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Adiabatic and Isocurvature Perturbations for Multifield Generalized Einstein Models

Fabrizio Di Marco, Fabio Finelli, Robert Brandenberger

TL;DR

This work extends the two-field perturbation formalism to generalized Einstein theories with a non-canonical kinetic term, revealing a new, unsuppressed coupling between adiabatic and isocurvature modes on super-Hubble scales. By applying the framework to an exact inflationary solution with an exponential potential, it shows that entropy perturbations can source and mix with curvature perturbations, producing distinct spectral indices and blue tilts for isocurvature modes. The contracting branch offers novel routes to scale-invariant fluctuations in bouncing scenarios, though its background solution is found to be unstable. Overall, the results highlight a robust mechanism for entropy-to-adiabatic transfer in string-motivated cosmologies and inform the viability of PBB/Ekpyrotic-like models with moduli fields and non-standard kinetic terms.

Abstract

Low energy effective field theories motivated by string theory will likely contain several scalar moduli fields which will be relevant to early Universe cosmology. Some of these fields are expected to couple with non-standard kinetic terms to gravity. In this paper, we study the splitting into adiabatic and isocurvature perturbations for a model with two scalar fields, one of which has a non-standard kinetic term in the Einstein-frame action. Such actions can arise, e.g., in the Pre-Big-Bang and Ekpyrotic scenarios. The presence of a non-standard kinetic term induces a new coupling between adiabatic and isocurvature perturbations which is non-vanishing when the potential for the matter fields is nonzero. This coupling is un-suppressed in the long wavelength limit and thus can lead to an important transfer of power from the entropy to the adiabatic mode on super-Hubble scales. We apply the formalism to the case of a previously found exact solution with an exponential potential and study the resulting mixing of adiabatic and isocurvature fluctuations in this example. We also discuss the possible relevance of the extra coupling in the perturbation equations for the process of generating an adiabatic component of the fluctuations spectrum from isocurvature perturbations without considering a later decay of the isocurvature component.

Adiabatic and Isocurvature Perturbations for Multifield Generalized Einstein Models

TL;DR

This work extends the two-field perturbation formalism to generalized Einstein theories with a non-canonical kinetic term, revealing a new, unsuppressed coupling between adiabatic and isocurvature modes on super-Hubble scales. By applying the framework to an exact inflationary solution with an exponential potential, it shows that entropy perturbations can source and mix with curvature perturbations, producing distinct spectral indices and blue tilts for isocurvature modes. The contracting branch offers novel routes to scale-invariant fluctuations in bouncing scenarios, though its background solution is found to be unstable. Overall, the results highlight a robust mechanism for entropy-to-adiabatic transfer in string-motivated cosmologies and inform the viability of PBB/Ekpyrotic-like models with moduli fields and non-standard kinetic terms.

Abstract

Low energy effective field theories motivated by string theory will likely contain several scalar moduli fields which will be relevant to early Universe cosmology. Some of these fields are expected to couple with non-standard kinetic terms to gravity. In this paper, we study the splitting into adiabatic and isocurvature perturbations for a model with two scalar fields, one of which has a non-standard kinetic term in the Einstein-frame action. Such actions can arise, e.g., in the Pre-Big-Bang and Ekpyrotic scenarios. The presence of a non-standard kinetic term induces a new coupling between adiabatic and isocurvature perturbations which is non-vanishing when the potential for the matter fields is nonzero. This coupling is un-suppressed in the long wavelength limit and thus can lead to an important transfer of power from the entropy to the adiabatic mode on super-Hubble scales. We apply the formalism to the case of a previously found exact solution with an exponential potential and study the resulting mixing of adiabatic and isocurvature fluctuations in this example. We also discuss the possible relevance of the extra coupling in the perturbation equations for the process of generating an adiabatic component of the fluctuations spectrum from isocurvature perturbations without considering a later decay of the isocurvature component.

Paper Structure

This paper contains 8 sections, 76 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Perturbations
  4. An Exact Inflationary Solution
  5. The Contracting Solution
  6. Discussion and Conclusions
  7. Appendix A: Perspective on Ekpyrotic Models without Moduli Potentials
  8. Appendix B: Stability Analysis

Figures (3)

  • Figure 1: The spectral index $\nu_s$ for isocurvature perturbations in the expanding model of Section IV is presented as a function of $p$ and $\tan \theta$ (denoted by $x$ in the figure) for two different ranges of the variables.
  • Figure 2: The spectral index $\nu_s$ for isocurvature perturbations in the contracting case is presented in function of $p$ and $\tan \theta$ (denoted by $x$) for two different range of the variables.
  • Figure 3: The functions $\beta_0^2 (p)$ (continuous line) and $2/p$ (dashed line). The two functions intersect in $p=1/3$, and $\beta_0^2 > 2/p$ for $p>1/3$.