# Cosmological perturbations in unimodular gravity

## Abstract

We study cosmological perturbation theory within the framework of unimodular gravity. We show that the Lagrangian constraint on the determinant of the metric required by unimodular gravity leads to an extra constraint on the gauge freedom of the metric perturbations. Although the main equation of motion for the gravitational potential remains the same, the shift variable, which is gauge artifact in General Relativity, cannot be set to zero in unimodular gravity. This non-vanishing shift variable affects the propagation of photons throughout the cosmological evolution and therefore modifies the Sachs-Wolfe relation between the relativistic gravitational potential and the microwave temperature anisotropies. However, for adiabatic fluctuations the difference between the result in General Relativity and unimodular gravity is suppressed on large angular scales. Thus, no strong constraints on the theory can be derived.

- Authors:

- Department of Physics and Astronomy, University of Mississippi, University, MS 38677 (United States)
- Department of Physics, McGill University, Montréal, QC H3A 2T8 (Canada)
- Department of Physics and Graduate Institute of Astrophysics, National Taiwan University, Taipei, 10617 Taiwan (China)

- Publication Date:

- OSTI Identifier:
- 22375884

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2014; Journal Issue: 09; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; EQUATIONS OF MOTION; EVOLUTION; FLUCTUATIONS; GENERAL RELATIVITY THEORY; GRAVITATION; LAGRANGIAN FUNCTION; METRICS; MICROWAVE RADIATION; PERTURBATION THEORY; PHOTONS; POTENTIALS; RELATIVISTIC RANGE

### Citation Formats

```
Gao, Caixia, Brandenberger, Robert H., Cai, Yifu, and Chen, Pisin, E-mail: cgao1@go.olemiss.edu, E-mail: rhb@hep.physics.mcgill.ca, E-mail: yifucai@physics.mcgill.ca, E-mail: chen@slac.stanford.edu.
```*Cosmological perturbations in unimodular gravity*. United States: N. p., 2014.
Web. doi:10.1088/1475-7516/2014/09/021.

```
Gao, Caixia, Brandenberger, Robert H., Cai, Yifu, & Chen, Pisin, E-mail: cgao1@go.olemiss.edu, E-mail: rhb@hep.physics.mcgill.ca, E-mail: yifucai@physics.mcgill.ca, E-mail: chen@slac.stanford.edu.
```*Cosmological perturbations in unimodular gravity*. United States. doi:10.1088/1475-7516/2014/09/021.

```
Gao, Caixia, Brandenberger, Robert H., Cai, Yifu, and Chen, Pisin, E-mail: cgao1@go.olemiss.edu, E-mail: rhb@hep.physics.mcgill.ca, E-mail: yifucai@physics.mcgill.ca, E-mail: chen@slac.stanford.edu. Mon .
"Cosmological perturbations in unimodular gravity". United States.
doi:10.1088/1475-7516/2014/09/021.
```

```
@article{osti_22375884,
```

title = {Cosmological perturbations in unimodular gravity},

author = {Gao, Caixia and Brandenberger, Robert H. and Cai, Yifu and Chen, Pisin, E-mail: cgao1@go.olemiss.edu, E-mail: rhb@hep.physics.mcgill.ca, E-mail: yifucai@physics.mcgill.ca, E-mail: chen@slac.stanford.edu},

abstractNote = {We study cosmological perturbation theory within the framework of unimodular gravity. We show that the Lagrangian constraint on the determinant of the metric required by unimodular gravity leads to an extra constraint on the gauge freedom of the metric perturbations. Although the main equation of motion for the gravitational potential remains the same, the shift variable, which is gauge artifact in General Relativity, cannot be set to zero in unimodular gravity. This non-vanishing shift variable affects the propagation of photons throughout the cosmological evolution and therefore modifies the Sachs-Wolfe relation between the relativistic gravitational potential and the microwave temperature anisotropies. However, for adiabatic fluctuations the difference between the result in General Relativity and unimodular gravity is suppressed on large angular scales. Thus, no strong constraints on the theory can be derived.},

doi = {10.1088/1475-7516/2014/09/021},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 09,

volume = 2014,

place = {United States},

year = {Mon Sep 01 00:00:00 EDT 2014},

month = {Mon Sep 01 00:00:00 EDT 2014}

}