# The inflationary bispectrum with curved field-space

## Abstract

We compute the covariant three-point function near horizon-crossing for a system of slowly-rolling scalar fields during an inflationary epoch, allowing for an arbitrary field-space metric. We show explicitly how to compute its subsequent evolution using a covariantized version of the separate universe or 'δN' expansion, which must be augmented by terms measuring curvature of the field-space manifold, and give the nonlinear gauge transformation to the comoving curvature perturbation. Nonlinearities induced by the field-space curvature terms are a new and potentially significant source of non-Gaussianity. We show how inflationary models with non-minimal coupling to the spacetime Ricci scalar can be accommodated within this framework. This yields a simple toolkit allowing the bispectrum to be computed in models with non-negligible field-space curvature.

- Authors:

- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London, E1 4NS (United Kingdom)
- Astronomy Centre, University of Sussex, Pevensey II building, Brighton, BN1 9QH (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22279888

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2012; Journal Issue: 11; 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; COSMOLOGY; COUPLING; EXPANSION; GAUGE INVARIANCE; INFLATIONARY UNIVERSE; INFLATONS; METRICS; NONLINEAR PROBLEMS; PERTURBATION THEORY; POTENTIALS; SCALAR FIELDS; SCALARS; SPACE-TIME; UNIVERSE

### Citation Formats

```
Elliston, Joseph, Tavakol, Reza, and Seery, David, E-mail: j.elliston@qmul.ac.uk, E-mail: d.seery@sussex.ac.uk, E-mail: r.tavakol@qmul.ac.uk.
```*The inflationary bispectrum with curved field-space*. United States: N. p., 2012.
Web. doi:10.1088/1475-7516/2012/11/060.

```
Elliston, Joseph, Tavakol, Reza, & Seery, David, E-mail: j.elliston@qmul.ac.uk, E-mail: d.seery@sussex.ac.uk, E-mail: r.tavakol@qmul.ac.uk.
```*The inflationary bispectrum with curved field-space*. United States. doi:10.1088/1475-7516/2012/11/060.

```
Elliston, Joseph, Tavakol, Reza, and Seery, David, E-mail: j.elliston@qmul.ac.uk, E-mail: d.seery@sussex.ac.uk, E-mail: r.tavakol@qmul.ac.uk. Thu .
"The inflationary bispectrum with curved field-space". United States. doi:10.1088/1475-7516/2012/11/060.
```

```
@article{osti_22279888,
```

title = {The inflationary bispectrum with curved field-space},

author = {Elliston, Joseph and Tavakol, Reza and Seery, David, E-mail: j.elliston@qmul.ac.uk, E-mail: d.seery@sussex.ac.uk, E-mail: r.tavakol@qmul.ac.uk},

abstractNote = {We compute the covariant three-point function near horizon-crossing for a system of slowly-rolling scalar fields during an inflationary epoch, allowing for an arbitrary field-space metric. We show explicitly how to compute its subsequent evolution using a covariantized version of the separate universe or 'δN' expansion, which must be augmented by terms measuring curvature of the field-space manifold, and give the nonlinear gauge transformation to the comoving curvature perturbation. Nonlinearities induced by the field-space curvature terms are a new and potentially significant source of non-Gaussianity. We show how inflationary models with non-minimal coupling to the spacetime Ricci scalar can be accommodated within this framework. This yields a simple toolkit allowing the bispectrum to be computed in models with non-negligible field-space curvature.},

doi = {10.1088/1475-7516/2012/11/060},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 11,

volume = 2012,

place = {United States},

year = {2012},

month = {11}

}