# Theory of cosmological perturbations with cuscuton

## Abstract

This paper presents the first derivation of the quadratic action for curvature perturbations, ζ, within the framework of cuscuton gravity. We study the scalar cosmological perturbations sourced by a canonical single scalar field in the presence of cuscuton field. We identify ζ as comoving curvature with respect to the source field and we show that it retains its conservation characteristic on super horizon scales. The result provides an explicit proof that cuscuton modification of gravity around Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is ghost free. We also investigate the potential development of other instabilities in cuscuton models. We find that in a large class of these models, there is no generic instability problem. However, depending on the details of slow-roll parameters, specific models may display gradient instabilities.

- Authors:

- Department of Applied Mathematics, University of Waterloo, 200 University Ave W., Waterloo, ON N2L 3G1 (Canada)

- Publication Date:

- OSTI Identifier:
- 22676102

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 07; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMOLOGICAL MODELS; DISTURBANCES; GRAVITATION; INSTABILITY; METRICS; MODIFICATIONS; PERTURBATION THEORY; SCALAR FIELDS

### Citation Formats

```
Boruah, Supranta S., Kim, Hyung J., and Geshnizjani, Ghazal, E-mail: ssarmabo@uwaterloo.ca, E-mail: h268kim@uwaterloo.ca, E-mail: ggeshniz@uwaterloo.ca.
```*Theory of cosmological perturbations with cuscuton*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/07/022.

```
Boruah, Supranta S., Kim, Hyung J., & Geshnizjani, Ghazal, E-mail: ssarmabo@uwaterloo.ca, E-mail: h268kim@uwaterloo.ca, E-mail: ggeshniz@uwaterloo.ca.
```*Theory of cosmological perturbations with cuscuton*. United States. doi:10.1088/1475-7516/2017/07/022.

```
Boruah, Supranta S., Kim, Hyung J., and Geshnizjani, Ghazal, E-mail: ssarmabo@uwaterloo.ca, E-mail: h268kim@uwaterloo.ca, E-mail: ggeshniz@uwaterloo.ca. Sat .
"Theory of cosmological perturbations with cuscuton". United States.
doi:10.1088/1475-7516/2017/07/022.
```

```
@article{osti_22676102,
```

title = {Theory of cosmological perturbations with cuscuton},

author = {Boruah, Supranta S. and Kim, Hyung J. and Geshnizjani, Ghazal, E-mail: ssarmabo@uwaterloo.ca, E-mail: h268kim@uwaterloo.ca, E-mail: ggeshniz@uwaterloo.ca},

abstractNote = {This paper presents the first derivation of the quadratic action for curvature perturbations, ζ, within the framework of cuscuton gravity. We study the scalar cosmological perturbations sourced by a canonical single scalar field in the presence of cuscuton field. We identify ζ as comoving curvature with respect to the source field and we show that it retains its conservation characteristic on super horizon scales. The result provides an explicit proof that cuscuton modification of gravity around Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is ghost free. We also investigate the potential development of other instabilities in cuscuton models. We find that in a large class of these models, there is no generic instability problem. However, depending on the details of slow-roll parameters, specific models may display gradient instabilities.},

doi = {10.1088/1475-7516/2017/07/022},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 07,

volume = 2017,

place = {United States},

year = {Sat Jul 01 00:00:00 EDT 2017},

month = {Sat Jul 01 00:00:00 EDT 2017}

}