Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements

Abstract

Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass m_eff for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independent parameters, namely spectral index for tensor perturbation ν_t and change in spectral index for scalar perturbation ν_st to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard ΛCDM model. Although BICEP-2 claimed a detection of r=0.2, estimates of dust contamination provided by Planck have left open the possibility that only upper bound on r will be expected in a joint analysis. As a result we consider different upper bounds on the value of r and show that PPL model can explain a lower value of tensor to scalar ratio (r< 0.1 or r< 0.01) for a scalar spectral index of n_s=0.96 by having a non-zero value of effective mass of the inflaton field m²_eff/H². The analysis with WP + Planck likelihood shows a non-zero detection of m²_eff/H² with 5.7 σ and 8.1 σ respectively for r< 0.1 and r< 0.01. Whereas, with BICEP-2 likelihood m2_eff/H² = −0.0237 ± 0.0135 which is consistent with zero.