Backreaction and Stochastic Effects in Single Field Inflation

Abstract

The formalism of stochastic inflation is a powerful tool for analyzing the backreaction of cosmological perturbations, and making precise predictions for inflationary observables. We demonstrate this with the simple $m^2{\varphi }^2$ model of inflation, wherein we obtain an effective field theory for IR modes of the inflaton, which remains coupled to UV modes through a classical noise. We compute slow-roll corrections to the evolution of UV modes (i.e. quantum fluctuations), and track this effect from the UV theory to the IR theory, where it manifests as a correction to the classical noise. We compute the stochastic correction to the spectral index of primordial perturbations, finding a small effect, and discuss models in which this effect can become large. We extend our analysis to tensor modes, and demonstrate that the stochastic approach allows us to recover the standard tensor tilt $n_T$, plus corrections.

24 pages, 5 figures

References in corpus (12)

• BICEP2 I: Detection Of B-mode Polarization at Degree Angular Scales
• Eternal inflation and its implications
• Warm Inflation and its Microphysical Basis
• Generation of fluctuations during inflation: comparison of stochastic and field-theoretic approaches
• Pointer states for primordial fluctuations in inflationary cosmology
• Heavy fields, reduced speeds of sound and decoupling during inflation
• Stochastic growth of quantum fluctuations during slow-roll inflation
• Hybrid inflation along waterfall trajectories
• Natural Inflation in Supergravity and Beyond
• Stochastic Inflation Revisited: Non-Slow Roll Statistics and DBI Inflation
• Perturbations in stochastic inflation
• Analytical Study of Mode Coupling in Hybrid Inflation

Cited by in corpus (17)

• Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production
• Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation
• Multiple Fields in Stochastic Inflation
• A manifestly covariant theory of multifield stochastic inflation in phase space: solving the discretisation ambiguity in stochastic inflation
• Review on stochastic approach to inflation
• Large fluctuations and Primordial Black Holes
• Numerical stochastic inflation constrained by frozen noise
• Numerically modeling stochastic inflation in slow-roll and beyond
• Stochastic Inflation in General Relativity
• Canonical description of cosmological backreaction
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Synchronous coordinates and gauge-invariant observables in cosmological spacetimes
• Multi-field inflation from single-field models
• Quantum backreaction on a classical universe
• Spinodal Backreaction During Inflation and Initial Conditions
• Stochastic Inflation in Numerical Relativity
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function