Multi-field Inflation with a Random Potential

TL;DR

This paper investigates how a random potential in multi-field inflation affects primordial density perturbations, revealing potential observable features in the CMB and implications for future data analysis.

Contribution

It introduces a stochastic formalism to analyze density perturbations in multi-field inflation with random potentials, highlighting new phenomenological effects.

Findings

Weak randomness yields a power spectrum similar to single-field slow-roll inflation.

Strong randomness causes rich features, including fluctuations across all scales.

Tensor-to-scalar ratio is enhanced, and large negative running of spectral index is possible.

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.