# Evolution of the spectral index after inflation

## Abstract

In this article we investigate the time evolution of the adiabatic (curvature) and isocurvature (entropy) spectral indices after inflation era for all cosmological scales with two different initial conditions. For this purpose, we first extract an explicit equation for the time evolution of the comoving curvature perturbation (which may be known as the generalized Mukhanov-Sasaki equation). It would be cleared that the evolution of adiabatic spectral index severely depends on the initial conditions moreover, as expected it is constant only for the super-Hubble scales and adiabatic initial conditions. Additionally, the adiabatic spectral index after recombination approaches a constant value for the isocurvature perturbations. Finally, we re-investigate the Sachs-Wolfe effect and show that the fudge factor 1/3 in the adiabatic ordinary Sachs-Wolfe formula must be replaced by 0.4.

- Authors:

- Department of Physics, School of Sciences, Tarbiat Modares University, P.O.Box 14155-4838, Tehran (Iran, Islamic Republic of)

- Publication Date:

- OSTI Identifier:
- 22375867

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2014; Journal Issue: 09; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMOLOGICAL INFLATION; DATA; ENTROPY; EQUATIONS; EVOLUTION; PERTURBATION THEORY

### Citation Formats

```
Asgari, A.A., and Abbassi, A.H., E-mail: aliakbar.asgari@modares.ac.ir, E-mail: ahabbasi@modares.ac.ir.
```*Evolution of the spectral index after inflation*. United States: N. p., 2014.
Web. doi:10.1088/1475-7516/2014/09/042.

```
Asgari, A.A., & Abbassi, A.H., E-mail: aliakbar.asgari@modares.ac.ir, E-mail: ahabbasi@modares.ac.ir.
```*Evolution of the spectral index after inflation*. United States. doi:10.1088/1475-7516/2014/09/042.

```
Asgari, A.A., and Abbassi, A.H., E-mail: aliakbar.asgari@modares.ac.ir, E-mail: ahabbasi@modares.ac.ir. Mon .
"Evolution of the spectral index after inflation". United States.
doi:10.1088/1475-7516/2014/09/042.
```

```
@article{osti_22375867,
```

title = {Evolution of the spectral index after inflation},

author = {Asgari, A.A. and Abbassi, A.H., E-mail: aliakbar.asgari@modares.ac.ir, E-mail: ahabbasi@modares.ac.ir},

abstractNote = {In this article we investigate the time evolution of the adiabatic (curvature) and isocurvature (entropy) spectral indices after inflation era for all cosmological scales with two different initial conditions. For this purpose, we first extract an explicit equation for the time evolution of the comoving curvature perturbation (which may be known as the generalized Mukhanov-Sasaki equation). It would be cleared that the evolution of adiabatic spectral index severely depends on the initial conditions moreover, as expected it is constant only for the super-Hubble scales and adiabatic initial conditions. Additionally, the adiabatic spectral index after recombination approaches a constant value for the isocurvature perturbations. Finally, we re-investigate the Sachs-Wolfe effect and show that the fudge factor 1/3 in the adiabatic ordinary Sachs-Wolfe formula must be replaced by 0.4.},

doi = {10.1088/1475-7516/2014/09/042},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 09,

volume = 2014,

place = {United States},

year = {Mon Sep 01 00:00:00 EDT 2014},

month = {Mon Sep 01 00:00:00 EDT 2014}

}