# On the breakdown of the curvature perturbation ζ during reheating

## Abstract

It is known that in single scalar field inflationary models the standard curvature perturbation ζ, which is supposedly conserved at superhorizon scales, diverges during reheating at times 0φ-dot =, i.e. when the time derivative of the background inflaton field vanishes. This happens because the comoving gauge 0φ=, where φ denotes the inflaton perturbation, breaks down when 0φ-dot =. The issue is usually bypassed by averaging out the inflaton oscillations but strictly speaking the evolution of ζ is ill posed mathematically. We solve this problem in the free theory by introducing a family of smooth gauges that still eliminates the inflaton fluctuation φ in the Hamiltonian formalism and gives a well behaved curvature perturbation ζ, which is now rigorously conserved at superhorizon scales. At the linearized level, this conserved variable can be used to unambiguously propagate the inflationary perturbations from the end of inflation to subsequent epochs. We discuss the implications of our results for the inflationary predictions.

- Authors:

- Department of Physics, Bo g-tilde aziçi University, 34342, Bebek, İstanbul (Turkey)

- Publication Date:

- OSTI Identifier:
- 22525899

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 04; 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; DISTURBANCES; FLUCTUATIONS; HAMILTONIANS; INFLATIONARY UNIVERSE; INFLATONS; OSCILLATIONS; SCALAR FIELDS

### Citation Formats

```
Algan, Merve Tarman, Kaya, Ali, and Kutluk, Emine Seyma, E-mail: merve.tarman@boun.edu.tr, E-mail: ali.kaya@boun.edu.tr, E-mail: seymakutluk@gmail.com.
```*On the breakdown of the curvature perturbation ζ during reheating*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/04/015.

```
Algan, Merve Tarman, Kaya, Ali, & Kutluk, Emine Seyma, E-mail: merve.tarman@boun.edu.tr, E-mail: ali.kaya@boun.edu.tr, E-mail: seymakutluk@gmail.com.
```*On the breakdown of the curvature perturbation ζ during reheating*. United States. doi:10.1088/1475-7516/2015/04/015.

```
Algan, Merve Tarman, Kaya, Ali, and Kutluk, Emine Seyma, E-mail: merve.tarman@boun.edu.tr, E-mail: ali.kaya@boun.edu.tr, E-mail: seymakutluk@gmail.com. Wed .
"On the breakdown of the curvature perturbation ζ during reheating". United States.
doi:10.1088/1475-7516/2015/04/015.
```

```
@article{osti_22525899,
```

title = {On the breakdown of the curvature perturbation ζ during reheating},

author = {Algan, Merve Tarman and Kaya, Ali and Kutluk, Emine Seyma, E-mail: merve.tarman@boun.edu.tr, E-mail: ali.kaya@boun.edu.tr, E-mail: seymakutluk@gmail.com},

abstractNote = {It is known that in single scalar field inflationary models the standard curvature perturbation ζ, which is supposedly conserved at superhorizon scales, diverges during reheating at times 0φ-dot =, i.e. when the time derivative of the background inflaton field vanishes. This happens because the comoving gauge 0φ=, where φ denotes the inflaton perturbation, breaks down when 0φ-dot =. The issue is usually bypassed by averaging out the inflaton oscillations but strictly speaking the evolution of ζ is ill posed mathematically. We solve this problem in the free theory by introducing a family of smooth gauges that still eliminates the inflaton fluctuation φ in the Hamiltonian formalism and gives a well behaved curvature perturbation ζ, which is now rigorously conserved at superhorizon scales. At the linearized level, this conserved variable can be used to unambiguously propagate the inflationary perturbations from the end of inflation to subsequent epochs. We discuss the implications of our results for the inflationary predictions.},

doi = {10.1088/1475-7516/2015/04/015},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 04,

volume = 2015,

place = {United States},

year = {Wed Apr 01 00:00:00 EDT 2015},

month = {Wed Apr 01 00:00:00 EDT 2015}

}