# Scalar field cosmologies with inverted potentials

## Abstract

Regular bouncing solutions in the framework of a scalar-tensor gravity model were found in a recent work. We reconsider the problem in the Einstein frame (EF) in the present work. Singularities arising at the limit of physical viability of the model in the Jordan frame (JF) are either of the Big Bang or of the Big Crunch type in the EF. As a result we obtain integrable scalar field cosmological models in general relativity (GR) with inverted double-well potentials unbounded from below which possess solutions regular in the future, tending to a de Sitter space, and starting with a Big Bang. The existence of the two fixed points for the field dynamics at late times found earlier in the JF becomes transparent in the EF.

- Authors:

- Université de Tours, Laboratoire de Mathématiques et Physique Théorique, CNRS/UMR 7350, 37200 Tours (France)
- Université Montpellier and CNRS, Laboratoire Charles Coulomb, UMR 5221, F-34095 Montpellier (France)

- Publication Date:

- OSTI Identifier:
- 22525245

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2015; Journal Issue: 10; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMOLOGICAL MODELS; COSMOLOGY; DE SITTER SPACE; GENERAL RELATIVITY THEORY; GRAVITATION; INTEGRAL CALCULUS; MATHEMATICAL SOLUTIONS; POTENTIALS; SCALAR FIELDS; SCALARS; SINGULARITY; TENSORS

### Citation Formats

```
Boisseau, B., Giacomini, H., and Polarski, D., E-mail: bruno.boisseau@lmpt.univ-tours.fr, E-mail: hector.giacomini@lmpt.univ-tours.fr, E-mail: david.polarski@umontpellier.fr.
```*Scalar field cosmologies with inverted potentials*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/10/033.

```
Boisseau, B., Giacomini, H., & Polarski, D., E-mail: bruno.boisseau@lmpt.univ-tours.fr, E-mail: hector.giacomini@lmpt.univ-tours.fr, E-mail: david.polarski@umontpellier.fr.
```*Scalar field cosmologies with inverted potentials*. United States. doi:10.1088/1475-7516/2015/10/033.

```
Boisseau, B., Giacomini, H., and Polarski, D., E-mail: bruno.boisseau@lmpt.univ-tours.fr, E-mail: hector.giacomini@lmpt.univ-tours.fr, E-mail: david.polarski@umontpellier.fr. Thu .
"Scalar field cosmologies with inverted potentials". United States. doi:10.1088/1475-7516/2015/10/033.
```

```
@article{osti_22525245,
```

title = {Scalar field cosmologies with inverted potentials},

author = {Boisseau, B. and Giacomini, H. and Polarski, D., E-mail: bruno.boisseau@lmpt.univ-tours.fr, E-mail: hector.giacomini@lmpt.univ-tours.fr, E-mail: david.polarski@umontpellier.fr},

abstractNote = {Regular bouncing solutions in the framework of a scalar-tensor gravity model were found in a recent work. We reconsider the problem in the Einstein frame (EF) in the present work. Singularities arising at the limit of physical viability of the model in the Jordan frame (JF) are either of the Big Bang or of the Big Crunch type in the EF. As a result we obtain integrable scalar field cosmological models in general relativity (GR) with inverted double-well potentials unbounded from below which possess solutions regular in the future, tending to a de Sitter space, and starting with a Big Bang. The existence of the two fixed points for the field dynamics at late times found earlier in the JF becomes transparent in the EF.},

doi = {10.1088/1475-7516/2015/10/033},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 10,

volume = 2015,

place = {United States},

year = {2015},

month = {10}

}

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