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Slow-roll Inflation for Generalized Two-Field Lagrangians

Fabrizio Di Marco, Fabio Finelli

TL;DR

This paper develops a slow-roll framework for generalized two-field inflation with a kinetic coupling between fields, deriving the evolution and coupling of adiabatic and isocurvature perturbations on large scales. By computing the power spectra and their spectral indices to first order in slow-roll, including the effects of the kinetic coupling and possible transfer between modes, it provides model-dependent predictions and a Brans-Dicke–specific consistency relation within the Einstein frame. The analysis highlights how kinetic coupling alters the correlation between curvature and isocurvature modes and discusses implications for scalar-tensor theories and dilaton physics in the early universe. Overall, the work offers a general, testable formalism for two-field inflation with kinetic couplings and identifies observable signatures that could inform CMB and LSS data analyses.

Abstract

We study the slow-roll regime of two field inflation, in which the two fields are also coupled through their kinetic terms. Such Lagrangians are motivated by particle physics and by scalar-tensor theories studied in the Einstein frame. We compute the power spectra of adiabatic and isocurvature perturbations on large scales to first order in the slow-roll parameters. We discuss the relevance of the extra coupling terms for the amplitude and indexes of the power spectra. Beyond the consistency condition which involves the amplitude of gravitational waves, additional relations may be found in particular models based on such Lagrangians: as an example, we find an additional general consistency condition in implicit form for Brans-Dicke theory in the Einstein frame.

Slow-roll Inflation for Generalized Two-Field Lagrangians

TL;DR

This paper develops a slow-roll framework for generalized two-field inflation with a kinetic coupling between fields, deriving the evolution and coupling of adiabatic and isocurvature perturbations on large scales. By computing the power spectra and their spectral indices to first order in slow-roll, including the effects of the kinetic coupling and possible transfer between modes, it provides model-dependent predictions and a Brans-Dicke–specific consistency relation within the Einstein frame. The analysis highlights how kinetic coupling alters the correlation between curvature and isocurvature modes and discusses implications for scalar-tensor theories and dilaton physics in the early universe. Overall, the work offers a general, testable formalism for two-field inflation with kinetic couplings and identifies observable signatures that could inform CMB and LSS data analyses.

Abstract

We study the slow-roll regime of two field inflation, in which the two fields are also coupled through their kinetic terms. Such Lagrangians are motivated by particle physics and by scalar-tensor theories studied in the Einstein frame. We compute the power spectra of adiabatic and isocurvature perturbations on large scales to first order in the slow-roll parameters. We discuss the relevance of the extra coupling terms for the amplitude and indexes of the power spectra. Beyond the consistency condition which involves the amplitude of gravitational waves, additional relations may be found in particular models based on such Lagrangians: as an example, we find an additional general consistency condition in implicit form for Brans-Dicke theory in the Einstein frame.

Paper Structure

This paper contains 12 sections, 78 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Basic Equations
  3. Slow-Roll Expansion
  4. Evolution of Fluctuations During Inflation
  5. After Inflation
  6. Model-Dependent Relations
  7. Application to Scalar-Tensor Theories in the Einstein Frame
  8. Extended inflation: $\sin \theta \sim 0$
  9. Chaotic inflation: $\cos \theta \sim 0$
  10. Brans-Dicke Theory
  11. Conclusions
  12. Acknowledgements

Figures (1)

  • Figure 1: Evolution of $\chi (t)$ (top) and $\varphi (t)$ (bottom) for $U(\chi) = m^2 \chi^2/2$ (left) and $U(\chi) = \lambda \chi^4/4$ (right). The fields are in $1/\sqrt{G}$ units and the $x$-axis is $m t$ for the massive case and $\sqrt{\lambda/G} t$ for the self-interacting case. After a slow-roll regime, $\varphi$ oscillates as well in the case of a self-interacting potential for $\chi$ bottom panel, to the right).