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

Title: On the initial state and consistency relations

Abstract

We study the effect of the initial state on the consistency conditions for adiabatic perturbations. In order to be consistent with the constraints of General Relativity, the initial state must be diffeomorphism invariant. As a result, we show that initial wavefunctional/density matrix has to satisfy a Slavnov-Taylor identity similar to that of the action. We then investigate the precise ways in which modified initial states can lead to violations of the consistency relations. We find two independent sources of violations: i) the state can include initial non-Gaussianities; ii) even if the initial state is Gaussian, such as a Bogoliubov state, the modified 2-point function can modify the q-vector → 0 analyticity properties of the vertex functional and result in violations of the consistency relations.

Authors:
;  [1]
  1. Center for Particle Cosmology, Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104 (United States)
Publication Date:
OSTI Identifier:
22375890
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; DENSITY MATRIX; FUNCTIONS; GENERAL RELATIVITY THEORY; VECTORS

Citation Formats

Berezhiani, Lasha, and Khoury, Justin, E-mail: lashaber@sas.upenn.edu, E-mail: jkhoury@sas.upenn.edu. On the initial state and consistency relations. United States: N. p., 2014. Web. doi:10.1088/1475-7516/2014/09/018.
Berezhiani, Lasha, & Khoury, Justin, E-mail: lashaber@sas.upenn.edu, E-mail: jkhoury@sas.upenn.edu. On the initial state and consistency relations. United States. doi:10.1088/1475-7516/2014/09/018.
Berezhiani, Lasha, and Khoury, Justin, E-mail: lashaber@sas.upenn.edu, E-mail: jkhoury@sas.upenn.edu. Mon . "On the initial state and consistency relations". United States. doi:10.1088/1475-7516/2014/09/018.
@article{osti_22375890,
title = {On the initial state and consistency relations},
author = {Berezhiani, Lasha and Khoury, Justin, E-mail: lashaber@sas.upenn.edu, E-mail: jkhoury@sas.upenn.edu},
abstractNote = {We study the effect of the initial state on the consistency conditions for adiabatic perturbations. In order to be consistent with the constraints of General Relativity, the initial state must be diffeomorphism invariant. As a result, we show that initial wavefunctional/density matrix has to satisfy a Slavnov-Taylor identity similar to that of the action. We then investigate the precise ways in which modified initial states can lead to violations of the consistency relations. We find two independent sources of violations: i) the state can include initial non-Gaussianities; ii) even if the initial state is Gaussian, such as a Bogoliubov state, the modified 2-point function can modify the q-vector → 0 analyticity properties of the vertex functional and result in violations of the consistency relations.},
doi = {10.1088/1475-7516/2014/09/018},
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}
}
  • We explore the consistency relations for the three-point functions, in the squeezed limit, of scalar and tensor perturbations in single-field inflation with general initial conditions for the perturbations. For slow-roll inflation, we find that all the three-point functions of scalar and tensor perturbations with a coherent state as the initial state are identical to the three-point functions with the Bunch-Davies initial state. On the other hand, there is an apparent violation of some of the consistency relations for initial states that are related to the Bunch-Davies state by Bogoliubov transformations and we identify the reason for this violation. The back-reactionmore » calculations indicate that the three-point functions for these states can be large enough to violate the consistency relations, however, they are too small to be observed in the near future.« less
  • We discuss conserved currents and operator product expansions (OPE{close_quote}s) in the context of a {ital O}({ital N}) invariant conformal field theory. Using OPE{close_quote}s we find explicit expressions for the first few terms in suitable short-distance limits for various four-point functions involving the fundamental {ital N}-component scalar field {phi}{sup {alpha}}({ital N}), {alpha}=1,2,...,{ital N}. We propose an alternative evaluation of these four-point functions based on graphical expansions. Requiring consistency of the algebraic and graphical treatments of the four-point functions we obtain the values of the dynamical parameters in either a free theory of {ital N} massless fields or a non-trivial conformally invariantmore » {ital O}({ital N}) vector model in 2{lt}{ital d}{lt}4, up to next-to-leading order in a 1/{ital N} expansion. Our approach suggests an interesting duality property of the critical {ital O}({ital N}) invariant theory. Also, solving our consistency relations we obtain the next-to-leading order in 1/{ital N} correction for {ital C}{sub {ital T}} which corresponds to the normalization of the energy momentum tensor two-point function. Copyright {copyright} 1996 Academic Press, Inc.« less
  • The authors use both old and new theoretical developments in QCD dispersion relation constraints on the scalar form factor in the decay K {r_arrow} {pi}l{nu}{sub l} to obtain constraints on the strange quark mass. The perturbative QCD side of the calculation incorporates up to four-loop corrections, while the hadronic side uses a recently developed parameterization constructed explicitly to satisfy the dispersive constraints. Using chiral perturbation theory ({chi}PT) as a model for soon-to-be measured data, they find a series of lower bounds on m{sub s} increasing with the accuracy to which one believes {chi}PT to represent the full QCD result.