# Curvature perturbation in multi-field inflation with non-minimal coupling

## Abstract

In this paper we discuss a multi-field model of inflation in which generally all fields are non-minimally coupled to the Ricci scalar and have non-canonical kinetic terms. The background evolution and first-order perturbations for the model are evaluated in both the Jordan and Einstein frames, and the respective curvature perturbations compared. We confirm that they are indeed not the same - unlike in the single-field case - and also that the difference is a direct consequence of the isocurvature perturbations inherent to multi-field models. This result leads us to conclude that the notion of adiabaticity is not invariant under conformal transformations. Using a two-field example we show that even if in one frame the evolution is adiabatic, meaning that the curvature perturbation is conserved on super-horizon scales, in general in the other frame isocurvature perturbations continue to source the curvature perturbation. We also find that it is possible to realise a particular model in which curvature perturbations in both frames are conserved but with each being of different magnitude. These examples highlight that the curvature perturbation itself, despite being gauge-invariant, does not correspond directly to an observable. The non-equivalence of the two curvature perturbations would also be important when consideringmore »

- Authors:

- Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502 (Japan)

- Publication Date:

- OSTI Identifier:
- 22280047

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2012; Journal Issue: 07; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASTROPHYSICS; COMPARATIVE EVALUATIONS; COSMOLOGY; COUPLING; DISTURBANCES; EVOLUTION; GAUGE INVARIANCE; INFLATIONARY UNIVERSE; INFLATONS; SCALARS; STANDARD MODEL; TRANSFORMATIONS

### Citation Formats

```
White, Jonathan, Minamitsuji, Masato, and Sasaki, Misao, E-mail: jwhite@yukawa.kyoto-u.ac.jp, E-mail: masato@yukawa.kyoto-u.ac.jp, E-mail: misao@yukawa.kyoto-u.ac.jp.
```*Curvature perturbation in multi-field inflation with non-minimal coupling*. United States: N. p., 2012.
Web. doi:10.1088/1475-7516/2012/07/039.

```
White, Jonathan, Minamitsuji, Masato, & Sasaki, Misao, E-mail: jwhite@yukawa.kyoto-u.ac.jp, E-mail: masato@yukawa.kyoto-u.ac.jp, E-mail: misao@yukawa.kyoto-u.ac.jp.
```*Curvature perturbation in multi-field inflation with non-minimal coupling*. United States. doi:10.1088/1475-7516/2012/07/039.

```
White, Jonathan, Minamitsuji, Masato, and Sasaki, Misao, E-mail: jwhite@yukawa.kyoto-u.ac.jp, E-mail: masato@yukawa.kyoto-u.ac.jp, E-mail: misao@yukawa.kyoto-u.ac.jp. Sun .
"Curvature perturbation in multi-field inflation with non-minimal coupling". United States. doi:10.1088/1475-7516/2012/07/039.
```

```
@article{osti_22280047,
```

title = {Curvature perturbation in multi-field inflation with non-minimal coupling},

author = {White, Jonathan and Minamitsuji, Masato and Sasaki, Misao, E-mail: jwhite@yukawa.kyoto-u.ac.jp, E-mail: masato@yukawa.kyoto-u.ac.jp, E-mail: misao@yukawa.kyoto-u.ac.jp},

abstractNote = {In this paper we discuss a multi-field model of inflation in which generally all fields are non-minimally coupled to the Ricci scalar and have non-canonical kinetic terms. The background evolution and first-order perturbations for the model are evaluated in both the Jordan and Einstein frames, and the respective curvature perturbations compared. We confirm that they are indeed not the same - unlike in the single-field case - and also that the difference is a direct consequence of the isocurvature perturbations inherent to multi-field models. This result leads us to conclude that the notion of adiabaticity is not invariant under conformal transformations. Using a two-field example we show that even if in one frame the evolution is adiabatic, meaning that the curvature perturbation is conserved on super-horizon scales, in general in the other frame isocurvature perturbations continue to source the curvature perturbation. We also find that it is possible to realise a particular model in which curvature perturbations in both frames are conserved but with each being of different magnitude. These examples highlight that the curvature perturbation itself, despite being gauge-invariant, does not correspond directly to an observable. The non-equivalence of the two curvature perturbations would also be important when considering the addition of Standard Model matter into the system.},

doi = {10.1088/1475-7516/2012/07/039},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 07,

volume = 2012,

place = {United States},

year = {2012},

month = {7}

}