation models. We do this within our approach to inflation as an effective field theory in the GinsburgLandau spirit with fourth degree trinomial potentials in the inflaton field phi.We derive explicit formu- lae and study in detail the spectral index ns of the adiabatic fluctuations the ratio r of tensor to scalar fluctuations and the running index dn_s/dln k. We use these analytic formulas as hard constraints on n_s and r in the MCMC analysis.Our analysis differs in this crucial aspect from previous MCMC studies in the literature involving the WMAP3 data. Our results are as follow: (i) The data strongly indicate the breaking (whether spontaneous or explicit) of the phi -> -phi symmetry of the inflaton potentials both for new and for chaotic inflation.(ii)Trinomial new inflation naturally satisfies this requirement and provides an excellent fit to the data.(iii)Trinomial chaotic inflation produces the best fit in a very narrow corner of the parameter space.(iv) The chaotic symmetric trinomial potential is almost certainly ruled out(at 95% CL).In tri- nomial chaotic inflation the MCMC runs go towards a potential in the boundary of the parameter space and which ressembles a spontaneously symmetry broken potential of new inflation. (v) The above results and further physical analysis here lead us to conclude that new inflation gives the best description of the data.(vi) We find a lower bound for r within trinomial new inflation potentials r > 0.016 (95% CL) and r > 0.049 (68% CL). (vii) The preferred new inflation trinomial potential is a double well, even function of the field yielding as most probable values: n_s ~ 0.958, r ~ 0.055. Such r could be observed soon.