# Mass eigenstates in bimetric theory with matter coupling

## Abstract

In this paper we study the ghost-free bimetric action extended by a recently proposed coupling to matter through a composite metric. The equations of motion for this theory are derived using a method which avoids varying the square-root matrix that appears in the matter coupling. We make an ansatz for which the metrics are proportional to each other and find that it can solve the equations provided that one parameter in the action is fixed. In this case, the proportional metrics as well as the effective metric that couples to matter solve Einstein's equations of general relativity including a matter source. Around these backgrounds we derive the quadratic action for perturbations and diagonalize it into generalized mass eigenstates. It turns out that matter only interacts with the massless spin-2 mode whose equation of motion has exactly the form of the linearized Einstein equations, while the field with Fierz-Pauli mass term is completely decoupled. Hence, bimetric theory, with one parameter fixed such that proportional solutions exist, is degenerate with general relativity up to linear order around these backgrounds.

- Authors:

- Department of Physics and The Oskar Klein Centre, Stockholm University, AlbaNova University Centre, Stockholm, SE-106 91 Sweden (Sweden)

- Publication Date:

- OSTI Identifier:
- 22382012

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 01; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COUPLING; EIGENSTATES; EINSTEIN FIELD EQUATIONS; EQUATIONS OF MOTION; GENERAL RELATIVITY THEORY; MASS; MATHEMATICAL SOLUTIONS; MATRICES; MATTER; METRICS; PERTURBATION THEORY; SPIN

### Citation Formats

```
Schmidt-May, Angnis, E-mail: angnis.schmidt-may@fysik.su.se.
```*Mass eigenstates in bimetric theory with matter coupling*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/01/039.

```
Schmidt-May, Angnis, E-mail: angnis.schmidt-may@fysik.su.se.
```*Mass eigenstates in bimetric theory with matter coupling*. United States. doi:10.1088/1475-7516/2015/01/039.

```
Schmidt-May, Angnis, E-mail: angnis.schmidt-may@fysik.su.se. Thu .
"Mass eigenstates in bimetric theory with matter coupling". United States.
doi:10.1088/1475-7516/2015/01/039.
```

```
@article{osti_22382012,
```

title = {Mass eigenstates in bimetric theory with matter coupling},

author = {Schmidt-May, Angnis, E-mail: angnis.schmidt-may@fysik.su.se},

abstractNote = {In this paper we study the ghost-free bimetric action extended by a recently proposed coupling to matter through a composite metric. The equations of motion for this theory are derived using a method which avoids varying the square-root matrix that appears in the matter coupling. We make an ansatz for which the metrics are proportional to each other and find that it can solve the equations provided that one parameter in the action is fixed. In this case, the proportional metrics as well as the effective metric that couples to matter solve Einstein's equations of general relativity including a matter source. Around these backgrounds we derive the quadratic action for perturbations and diagonalize it into generalized mass eigenstates. It turns out that matter only interacts with the massless spin-2 mode whose equation of motion has exactly the form of the linearized Einstein equations, while the field with Fierz-Pauli mass term is completely decoupled. Hence, bimetric theory, with one parameter fixed such that proportional solutions exist, is degenerate with general relativity up to linear order around these backgrounds.},

doi = {10.1088/1475-7516/2015/01/039},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 01,

volume = 2015,

place = {United States},

year = {Thu Jan 01 00:00:00 EST 2015},

month = {Thu Jan 01 00:00:00 EST 2015}

}