Manyfield inflation in random potentials

Abstract

We construct models of inflation with many randomly interacting fields and use these to study the generation of cosmological observables. We model the potentials as multi-dimensional Gaussian random fields (GRFs) and identify powerful algebraic simplifications that, for the first time, make it possible to access the manyfield limit of inflation in GRF potentials. Focussing on small-field, slow-roll, approximate saddle-point inflation in potentials with structure on sub-Planckian scales, we construct explicit examples involving up to 100 fields and generate statistical ensembles comprising of 164,000 models involving 5 to 50 fields. For the subset of these that support at least sixty e-folds of inflation, we use the 'transport method' and δ N formalism to determine the predictions for cosmological observables at the end of inflation, including the power spectrum and the local non-Gaussianities of the primordial perturbations. We find three key results: i) Planck compatibility is not rare, but future experiments may rule out this class of models; ii) In the manyfield limit, the predictions from these models agree well with, but are sharper than, previous results derived using potentials constructed through non-equilibrium Random Matrix Theory; iii) Despite substantial multifield effects, non-Gaussianities are typically very small: fNLloc ≪ 1. We conclude that many of the 'generic predictions' of single-field inflation can be emergent features of complex inflation models.

Many-field inflation: universality or prior dependence?

“…These models can make universal landscape predictions based in part on the universality of N-flation [24]. A similar predictivity has been found in recent many-field numerical investigations in other contexts [14,15,25,26]. It is the goal of this paper to elucidate these simple predictions of manyfield models and investigate their prior dependence.…”

Stochastic particle production in a de Sitter background

“…To simplify the analysis and focus on the impact of expansion, we considered the case with spectator fields being non-adiabatically excited by of a series of delta-function scatterers with random strengths. 15 We carried out detailed numerical calculations using the transfer matrix approach for a wide range of parameters (including strong and weak scattering), and we explored both the individual and the statistical properties of quantities related to particle production. We developed a Fokker-Planck equation to analytically understand the results of our numerical simulations in the weak scattering limit.…”

Building analytical three-field cosmological models

“…As we are interested in polynomial potentials, we are going to choose a 12 = a 15 = a 16 24 = a 26 = a 27 = 0, in order to avoid rational exponents. Such choices result in the constraints a 11 + a 13 + a 14 = 1, b 2 = 1 and a 25 = 1.…”

“…In the second scenario we also need to consider a 12 = a 15 = a 16 24 = a 26 = a 27 = 0 as we would like to avoid rational powers in the effective potential (or superpotential). Consequently we keep the constraints a 11 + a 13 + a 14 = 1, b 2 = 1 and a 25 = 1.…”

“…Moreover, multiple fields allow us to address new features for the physical systems and for the cosmological parameters, which cannot be derived from single field models, as pointed out very recently in [23,24].…”