Twopoint correlators revisited: fast and slow scales in multifield models of inflation
Abstract
We study the structure of twopoint correlators of the inflationary field fluctuations in order to improve the accuracy and efficiency of the existing methods to calculate primordial spectra. We present a description motivated by the separation of the fast and slow evolving components of the spectrum which is based on Cholesky decomposition of the field correlator matrix. Our purpose is to rewrite all the relevant equations of motion in terms of slowly varying quantities. This is important in order to consider the contribution from highfrequency modes to the spectrum without affecting computational performance. The slowroll approximation is not required to reproduce the main distinctive features in the power spectrum for each specific model of inflation.
 Authors:
 Department of Physics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia V5A 1S6 (Canada)
 Publication Date:
 OSTI Identifier:
 22676193
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 05; Other Information: Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACCURACY; APPROXIMATIONS; COMPUTERIZED SIMULATION; DECOMPOSITION; EFFICIENCY; EQUATIONS OF MOTION; FLUCTUATIONS; INFLATIONARY UNIVERSE; SPECTRA
Citation Formats
Ghersi, José T. Gálvez, and Frolov, Andrei V., Email: joseg@sfu.ca, Email: frolov@sfu.ca. Twopoint correlators revisited: fast and slow scales in multifield models of inflation. United States: N. p., 2017.
Web. doi:10.1088/14757516/2017/05/047.
Ghersi, José T. Gálvez, & Frolov, Andrei V., Email: joseg@sfu.ca, Email: frolov@sfu.ca. Twopoint correlators revisited: fast and slow scales in multifield models of inflation. United States. doi:10.1088/14757516/2017/05/047.
Ghersi, José T. Gálvez, and Frolov, Andrei V., Email: joseg@sfu.ca, Email: frolov@sfu.ca. Mon .
"Twopoint correlators revisited: fast and slow scales in multifield models of inflation". United States.
doi:10.1088/14757516/2017/05/047.
@article{osti_22676193,
title = {Twopoint correlators revisited: fast and slow scales in multifield models of inflation},
author = {Ghersi, José T. Gálvez and Frolov, Andrei V., Email: joseg@sfu.ca, Email: frolov@sfu.ca},
abstractNote = {We study the structure of twopoint correlators of the inflationary field fluctuations in order to improve the accuracy and efficiency of the existing methods to calculate primordial spectra. We present a description motivated by the separation of the fast and slow evolving components of the spectrum which is based on Cholesky decomposition of the field correlator matrix. Our purpose is to rewrite all the relevant equations of motion in terms of slowly varying quantities. This is important in order to consider the contribution from highfrequency modes to the spectrum without affecting computational performance. The slowroll approximation is not required to reproduce the main distinctive features in the power spectrum for each specific model of inflation.},
doi = {10.1088/14757516/2017/05/047},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 05,
volume = 2017,
place = {United States},
year = {Mon May 01 00:00:00 EDT 2017},
month = {Mon May 01 00:00:00 EDT 2017}
}

We examine the dynamics of inflation driven by multiple, interacting scalar fields and derive a multifield version of the Hubble slow roll expansion. We show that the properties of this expansion naturally generalize those of the single field case. We present an analogous hierarchy of slow roll parameters, and derive the system of flow equations that describes their evolution, and show that when this system is truncated at finite order, it can always be solved exactly. Lastly, we express the scalar and tensor perturbation spectra in terms of the slow roll parameters.

A statistical approach to multifield inflation: manyfield perturbations beyond slow roll
We study multifield contributions to the scalar power spectrum in an ensemble of sixfield inflationary models obtained in string theory. We identify examples in which inflation occurs by chance, near an approximate inflection point, and we compute the primordial perturbations numerically, both exactly and using an array of truncated models. The scalar mass spectrum and the number of fluctuating fields are accurately described by a simple random matrix model. During the approach to the inflection point, bending trajectories and violations of slow roll are commonplace, and 'manyfield' effects, in which three or more fields influence the perturbations, are often important.more » 
Interactions of fast and slow waves in problems with two time scales
Consideration is given to certain symmetric hyperbolic systems of nonlinear partial differential equations whose solutions vary on two time scales, a slow scale t and a fast scale t/epsilon. It is shown that if the initial data are not prepared correctly for the suppression of the fast scale motion and contain errors of amplitude O(epsilon to the mu), so that only mu time derivatives of the solution are bounded at t 0, then fast waves of amplitude O(epsilon to the mu) will be present in the solution. The error introduced in the slow scale motion by nonlinear interactions of thesemore » 
Predictions in multifield models of inflation
This paper presents a method for obtaining an analytic expression for the density function of observables in multifield models of inflation with sumseparable potentials. The most striking result is that the density function in general possesses a sharp peak and the location of this peak is only mildly sensitive to the distribution of initial conditions. A simple argument is given for why this result holds for a more general class of models than just those with sumseparable potentials and why for such models, it is possible to obtain robust predictions for observable quantities. As an example, the joint density functionmore » 
Computing observables in curved multifield models of inflation—A guide (with code) to the transport method
We describe how to apply the transport method to compute inflationary observables in a broad range of multiplefield models. The method is efficient and encompasses scenarios with curved fieldspace metrics, violations of slowroll conditions and turns of the trajectory in field space. It can be used for an arbitrary mass spectrum, including massive modes and models with quasisinglefield dynamics. In this note we focus on practical issues. It is accompanied by a Mathematica code which can be used to explore suitable models, or as a basis for further development.