# The Initial State of a Primordial Anisotropic Stage of Inflation

## Abstract

We investigate the possibility that the inflationary period in the early universe was preceded by a primordial stage of strong anisotropy. In particular we focus on the simplest model of this kind, where the spacetime is described by a non-singular Kasner solution that quickly evolves into an isotropic de Sitter space, the so-called Kasner-de Sitter solution. The initial Big Bang singularity is replaced, in this case, by a horizon. We show that the extension of this metric to the region behind the horizon contains a timelike singularity which will be visible by cosmological observers. This makes it impossible to have a reliable prediction of the quantum state of the cosmological perturbations in the region of interest. In this paper we consider the possibility that this Kasner-de Sitter universe is obtained as a result of a quantum tunneling process effectively substituting the region behind the horizon by an anisotropic parent vacuum state, namely a 1+1 dimensional spacetime compactified over an internal flat torus, T{sub 2}, which we take it to be of the form de Sitter{sub 2}×T{sub 2} or Minkowski{sub 2}×T{sub 2}. As a first approximation to understand the effects of this anisotropic initial state, we compute the power spectrum ofmore »

- Authors:

- Department of Theoretical Physics, University of the Basque Country UPV/EHU,48080 Bilbao (Spain)
- (Spain)
- Yukawa Institute for Theoretical Physics, Kyoto University,Kitashirakawa-Oiwakecho, Sakyo-Ku, Kyoto 606-8502 (Japan)
- (Portugal)

- Publication Date:

- Sponsoring Org.:
- SCOAP3, CERN, Geneva (Switzerland)

- OSTI Identifier:
- 22454559

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2015; Journal Issue: 06; Other Information: PUBLISHER-ID: JCAP06(2015)024; OAI: oai:repo.scoap3.org:10790; Article funded by SCOAP3. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANISOTROPY; COSMOLOGICAL INFLATION; DE SITTER GROUP; DE SITTER SPACE; MINKOWSKI SPACE; PERTURBATION THEORY; QUANTUM STATES; RELICT RADIATION; SCALAR FIELDS; SINGULARITY; SPACE-TIME; TUNNEL EFFECT; UNIVERSE; VACUUM STATES

### Citation Formats

```
Blanco-Pillado, Jose J., IKERBASQUE, Basque Foundation for Science,Maria Diaz de Haro 3, 48013 Bilbao, Minamitsuji, Masato, and CENTRA, Instituto Superior Tecnico, Universidade de Lisboa,Avenida Rovisco Pais 1, 1049-001 Lisboa.
```*The Initial State of a Primordial Anisotropic Stage of Inflation*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/06/024.

```
Blanco-Pillado, Jose J., IKERBASQUE, Basque Foundation for Science,Maria Diaz de Haro 3, 48013 Bilbao, Minamitsuji, Masato, & CENTRA, Instituto Superior Tecnico, Universidade de Lisboa,Avenida Rovisco Pais 1, 1049-001 Lisboa.
```*The Initial State of a Primordial Anisotropic Stage of Inflation*. United States. doi:10.1088/1475-7516/2015/06/024.

```
Blanco-Pillado, Jose J., IKERBASQUE, Basque Foundation for Science,Maria Diaz de Haro 3, 48013 Bilbao, Minamitsuji, Masato, and CENTRA, Instituto Superior Tecnico, Universidade de Lisboa,Avenida Rovisco Pais 1, 1049-001 Lisboa. Fri .
"The Initial State of a Primordial Anisotropic Stage of Inflation". United States. doi:10.1088/1475-7516/2015/06/024.
```

```
@article{osti_22454559,
```

title = {The Initial State of a Primordial Anisotropic Stage of Inflation},

author = {Blanco-Pillado, Jose J. and IKERBASQUE, Basque Foundation for Science,Maria Diaz de Haro 3, 48013 Bilbao and Minamitsuji, Masato and CENTRA, Instituto Superior Tecnico, Universidade de Lisboa,Avenida Rovisco Pais 1, 1049-001 Lisboa},

abstractNote = {We investigate the possibility that the inflationary period in the early universe was preceded by a primordial stage of strong anisotropy. In particular we focus on the simplest model of this kind, where the spacetime is described by a non-singular Kasner solution that quickly evolves into an isotropic de Sitter space, the so-called Kasner-de Sitter solution. The initial Big Bang singularity is replaced, in this case, by a horizon. We show that the extension of this metric to the region behind the horizon contains a timelike singularity which will be visible by cosmological observers. This makes it impossible to have a reliable prediction of the quantum state of the cosmological perturbations in the region of interest. In this paper we consider the possibility that this Kasner-de Sitter universe is obtained as a result of a quantum tunneling process effectively substituting the region behind the horizon by an anisotropic parent vacuum state, namely a 1+1 dimensional spacetime compactified over an internal flat torus, T{sub 2}, which we take it to be of the form de Sitter{sub 2}×T{sub 2} or Minkowski{sub 2}×T{sub 2}. As a first approximation to understand the effects of this anisotropic initial state, we compute the power spectrum of a massless scalar field in these backgrounds. In both cases, the spectrum converges at small scales to the isotropic scale invariant form and only present important deviations from it at the largest possible scales. We find that the decompactification scenario from M{sub 2}×T{sub 2} leads to a suppressed and slightly anisotropic power spectrum at large scales which could be related to some of the anomalies present in the current CMB data. On the other hand, the spectrum of the universe with a dS{sub 2}×T{sub 2} parent vacuum presents an enhancement in power at large scales not consistent with observations.},

doi = {10.1088/1475-7516/2015/06/024},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 06,

volume = 2015,

place = {United States},

year = {2015},

month = {6}

}