# Consistency equation hierarchy in single-field inflation models

## Abstract

Inflationary consistency equations relate the scalar and tensor perturbations. We elucidate the infinite hierarchy of consistency equations of single-field inflation, the first of which is the well-known relation A{sub T}{sup 2}/A{sub S}{sup 2}=-n{sub T}/2 between the amplitudes and the tensor spectral index. We write a general expression for all consistency equations both to first and second order in the slow-roll expansion. We discuss the relation to other consistency equations that have appeared in the literature, demonstrating in particular that the approximate consistency equation recently introduced by Chung and collaborators is equivalent to the second consistency equation of Lidsey et al. (1997)

- Authors:

- Astronomy Centre, University of Sussex, Brighton BN1 9QH (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 20782894

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.73.083523; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; COSMOLOGY; DISTURBANCES; EXPANSION; FIELD EQUATIONS; INDEXES; INFLATIONARY UNIVERSE; SCALARS; TENSORS

### Citation Formats

```
Cortes, Marina, and Liddle, Andrew R.
```*Consistency equation hierarchy in single-field inflation models*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVD.73.083523.

```
Cortes, Marina, & Liddle, Andrew R.
```*Consistency equation hierarchy in single-field inflation models*. United States. doi:10.1103/PHYSREVD.73.083523.

```
Cortes, Marina, and Liddle, Andrew R. Sat .
"Consistency equation hierarchy in single-field inflation models". United States.
doi:10.1103/PHYSREVD.73.083523.
```

```
@article{osti_20782894,
```

title = {Consistency equation hierarchy in single-field inflation models},

author = {Cortes, Marina and Liddle, Andrew R.},

abstractNote = {Inflationary consistency equations relate the scalar and tensor perturbations. We elucidate the infinite hierarchy of consistency equations of single-field inflation, the first of which is the well-known relation A{sub T}{sup 2}/A{sub S}{sup 2}=-n{sub T}/2 between the amplitudes and the tensor spectral index. We write a general expression for all consistency equations both to first and second order in the slow-roll expansion. We discuss the relation to other consistency equations that have appeared in the literature, demonstrating in particular that the approximate consistency equation recently introduced by Chung and collaborators is equivalent to the second consistency equation of Lidsey et al. (1997)},

doi = {10.1103/PHYSREVD.73.083523},

journal = {Physical Review. D, Particles Fields},

number = 8,

volume = 73,

place = {United States},

year = {Sat Apr 15 00:00:00 EDT 2006},

month = {Sat Apr 15 00:00:00 EDT 2006}

}

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