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

TL;DR

This paper investigates the Perturbed Power Law inflation model using recent CMB data, estimating inflation parameters and demonstrating the model's ability to explain observed spectral features and tensor-to-scalar ratios.

Contribution

It provides the first estimation of inflation parameters for the PPL model using recent CMB measurements, highlighting the model's compatibility with various bounds on tensor-to-scalar ratio.

Findings

PPL model can explain lower tensor-to-scalar ratios for certain spectral indices.

Non-zero effective mass of the inflaton is detected with high significance under specific bounds.

The model's parameters are consistent with current CMB observations and dust contamination estimates.

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 $m_{\rm eff}$ 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 $\nu_t$ and change in spectral index for scalar perturbation $\nu_{st}$ 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 $\Lambda$CDM 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 $\frac{m^2_{\rm eff}}{H^2}$. The analysis with WP+ Planck likelihood shows a non-zero detection of $\frac{m^2_{\rm eff}}{H^2}$ with $5.7\,\sigma$ and $8.1\,\sigma$ respectively for $r<0.1$ and $r<0.01$. Whereas, with BICEP-2 likelihood $\frac{m^2_{\rm eff}}{H^2} = -0.0237 \pm 0.0135$ which is consistent with zero.