# Dynamics of Robertson–Walker spacetimes with diffusion

## Abstract

We study the dynamics of spatially homogeneous and isotropic spacetimes containing a fluid undergoing microscopic velocity diffusion in a cosmological scalar field. After deriving a few exact solutions of the equations, we continue by analyzing the qualitative behavior of general solutions. To this purpose we recast the equations in the form of a two dimensional dynamical system and perform a global analysis of the flow. Among the admissible behaviors, we find solutions that are asymptotically de-Sitter both in the past and future time directions and which undergo accelerated expansion at all times.

- Authors:

- Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Instituto Superior Técnico, Lisboa (Portugal)
- Department of Mathematical Sciences, Chalmers University of Technology, University of Gothenburg, Gothenburg (Sweden)
- Departamento de Matemática e Aplicações, Universidade do Minho, Guimarães (Portugal)
- Centro de Matemática, Universidade do Minho, Braga (Portugal)

- Publication Date:

- OSTI Identifier:
- 22447614

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 354; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMOLOGY; DE SITTER GROUP; DIFFUSION; EXACT SOLUTIONS; SCALAR FIELDS; SPACE-TIME; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Alho, A., E-mail: aalho@math.ist.utl.pt, Calogero, S., E-mail: calogero@chalmers.se, Machado Ramos, M.P., E-mail: mpr@mct.uminho.pt, and Soares, A.J., E-mail: ajsoares@math.uminho.pt.
```*Dynamics of Robertson–Walker spacetimes with diffusion*. United States: N. p., 2015.
Web. doi:10.1016/J.AOP.2015.01.010.

```
Alho, A., E-mail: aalho@math.ist.utl.pt, Calogero, S., E-mail: calogero@chalmers.se, Machado Ramos, M.P., E-mail: mpr@mct.uminho.pt, & Soares, A.J., E-mail: ajsoares@math.uminho.pt.
```*Dynamics of Robertson–Walker spacetimes with diffusion*. United States. doi:10.1016/J.AOP.2015.01.010.

```
Alho, A., E-mail: aalho@math.ist.utl.pt, Calogero, S., E-mail: calogero@chalmers.se, Machado Ramos, M.P., E-mail: mpr@mct.uminho.pt, and Soares, A.J., E-mail: ajsoares@math.uminho.pt. Sun .
"Dynamics of Robertson–Walker spacetimes with diffusion". United States.
doi:10.1016/J.AOP.2015.01.010.
```

```
@article{osti_22447614,
```

title = {Dynamics of Robertson–Walker spacetimes with diffusion},

author = {Alho, A., E-mail: aalho@math.ist.utl.pt and Calogero, S., E-mail: calogero@chalmers.se and Machado Ramos, M.P., E-mail: mpr@mct.uminho.pt and Soares, A.J., E-mail: ajsoares@math.uminho.pt},

abstractNote = {We study the dynamics of spatially homogeneous and isotropic spacetimes containing a fluid undergoing microscopic velocity diffusion in a cosmological scalar field. After deriving a few exact solutions of the equations, we continue by analyzing the qualitative behavior of general solutions. To this purpose we recast the equations in the form of a two dimensional dynamical system and perform a global analysis of the flow. Among the admissible behaviors, we find solutions that are asymptotically de-Sitter both in the past and future time directions and which undergo accelerated expansion at all times.},

doi = {10.1016/J.AOP.2015.01.010},

journal = {Annals of Physics},

number = ,

volume = 354,

place = {United States},

year = {Sun Mar 15 00:00:00 EDT 2015},

month = {Sun Mar 15 00:00:00 EDT 2015}

}

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