# Cosmic infinity: a dynamical system approach

## Abstract

Dynamical system techniques are extremely useful to study cosmology. It turns out that in most of the cases, we deal with finite isolated fixed points corresponding to a given cosmological epoch. However, it is equally important to analyse the asymptotic behaviour of the universe. On this paper, we show how this can be carried out for 3-form models. In fact, we show that there are fixed points at infinity mainly by introducing appropriate compactifications and defining a new time variable that washes away any potential divergence of the system. The richness of 3-form models allows us as well to identify normally hyperbolic non-isolated fixed points. We apply this analysis to three physically interesting situations: (i) a pre-inflationary era; (ii) an inflationary era; (iii) the late-time dark matter/dark energy epoch.

- Authors:

- Departamento de Física, Universidade da Beira Interior, Rua Marquês D'Ávila e Bolama, 6201-001 Covilhã (Portugal)
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, 48080 Bilbao (Spain)
- Centro de Matemática e Aplicações da Universidade da Beira Interior (CMA-UBI), Rua Marquês D'Ávila e Bolama, 6201-001 Covilhã (Portugal)

- Publication Date:

- OSTI Identifier:
- 22679962

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; 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; ASYMPTOTIC SOLUTIONS; COMPACTIFICATION; COSMOLOGY; INFLATIONARY UNIVERSE; NONLUMINOUS MATTER; UNIVERSE

### Citation Formats

```
Bouhmadi-López, Mariam, Marto, João, Morais, João, and Silva, César M., E-mail: mbl@ubi.pt, E-mail: jmarto@ubi.pt, E-mail: jviegas001@ikasle.ehu.eus, E-mail: csilva@ubi.pt.
```*Cosmic infinity: a dynamical system approach*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/03/042.

```
Bouhmadi-López, Mariam, Marto, João, Morais, João, & Silva, César M., E-mail: mbl@ubi.pt, E-mail: jmarto@ubi.pt, E-mail: jviegas001@ikasle.ehu.eus, E-mail: csilva@ubi.pt.
```*Cosmic infinity: a dynamical system approach*. United States. doi:10.1088/1475-7516/2017/03/042.

```
Bouhmadi-López, Mariam, Marto, João, Morais, João, and Silva, César M., E-mail: mbl@ubi.pt, E-mail: jmarto@ubi.pt, E-mail: jviegas001@ikasle.ehu.eus, E-mail: csilva@ubi.pt. Wed .
"Cosmic infinity: a dynamical system approach". United States.
doi:10.1088/1475-7516/2017/03/042.
```

```
@article{osti_22679962,
```

title = {Cosmic infinity: a dynamical system approach},

author = {Bouhmadi-López, Mariam and Marto, João and Morais, João and Silva, César M., E-mail: mbl@ubi.pt, E-mail: jmarto@ubi.pt, E-mail: jviegas001@ikasle.ehu.eus, E-mail: csilva@ubi.pt},

abstractNote = {Dynamical system techniques are extremely useful to study cosmology. It turns out that in most of the cases, we deal with finite isolated fixed points corresponding to a given cosmological epoch. However, it is equally important to analyse the asymptotic behaviour of the universe. On this paper, we show how this can be carried out for 3-form models. In fact, we show that there are fixed points at infinity mainly by introducing appropriate compactifications and defining a new time variable that washes away any potential divergence of the system. The richness of 3-form models allows us as well to identify normally hyperbolic non-isolated fixed points. We apply this analysis to three physically interesting situations: (i) a pre-inflationary era; (ii) an inflationary era; (iii) the late-time dark matter/dark energy epoch.},

doi = {10.1088/1475-7516/2017/03/042},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 03,

volume = 2017,

place = {United States},

year = {Wed Mar 01 00:00:00 EST 2017},

month = {Wed Mar 01 00:00:00 EST 2017}

}