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 φ 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 nT , plus corrections.

Implications of stochastic effects for primordial black hole production in ultra-slow-roll inflation

“…We discuss the details in section 3.2. We also use a recursive treatment where the modes are first taken to evolve on the FLRW background, and the noise given by these modes determines the coarse-grained background for the next iteration, as in [68,69,73]. We find that one iteration is sufficient to reproduce the results of the full treatment.…”

“…This makes the results potentially sensitive to the choice of window function and the value of σ. Dependence of the noise on the window function has been discussed in [57], see also [53,73,83,111,112]. The validity of the choice of σ (more generally, the form of the Langevin equation) would ultimately have to be checked with a first principle derivation of the separation between system and environment in quantum field theory.…”

“…However, for consistency, the backreaction of non-trivial mode evolution and change of the environment should be included, particularly in USR where modes can evolve after Hubble crossing. This has been done recursively in [68,69,73], and consistently at every timestep in P aper I.…”

“…We considered the non-linearity of the system by taking into account that the noise depends on the inflaton perturbations, while the perturbations evolve on the coarse-grained background affected by the noise. In [68,69,73], such backreaction effects had been considered recursively. However, to our knowledge, to date no calculation apart from P aper I has included the non-Markovian effects at every timestep, realisation by realisation.…”

Multiple fields in stochastic inflation

“…The stochastic formalism accounts for the quantum modification of the super-Hubble scales dynamics, and allows us to study how quantum effects modify inflationary observable predictions. Stochastic inflation is indeed a powerful tool for calculating correlation functions of quantum fields during inflation [27][28][29][30][31][32][33][34][35][36][37][38][39][40] (see also Ref. [41,42] for the case of scalar electrodynamics during inflation and Ref.…”