# Cosmological Perturbation Theory for streams of relativistic particles

## Abstract

Motion equations describing streams of relativistic particles and their properties are explored in detail in the framework of Cosmological Perturbation Theory. Those equations, derived in any metric both in the linear and nonlinear regimes, express the matter and momentum conservation. In this context we extend the setup of adiabatic initial conditions—that was initially performed in the conformal Newtonian gauge—to the synchronous gauge. The subhorizon limit of the nonlinear motion equations written in a generic perturbed Friedmann-Lemaître metric is then derived and analyzed. We show in particular that the momentum field P{sub i}(x) is always potential in the linear regime and remains so at subhorizon scales in the nonlinear regime. Finally the equivalence principle is exploited to highlight invariance properties satisfied by such a system of equations, extending that known for streams of non-relativistic particles, namely the extended Galilean invariance.

- Authors:

- Institut de Physique Théorique, CEA (CNRS: URA 2306) Orme des merisiers 91191 Gif-sur-Yvette (France)
- Institut d'Astrophysique de Paris, UPMC (CNRS: UMR 7095) 98 bis boulevard Arago 75014 Paris (France)

- Publication Date:

- OSTI Identifier:
- 22525940

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 03; 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; EQUATIONS OF MOTION; EQUIVALENCE PRINCIPLE; INVARIANCE PRINCIPLES; METRICS; NONLINEAR PROBLEMS; PERTURBATION THEORY; POTENTIALS; RELATIVISTIC RANGE; STREAMS

### Citation Formats

```
Dupuy, Hélène, and Bernardeau, Francis, E-mail: helene.dupuy@cea.fr, E-mail: francis.bernardeau@iap.fr.
```*Cosmological Perturbation Theory for streams of relativistic particles*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/03/030.

```
Dupuy, Hélène, & Bernardeau, Francis, E-mail: helene.dupuy@cea.fr, E-mail: francis.bernardeau@iap.fr.
```*Cosmological Perturbation Theory for streams of relativistic particles*. United States. doi:10.1088/1475-7516/2015/03/030.

```
Dupuy, Hélène, and Bernardeau, Francis, E-mail: helene.dupuy@cea.fr, E-mail: francis.bernardeau@iap.fr. Sun .
"Cosmological Perturbation Theory for streams of relativistic particles". United States.
doi:10.1088/1475-7516/2015/03/030.
```

```
@article{osti_22525940,
```

title = {Cosmological Perturbation Theory for streams of relativistic particles},

author = {Dupuy, Hélène and Bernardeau, Francis, E-mail: helene.dupuy@cea.fr, E-mail: francis.bernardeau@iap.fr},

abstractNote = {Motion equations describing streams of relativistic particles and their properties are explored in detail in the framework of Cosmological Perturbation Theory. Those equations, derived in any metric both in the linear and nonlinear regimes, express the matter and momentum conservation. In this context we extend the setup of adiabatic initial conditions—that was initially performed in the conformal Newtonian gauge—to the synchronous gauge. The subhorizon limit of the nonlinear motion equations written in a generic perturbed Friedmann-Lemaître metric is then derived and analyzed. We show in particular that the momentum field P{sub i}(x) is always potential in the linear regime and remains so at subhorizon scales in the nonlinear regime. Finally the equivalence principle is exploited to highlight invariance properties satisfied by such a system of equations, extending that known for streams of non-relativistic particles, namely the extended Galilean invariance.},

doi = {10.1088/1475-7516/2015/03/030},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 03,

volume = 2015,

place = {United States},

year = {Sun Mar 01 00:00:00 EST 2015},

month = {Sun Mar 01 00:00:00 EST 2015}

}