# Covariant generalization of cosmological perturbation theory

## Abstract

We present an approach to cosmological perturbations based on a covariant perturbative expansion between two worldlines in the real inhomogeneous universe. As an application, at an arbitrary order we define an exact scalar quantity which describes the inhomogeneities in the number of e-folds on uniform density hypersurfaces and which is conserved on all scales for a barotropic ideal fluid. We derive a compact form for its conservation equation at all orders and assign it a simple physical interpretation. To make a comparison with the standard perturbation theory, we develop a method to construct gauge-invariant quantities in a coordinate system at arbitrary order, which we apply to derive the form of the nth order perturbation in the number of e-folds on uniform density hypersurfaces and its exact evolution equation. On large scales, this provides the gauge-invariant expression for the curvature perturbation on uniform density hypersurfaces and its evolution equation at any order.

- Authors:

- Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FIN-00014 (Finland)
- (Finland)
- Department of Physical Sciences, University of Helsinki, P.O. Box 64, FIN-00014 (Finland)
- (Italy)

- Publication Date:

- OSTI Identifier:
- 20935214

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.023515; (c) 2007 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; COORDINATES; COSMOLOGICAL MODELS; EQUATIONS; EXACT SOLUTIONS; EXPANSION; GAUGE INVARIANCE; IDEAL FLOW; MATHEMATICAL EVOLUTION; PERTURBATION THEORY; SCALARS; UNIVERSE

### Citation Formats

```
Enqvist, Kari, Department of Physical Sciences, University of Helsinki, P.O. Box 64, FIN-00014, Hoegdahl, Janne, Nurmi, Sami, Vernizzi, Filippo, and Abdus Salam ICTP, Strada Costiera 11, 34100 Trieste.
```*Covariant generalization of cosmological perturbation theory*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.023515.

```
Enqvist, Kari, Department of Physical Sciences, University of Helsinki, P.O. Box 64, FIN-00014, Hoegdahl, Janne, Nurmi, Sami, Vernizzi, Filippo, & Abdus Salam ICTP, Strada Costiera 11, 34100 Trieste.
```*Covariant generalization of cosmological perturbation theory*. United States. doi:10.1103/PHYSREVD.75.023515.

```
Enqvist, Kari, Department of Physical Sciences, University of Helsinki, P.O. Box 64, FIN-00014, Hoegdahl, Janne, Nurmi, Sami, Vernizzi, Filippo, and Abdus Salam ICTP, Strada Costiera 11, 34100 Trieste. Mon .
"Covariant generalization of cosmological perturbation theory". United States.
doi:10.1103/PHYSREVD.75.023515.
```

```
@article{osti_20935214,
```

title = {Covariant generalization of cosmological perturbation theory},

author = {Enqvist, Kari and Department of Physical Sciences, University of Helsinki, P.O. Box 64, FIN-00014 and Hoegdahl, Janne and Nurmi, Sami and Vernizzi, Filippo and Abdus Salam ICTP, Strada Costiera 11, 34100 Trieste},

abstractNote = {We present an approach to cosmological perturbations based on a covariant perturbative expansion between two worldlines in the real inhomogeneous universe. As an application, at an arbitrary order we define an exact scalar quantity which describes the inhomogeneities in the number of e-folds on uniform density hypersurfaces and which is conserved on all scales for a barotropic ideal fluid. We derive a compact form for its conservation equation at all orders and assign it a simple physical interpretation. To make a comparison with the standard perturbation theory, we develop a method to construct gauge-invariant quantities in a coordinate system at arbitrary order, which we apply to derive the form of the nth order perturbation in the number of e-folds on uniform density hypersurfaces and its exact evolution equation. On large scales, this provides the gauge-invariant expression for the curvature perturbation on uniform density hypersurfaces and its evolution equation at any order.},

doi = {10.1103/PHYSREVD.75.023515},

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

number = 2,

volume = 75,

place = {United States},

year = {Mon Jan 15 00:00:00 EST 2007},

month = {Mon Jan 15 00:00:00 EST 2007}

}