# 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{sub 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{sub t} and change in spectral index for scalar perturbation ν{sub 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 uppermore »

- Authors:

- Inter University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune-411007 (India)
- Dept. of Physics, Alphonsa College, Pala, 686574 India (India)

- Publication Date:

- OSTI Identifier:
- 22382007

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 01; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMOLOGICAL INFLATION; DETECTION; EFFECTIVE MASS; PERTURBATION THEORY; POLARIZATION; RELICT RADIATION; SCALARS; SPECTRA; TENSORS

### Citation Formats

```
Mukherjee, Suvodip, Das, Santanu, Souradeep, Tarun, and Joy, Minu, E-mail: suvodip@iucaa.ernet.in, E-mail: santanud@iucaa.ernet.in, E-mail: minujoy@gmail.com, E-mail: tarun@iucaa.ernet.in.
```*Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/01/043.

```
Mukherjee, Suvodip, Das, Santanu, Souradeep, Tarun, & Joy, Minu, E-mail: suvodip@iucaa.ernet.in, E-mail: santanud@iucaa.ernet.in, E-mail: minujoy@gmail.com, E-mail: tarun@iucaa.ernet.in.
```*Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements*. United States. doi:10.1088/1475-7516/2015/01/043.

```
Mukherjee, Suvodip, Das, Santanu, Souradeep, Tarun, and Joy, Minu, E-mail: suvodip@iucaa.ernet.in, E-mail: santanud@iucaa.ernet.in, E-mail: minujoy@gmail.com, E-mail: tarun@iucaa.ernet.in. Thu .
"Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements". United States.
doi:10.1088/1475-7516/2015/01/043.
```

```
@article{osti_22382007,
```

title = {Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements},

author = {Mukherjee, Suvodip and Das, Santanu and Souradeep, Tarun and Joy, Minu, E-mail: suvodip@iucaa.ernet.in, E-mail: santanud@iucaa.ernet.in, E-mail: minujoy@gmail.com, E-mail: tarun@iucaa.ernet.in},

abstractNote = {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{sub 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{sub t} and change in spectral index for scalar perturbation ν{sub 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{sub s}=0.96 by having a non-zero value of effective mass of the inflaton field m{sup 2}{sub eff}/H{sup 2}. The analysis with WP + Planck likelihood shows a non-zero detection of m{sup 2}{sub eff}/H{sup 2} with 5.7 σ and 8.1 σ respectively for r<0.1 and r<0.01. Whereas, with BICEP-2 likelihood m{sup 2}{sub eff}/H{sup 2} = −0.0237 ± 0.0135 which is consistent with zero.},

doi = {10.1088/1475-7516/2015/01/043},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 01,

volume = 2015,

place = {United States},

year = {Thu Jan 01 00:00:00 EST 2015},

month = {Thu Jan 01 00:00:00 EST 2015}

}