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Perturbations in generalized multi-field inflation (0801.1085v2)

Published 7 Jan 2008 in hep-th and gr-qc

Abstract: We study the linear perturbations of multi-field inflationary models governed by a Lagrangian which is a general function of the scalar fields and of a global kinetic term combining their spacetime gradients with an arbitrary field space metric. Our analysis includes k-inflation, DBI inflation and its multi-field extensions which have been recently studied. For this general class of models, we calculate the action to second order in the linear perturbations. We decompose the perturbations into an (instantaneous) adiabatic mode, parallel to the background trajectory, and entropy modes. We show that all the entropy modes propagate with the speed of light whereas the adiabatic mode propagates with an effective speed of sound. We also identify the specific combination of entropy modes which sources the curvature perturbation on large scales. We then study in some detail the case of two scalar fields: we write explicitly the equations of motion for the adiabatic and entropy modes in a compact form and discuss their quantum fluctuations and primordial power spectra.

Citations (225)

Summary

  • The paper expands second-order perturbative analysis in multi-field inflation, decomposing fluctuations into adiabatic modes with an effective sound speed and entropy modes propagating at light speed.
  • The paper reveals that non-canonical kinetic terms and field space geometry critically modulate large-scale curvature evolution through trajectory bending.
  • The paper applies its framework to DBI inflation, establishing quantum initial conditions that underlie observable primordial power spectra.

Overview of "Perturbations in Generalized Multi-Field Inflation"

This paper presents a detailed analysis of perturbations in a broad class of multi-field inflationary models, incorporating complex kinetic term dynamics governed by a non-trivial metric in field space. The paper revises and expands upon traditional paradigms by examining frameworks such as k-inflation and Dirac-Born-Infeld (DBI) inflation alongside their multi-field adaptations. Core focus lies on the calculation of the action to second order in linear perturbations, providing new insights into the interaction between adiabatic and entropy modes.

Key Findings

  1. Perturbative Expansion and Wave Equation Dynamics: The authors meticulously expand the action up to second order, facilitating the derivation of classical equations of motion for perturbations. They decompose perturbations into adiabatic and entropy modes, revealing that the adiabatic mode propagates with an effective sound speed csc_s, while entropy modes propagate at the speed of light.
  2. Entropy Mode Influence on Curvature Perturbation: The analysis shows that curvature perturbation on large scales is influenced by both the bending of the trajectory in the field space and an additional term associated with the function P's non-trivial dependency on kinetic terms. This implies that non-standard kinetic terms can significantly alter the large-scale evolution of curvature perturbations.
  3. Quantum Fluctuations and Primordial Spectra: The researchers derive quantum initial conditions and address the normalization of vacuum quantum fluctuations, thereby facilitating the calculation of primordial power spectra. They assert how the propagation speeds impact the scales at which these perturbations become significant.
  4. DBI Inflation as a Case Study: The paper applies its theoretical framework to DBI inflation, offering a direct comparison of derived quantities with specific DBI models. This highlights the broader applicability of the derived equations.

Implications for Cosmology and Theory

This paper’s comprehensive treatment of perturbations in multi-field inflation models underscores significant theoretical ramifications. In particular, it emphasizes the critical role of field space geometry and non-canonical kinetic terms in influencing inflationary dynamics and structure formation. From an observational standpoint, these findings could guide future CMB studies in distinguishing between different inflationary scenarios.

The implications extend to string theory cosmology, where this class of models may help connect high energy physics with observational cosmology. The differences in propagation speeds of adiabatic and entropy modes suggest observable signatures in the CMB that could validate or exclude specific multi-field inflation models.

Future Directions

The paper concludes with a call for further exploration, particularly into the field of non-linear perturbations and potential non-Gaussianities. As cosmological observations become ever more precise, a deeper understanding of multi-field dynamics will likely prove essential for interpreting data and refining theoretical models. The authors highlight the need for further investigation into coupled adiabatic and entropy modes and their implications for early universe cosmology.

In summary, this research extends the theoretical landscape of inflationary cosmology, providing essential tools for analyzing complex multi-field systems. The integration of sophisticated mathematical treatment with an eye toward observational implications makes this work a substantial contribution to the field.