Gravitational Wave Consistency Relations for Multifield Inflation

Abstract

We study the tensor spectral index nt and the tensor-to-scalar ratio r in the simplest multifield extension to single-field, slow-roll inflation models. We show that multifield models with potentials V ∼ i λi|φi| p have different predictions for nt/r than single-field models, even when all the couplings are equal λi = λj, due to the probabilistic nature of the fields' initial values. We analyze well-motivated prior probabilities for the λi and initial conditions to make detailed predictions for the marginalized probability distribution of nt/r. With O(100) fields and p > 3/4, we find that nt/r differs from the single-field result of nt/r = −1/8 at the 5σ level. This gives a novel and testable prediction for the simplest multifield 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.…”

“…The method to obtain a random point includes sampling from the multi-variate distribution N (0, 1) and then dividing by the norm of the vector. Assuming that the φ i 's are uncorrelated with the masses (including the time dependent term e −2λiτ * ) and employing similar techniques as [25], one can show that at the limit of infinite number of fields the ratio in Eq. (4) is normally distributed with mean…”

Effect of reheating on predictions following multiple-field inflation

“…The regime of many-field inflation (N 10) typically yields a range of predictions for curvature perturbations at the end of inflation that is surprisingly easy to categorize in comparison to the apparently large dimensionality of parameter space (see e.g. Refs [40][41][42][43][44][45][46][47][48], though stochastic effects can be important in the presence of many fields [49]). Scenarios with many fields also tend to predict an amount of isocurvature perturbations at the end of inflation which increases with the number of fields [42,47], thereby elevating the importance of studying the effects of reheating for these models.…”

“…VI with N = 5 fields with kpiv = 0.05 Mpc −1 . Colored circles show the results from simulations for a particular choice of decay rates Γi, chosen as described in text following Eq (44)…”

Inflation as an information bottleneck: a strategy for identifying universality classes and making robust predictions

“…In the case of manyfield inflation, numerical studies of a specific model of n-flation in Refs. [31,43,46] found that models consisting of O(100) fields had similar predictive power to single field models 8 . This is despite the fact that for a modest number of fields 1 < n 10 the model is less predictive.…”