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Multi-field Inflation with a Random Potential

S. -H. Henry Tye, Jiajun Xu, Yang Zhang

TL;DR

This work addresses primordial perturbations from multi-field inflation in a rugged landscape by modeling the inflaton as undergoing Brownian motion with drift in a $D$-dimensional field space. The authors develop a stochastic, delta-N framework to compute the two-point and three-point functions, revealing two regimes: (i) weak randomness where the power spectrum closely resembles the single-field slow-roll result with up to a $2\%$ red tilt increase, and (ii) strong randomness where entropic perturbations continually feed the adiabatic mode, producing fluctuations across all angular scales, potentially enhancing the tensor-to-scalar ratio and enabling a large negative running of the spectral index. Non-Gaussianity is generally suppressed in the inflationary phase but can be enhanced by resonant effects or during reheating. The formalism applies to broad multi-field scenarios, including N-flation, and makes concrete, testable predictions for high-resolution CMB data, such as features in the TT/TE/EE spectra and a possibly elevated $r$, while remaining consistent with current isocurvature constraints.

Abstract

Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian motion with a drift in the D-dimensional field space. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, leads to rich phenomenologies, such as primordial fluctuations in the power spectrum on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and can be detected or falsified with more data coming in the future. The tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced. In addition a large negative running of the power spectral index is possible. Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, but can possibly be enhanced by resonant effects or arise from the entropic perturbations during the onset of (p)reheating. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.

Multi-field Inflation with a Random Potential

TL;DR

This work addresses primordial perturbations from multi-field inflation in a rugged landscape by modeling the inflaton as undergoing Brownian motion with drift in a -dimensional field space. The authors develop a stochastic, delta-N framework to compute the two-point and three-point functions, revealing two regimes: (i) weak randomness where the power spectrum closely resembles the single-field slow-roll result with up to a red tilt increase, and (ii) strong randomness where entropic perturbations continually feed the adiabatic mode, producing fluctuations across all angular scales, potentially enhancing the tensor-to-scalar ratio and enabling a large negative running of the spectral index. Non-Gaussianity is generally suppressed in the inflationary phase but can be enhanced by resonant effects or during reheating. The formalism applies to broad multi-field scenarios, including N-flation, and makes concrete, testable predictions for high-resolution CMB data, such as features in the TT/TE/EE spectra and a possibly elevated , while remaining consistent with current isocurvature constraints.

Abstract

Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian motion with a drift in the D-dimensional field space. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, leads to rich phenomenologies, such as primordial fluctuations in the power spectrum on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and can be detected or falsified with more data coming in the future. The tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced. In addition a large negative running of the power spectral index is possible. Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, but can possibly be enhanced by resonant effects or arise from the entropic perturbations during the onset of (p)reheating. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.

Paper Structure

This paper contains 14 sections, 105 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Review of the Multifield Inflation Formalism
  3. The Background Equations
  4. Linear Perturbations
  5. The $\delta N$ Formalism
  6. Inflation with a Random Multi-Field Potential
  7. The Power Spectrum
  8. Non-Gaussianity
  9. Non-Gaussianity Generated During Inflation
  10. Non-Gaussianity Generated During the Onset of (P)reheating
  11. Discussions
  12. Summary and Remarks
  13. An Explicit Derivation of $\delta N$ under Entropic Perturbations $Q_s$
  14. The Evolution of $Q_\sigma$ and $Q_s$ During Inflation

Figures (1)

  • Figure 1: Perturbation of the inflaton trajectory under $Q_s$. The solid line (AB) is the unperturbed trajectory, while the dashed line (CD) is the perturbed trajectory under the perturbation $Q_s$.