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Title: 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 » 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.« less

Authors:
 [1];  [2];  [3];  [4]
  1. Department of Theoretical Physics, University of the Basque Country UPV/EHU,48080 Bilbao (Spain)
  2. (Spain)
  3. Yukawa Institute for Theoretical Physics, Kyoto University,Kitashirakawa-Oiwakecho, Sakyo-Ku, Kyoto 606-8502 (Japan)
  4. (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: 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)
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},
number = 06,
volume = 2015,
place = {United States},
year = {Fri Jun 12 00:00:00 EDT 2015},
month = {Fri Jun 12 00:00:00 EDT 2015}
}
  • 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 havemore » 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.« less
  • 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 no-hair 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 ''in-in'' formalism of perturbation theory. We find that the primordial power spectra of cosmological perturbations gain significantmore » direction dependence and that the fractional direction dependence of the tensor power spectrum is suppressed in comparison to that of the scalar power spectrum.« less
  • Inflationary models can correlate small-scale density perturbations with the long-wavelength gravitational waves (GW) in the form of the Tensor-Scalar-Scalar (TSS) bispectrum. This correlation affects the mass-distribution in the Universe and leads to the off-diagonal 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 re-enters the horizon, known as the fossil effect. As a result, the off-diagonal correlation function between different Fourier modes of the density fluctuations can be thought as a way to probe the large-scale GW and the mechanism of inflation behind themore » fossil effect. Models of single field slow roll inflation generically predict a very small quadrupole anisotropy in TSS while in models of multiple fields inflation this effect can be observable. Therefore this large scale quadrupole anisotropy can be thought as a spectroscopy for different inflationary models. In addition, in models of anisotropic inflation there exists quadrupole anisotropy in curvature perturbation power spectrum. Here we consider TSS in models of anisotropic inflation and show that the shape of quadrupole anisotropy is different than in single field models. In fact, in these models, quadrupole anisotropy is projected into the preferred direction and its amplitude is proportional to g{sub *} N{sub e} where N{sub e} is the number of e-folds and g{sub *} is the amplitude of quadrupole anisotropy in curvature perturbation power spectrum. We use this correlation function to estimate the large scale GW as well as the preferred direction and discuss the detectability of the signal in the galaxy surveys like Euclid and 21 cm surveys.« less
  • A two-component 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.
  • 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 Robertson-Walker (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 » at large wave number, and evolve in time according to an effective classical Hamiltonian. The one complex parameter family of {alpha} squeezed states in de Sitter spacetime does not fall into this UV allowed class, except for the special value of the parameter corresponding to the Bunch-Davies state. We determine the finite contributions to the inflationary power spectrum and stress tensor expectation value of general UV allowed adiabatic states, and obtain quantitative limits on the observability and backreaction effects of some recently proposed models of short distance modifications of the initial state of inflation. For all UV allowed states, the second order adiabatic basis provides a good description of particles created in the expanding RW universe. Because of the absence of particle creation for the massless, minimally coupled scalar field in de Sitter space, there is no phase decoherence in the simplest free field inflationary models. We apply adiabatic regularization to the renormalization of the decoherence functional in cosmology to corroborate this result.« less