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 nonsingular Kasner solution that quickly evolves into an isotropic de Sitter space, the socalled Kasnerde 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 Kasnerde 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,KitashirakawaOiwakecho, SakyoKu, Kyoto 6068502 (Japan)
 (Portugal)
 Publication Date:
 Sponsoring Org.:
 SCOAP3, CERN, Geneva (Switzerland)
 OSTI Identifier:
 22454559
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 06; Other Information: PUBLISHERID: 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)
 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; SPACETIME; TUNNEL EFFECT; UNIVERSE; VACUUM STATES
Citation Formats
BlancoPillado, 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, 1049001 Lisboa. The Initial State of a Primordial Anisotropic Stage of Inflation. United States: N. p., 2015.
Web. doi:10.1088/14757516/2015/06/024.
BlancoPillado, 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, 1049001 Lisboa. The Initial State of a Primordial Anisotropic Stage of Inflation. United States. doi:10.1088/14757516/2015/06/024.
BlancoPillado, 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, 1049001 Lisboa. 2015.
"The Initial State of a Primordial Anisotropic Stage of Inflation". United States.
doi:10.1088/14757516/2015/06/024.
@article{osti_22454559,
title = {The Initial State of a Primordial Anisotropic Stage of Inflation},
author = {BlancoPillado, 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, 1049001 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 nonsingular Kasner solution that quickly evolves into an isotropic de Sitter space, the socalled Kasnerde 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 Kasnerde 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 = {10.1088/14757516/2015/06/024},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 06,
volume = 2015,
place = {United States},
year = 2015,
month = 6
}

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 nonsingular Kasner solution that quickly evolves into an isotropic de Sitter space, the socalled Kasnerde 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 havemore »

Primordial power spectra from anisotropic inflation
We examine cosmological perturbations in a dynamical theory of inflation in which an Abelian gauge field couples directly to the inflaton, breaking conformal invariance. When the coupling between the gauge field and the inflaton takes a specific form, inflation becomes anisotropic and anisotropy can persist throughout inflation, avoiding Wald's nohair theorem. After discussing scenarios in which anisotropy can persist during inflation, we calculate the dominant effects of a small persistent anisotropy on the primordial gravitational wave and curvature perturbation power spectra using the ''inin'' formalism of perturbation theory. We find that the primordial power spectra of cosmological perturbations gain significantmore » 
Clustering fossil from primordial gravitational waves in anisotropic inflation
Inflationary models can correlate smallscale density perturbations with the longwavelength gravitational waves (GW) in the form of the TensorScalarScalar (TSS) bispectrum. This correlation affects the massdistribution in the Universe and leads to the offdiagonal correlations of the density field modes in the form of the quadrupole anisotropy. Interestingly, this effect survives even after the tensor mode decays when it reenters the horizon, known as the fossil effect. As a result, the offdiagonal correlation function between different Fourier modes of the density fluctuations can be thought as a way to probe the largescale GW and the mechanism of inflation behind themore » 
Fresh inflation: A warm inflationary model from a zero temperature initial state
A twocomponent mixture fluid which complies with the gamma law is considered in the framework of inflation with finite temperature. The model is developed for a quartic scalar potential without symmetry breaking. The radiation energy density is assumed to be zero when inflation starts and remains below the grand unified theory (GUT) temperature during the inflationary stage. Furthermore, it provides the necessary number of e folds and sufficient radiation energy density so GUT baryogenesis can take place near the minimum energetic configuration. 
Short distance and initial state effects in inflation: Stress tensor and decoherence
We present a consistent low energy effective field theory framework for parametrizing the effects of novel short distance physics in inflation, and their possible observational signatures in the cosmic microwave background. We consider the class of general homogeneous, isotropic initial states for quantum scalar fields in RobertsonWalker (RW) spacetimes, subject to the requirement that their ultraviolet behavior be consistent with renormalizability of the covariantly conserved stress tensor which couples to gravity. In the functional Schroedinger picture such states are coherent, squeezed, mixed states characterized by a Gaussian density matrix. This Gaussian has parameters which approach those of the adiabatic vacuummore »