skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Evolution of the spectral index after inflation

Abstract

In this article we investigate the time evolution of the adiabatic (curvature) and isocurvature (entropy) spectral indices after inflation era for all cosmological scales with two different initial conditions. For this purpose, we first extract an explicit equation for the time evolution of the comoving curvature perturbation (which may be known as the generalized Mukhanov-Sasaki equation). It would be cleared that the evolution of adiabatic spectral index severely depends on the initial conditions moreover, as expected it is constant only for the super-Hubble scales and adiabatic initial conditions. Additionally, the adiabatic spectral index after recombination approaches a constant value for the isocurvature perturbations. Finally, we re-investigate the Sachs-Wolfe effect and show that the fudge factor  1/3 in the adiabatic ordinary Sachs-Wolfe formula must be replaced by 0.4.

Authors:
;  [1]
  1. Department of Physics, School of Sciences, Tarbiat Modares University, P.O.Box 14155-4838, Tehran (Iran, Islamic Republic of)
Publication Date:
OSTI Identifier:
22375867
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2014; Journal Issue: 09; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMOLOGICAL INFLATION; DATA; ENTROPY; EQUATIONS; EVOLUTION; PERTURBATION THEORY

Citation Formats

Asgari, A.A., and Abbassi, A.H., E-mail: aliakbar.asgari@modares.ac.ir, E-mail: ahabbasi@modares.ac.ir. Evolution of the spectral index after inflation. United States: N. p., 2014. Web. doi:10.1088/1475-7516/2014/09/042.
Asgari, A.A., & Abbassi, A.H., E-mail: aliakbar.asgari@modares.ac.ir, E-mail: ahabbasi@modares.ac.ir. Evolution of the spectral index after inflation. United States. doi:10.1088/1475-7516/2014/09/042.
Asgari, A.A., and Abbassi, A.H., E-mail: aliakbar.asgari@modares.ac.ir, E-mail: ahabbasi@modares.ac.ir. Mon . "Evolution of the spectral index after inflation". United States. doi:10.1088/1475-7516/2014/09/042.
@article{osti_22375867,
title = {Evolution of the spectral index after inflation},
author = {Asgari, A.A. and Abbassi, A.H., E-mail: aliakbar.asgari@modares.ac.ir, E-mail: ahabbasi@modares.ac.ir},
abstractNote = {In this article we investigate the time evolution of the adiabatic (curvature) and isocurvature (entropy) spectral indices after inflation era for all cosmological scales with two different initial conditions. For this purpose, we first extract an explicit equation for the time evolution of the comoving curvature perturbation (which may be known as the generalized Mukhanov-Sasaki equation). It would be cleared that the evolution of adiabatic spectral index severely depends on the initial conditions moreover, as expected it is constant only for the super-Hubble scales and adiabatic initial conditions. Additionally, the adiabatic spectral index after recombination approaches a constant value for the isocurvature perturbations. Finally, we re-investigate the Sachs-Wolfe effect and show that the fudge factor  1/3 in the adiabatic ordinary Sachs-Wolfe formula must be replaced by 0.4.},
doi = {10.1088/1475-7516/2014/09/042},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 09,
volume = 2014,
place = {United States},
year = {Mon Sep 01 00:00:00 EDT 2014},
month = {Mon Sep 01 00:00:00 EDT 2014}
}
  • Supergravity corrections due to the energy density of a right-handed sneutrino can generate a negative mass squared for the inflaton, flattening the inflaton potential and reducing the spectral index and inflaton energy density. For the case of D-term hybrid inflation, we show that the spectral index can be lowered from the conventional value n=0.98 to a value within the range favored by the latest WMAP analysis, n=0.951{sub -0.019}{sup +0.015}. The modified energy density is consistent with nonobservation of cosmic strings in the CMB if n<0.946. The WMAP lower bound on the spectral index implies that the D-term cosmic string contributionmore » may be very close present CMB limits, contributing at least 5% to the CMB multipoles.« less
  • We study the single field slow-roll inflation models that better agree with the available CMB and LSS data including the three years WMAP data: new inflation and hybrid inflation. We study these models as effective field theories in the Ginsburg-Landau context: a trinomial potential turns out to be a simple and well motivated model. The spectral index n{sub s} of the adiabatic fluctuations, the ratio r of tensor to scalar fluctuations and the running index dn{sub s}/dlnk are studied in detail. We derive explicit formulas for n{sub s}, r and dn{sub s}/dlnk and provide relevant plots. In new inflation, andmore » for the chosen central value n{sub s}=0.95, we predict 0.03<r<0.04 and -0.000 70<dn{sub s}/dlnk<-0.000 55. In hybrid inflation, and for n{sub s}=0.95, we predict r{approx_equal}0.2 and dn{sub s}/dlnk{approx_equal}-0.001. Interestingly enough, we find that in new inflation n{sub s} is bounded from above by n{sub smax}=0.961 528... and that r is a two valued function of n{sub s} in the interval 0.96<n{sub s}<n{sub smax}. In the first branch we find r<r{sub max}=0.114 769.... In hybrid inflation we find a critical value {mu}{sub 0crit}{sup 2} for the mass parameter {mu}{sub 0}{sup 2} of the field {sigma} coupled to the inflaton. For {mu}{sub 0}{sup 2}<{lambda}{sub 0}M{sub Pl}{sup 2}/192, where {lambda}{sub 0} is the cosmological constant, hybrid inflation yields a blue tilted n{sub s}>1 behavior. Hybrid inflation for {mu}{sub 0}{sup 2}>{lambda}{sub 0}M{sub Pl}{sup 2}/192 fulfills all the present CMB+LSS data for a large enough initial inflaton amplitude. Even if chaotic inflation predicts n{sub s} values compatible with the data, chaotic inflation is disfavored since it predicts a too high value r{approx_equal}0.27 for the ratio of tensor to scalar fluctuations. The model which best agrees with the current data and which best prepares the way to the expected data r(less-or-similar sign)0.1, is the trinomial potential with negative mass term: new inflation.« less
  • We conjecture that the inflation models with trans-Planckian excursions in the field space should be in the swampland. We check this conjecture in a few examples and investigate the constraints on the spectral index for the slow-roll inflation model in the string landscape where the variation of the inflaton during the period of inflation is less than the Planck scale M{sub p}. A red primordial power spectrum with a lower bound on the spectral index is preferred. Both the tensor-scalar ratio and the running can be ignored.
  • We quantify the slow-roll corrections to primordial density perturbations arising from inflation driven by a four-dimensional scalar field with a monomial potential in a five-dimensional noncompact bulk space-time. Although the difference between the classical brane-world solutions and standard four-dimensional solutions is large at early times, the change to the amplitude at late times of perturbations generated from quantum fluctuations is first order in slow-roll parameters, leading to second-order slow-roll corrections to the spectral index. This confirms that the leading-order effects are correctly given by previous work in the literature.
  • Supernatural inflation is an attractive model based on just a flat direction with soft supersymmetry breaking mass terms in the framework of supersymmetry. The beauty of the model is that it needs no fine-tuning. However, the prediction of the spectral index is n{sub s} > or approx. 1, in contrast to experimental data. In this paper, we discuss supernatural inflation with the spectral index reduced to n{sub s}=0.96 without any fine-tuning, considering the general feature that a flat direction is lifted by a nonrenormalizable term with an A-term.