# Induced matter brane gravity and Einstein static universe

## Abstract

We investigate stability of the Einstein static universe against the scalar, vector and tensor perturbations in the context of induced matter brane gravity. It is shown that in the framework of this model, the Einstein static universe has a positive spatial curvature. In contrast to the classical general relativity, it is found that a stable Einstein static universe against the scalar perturbations does exist provided that the variation of time dependent geometrical equation of state parameter is proportional to the minus of the variation of the scale factor, δ ω{sub g}(t) = −Cδ a(t). We obtain neutral stability against the vector perturbations, and the stability against the tensor perturbations is guaranteed due to the positivity of the spatial curvature of the Einstein static universe in induced matter brane gravity.

- Authors:

- Department of Physics, Azarbaijan Shahid Madani University, 35 Km Tabriz-Maraghe Road, 53714-161, Tabriz (Iran, Islamic Republic of)

- Publication Date:

- OSTI Identifier:
- 22525884

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 04; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; BRANES; DISTURBANCES; EINSTEIN FIELD EQUATIONS; EQUATIONS OF STATE; GENERAL RELATIVITY THEORY; GRAVITATION; SCALARS; TIME DEPENDENCE; UNIVERSE; VARIATIONS; VECTORS

### Citation Formats

```
Heydarzade, Y., and Darabi, F., E-mail: heydarzade@azaruniv.edu, E-mail: f.darabi@azaruniv.edu.
```*Induced matter brane gravity and Einstein static universe*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/04/028.

```
Heydarzade, Y., & Darabi, F., E-mail: heydarzade@azaruniv.edu, E-mail: f.darabi@azaruniv.edu.
```*Induced matter brane gravity and Einstein static universe*. United States. doi:10.1088/1475-7516/2015/04/028.

```
Heydarzade, Y., and Darabi, F., E-mail: heydarzade@azaruniv.edu, E-mail: f.darabi@azaruniv.edu. Wed .
"Induced matter brane gravity and Einstein static universe". United States.
doi:10.1088/1475-7516/2015/04/028.
```

```
@article{osti_22525884,
```

title = {Induced matter brane gravity and Einstein static universe},

author = {Heydarzade, Y. and Darabi, F., E-mail: heydarzade@azaruniv.edu, E-mail: f.darabi@azaruniv.edu},

abstractNote = {We investigate stability of the Einstein static universe against the scalar, vector and tensor perturbations in the context of induced matter brane gravity. It is shown that in the framework of this model, the Einstein static universe has a positive spatial curvature. In contrast to the classical general relativity, it is found that a stable Einstein static universe against the scalar perturbations does exist provided that the variation of time dependent geometrical equation of state parameter is proportional to the minus of the variation of the scale factor, δ ω{sub g}(t) = −Cδ a(t). We obtain neutral stability against the vector perturbations, and the stability against the tensor perturbations is guaranteed due to the positivity of the spatial curvature of the Einstein static universe in induced matter brane gravity.},

doi = {10.1088/1475-7516/2015/04/028},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 04,

volume = 2015,

place = {United States},

year = {Wed Apr 01 00:00:00 EDT 2015},

month = {Wed Apr 01 00:00:00 EDT 2015}

}