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 $m_{\mathrm{eff}}$ 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 $\frac{m_{\mathrm{eff}}^2}{H^2}$. The analysis with WP+ Planck likelihood shows a non-zero detection of $\frac{m_{\mathrm{eff}}^2}{H^2}$ with $5.7\sigma$ and $8.1\sigma$ respectively for $r<0.1$ and $r<0.01$. Whereas, with BICEP-2 likelihood $\frac{m_{\mathrm{eff}}^2}{H^2}=-0.0237\pm 0.0135$ which is consistent with zero.

arXiv comment11 Pages, 4 Figures. Matches the published version

References in corpus (12)

• Planck 2013 results. XVI. Cosmological parameters
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results
• BICEP2 I: Detection Of B-mode Polarization at Degree Angular Scales
• Planck 2013 results. XXII. Constraints on inflation
• Encyclopaedia Inflationaris
• Reconstructing the Inflaton Potential --- an Overview
• Planck 2013 results. XV. CMB power spectra and likelihood
• Density Perturbations,Gravity Waves and the Cosmic Microwave Background
• Compatibility of Planck and BICEP2 in the Light of Inflation
• SCoPE: An efficient method of Cosmological Parameter Estimation
• Perturbed Power-law parameters from WMAP7

Cited by in corpus (3)

• Cosmic Microwave Background Anisotropy numerical solution (CMBAns) I: An introduction to $C_l$ calculation
• Constraints on Tensor to Scalar Ratio using WKB Approximation
• Gravitational wave production after inflation for a hybrid inflationary model