We explore whether multifield inflationary models make unambiguous predictions for fundamental cosmological observables. Focusing on N -quadratic inflation, we numerically evaluate the full perturbation equations for models with 2, 3, and O(100) fields, using several distinct methods for specifying the initial values of the background fields. All scenarios are highly predictive, with the probability distribution functions of the cosmological observables becoming more sharply peaked as N increases. For N = 100 fields, 95% of our Monte Carlo samples fall in the ranges ns ∈ (0.9455, 0.9534); α ∈ (−9.741, −7.047) × 10 −4 ; r ∈ (0.1445, 0.1449); and riso ∈ (0.02137, 3.510) × 10 −3 for the spectral index, running, tensor-to-scalar ratio, and isocurvature-to-adiabatic ratio, respectively. The expected amplitude of isocurvature perturbations grows with N , raising the possibility that manyfield models may be sensitive to post-inflationary physics and suggesting new avenues for testing these scenarios.The study of inflation has been transformed by the advent of precision cosmology. In 2013 the Planck Collaboration [1, 2] announced a 5σ detection of scaledependence in the primordial power spectrum, P(k). Likewise, the non-Gaussian component of the initial perturbations is less than 0.01% [3] and there are strong limits on isocurvature perturbations [2]. These results are entirely consistent with single-field slow roll inflation.The key theoretical challenge for inflation is to show how a phase of accelerated expansion is realized in particle physics. However, single-field models are not always natural; e.g., string compactifications often result in hundreds of scalar fields [4][5][6][7]. Multifield models yield a wider range of possible P(k) and higher-order correlators than simple single-field scenarios. Consequently, it is vital to determine not only what is possible in multifield models, but whether specific multifield models yield generic predictions that can be tested against data.Multifield models permit many distinct inflationary trajectories, and can thus be sensitive to the initial values of the background fields. The relative likelihood for different initial conditions (ICs) in the overall phase-space of the inflationary dynamical system must be encoded in the Bayesian prior for the model. Inflationary models are, to some extent, ad hoc hypotheses, so the IC priors typically cannot be computed or reliably predicted a priori. Recently it was pointed out that some multifield models make predictions for the inflationary observables that do not depend strongly on the specific IC prior [8][9][10][11][12], and this class of model unambiguously predicts the distributions of the inflationary observables. On the other hand, observational data could constrain the initial field configuration for models with strong sensitivity to their initial conditions.In this Letter we present the first generic predictions for a multifield inflation model in the many-field limit. By numerically evolving the perturbations, we find the pro...

Axions arise in many theoretical extensions of the Standard Model of particle physics, in particular the "string axiverse". If the axion masses, ma, and (effective) decay constants, fa, lie in specific ranges, then axions contribute to the cosmological dark matter and dark energy densities. We compute the background cosmological (quasi-)observables for models with a large number of axion fields, nax ∼ O(10 − 100), with the masses and decay constants drawn from statistical distributions. This reduces the number of parameters from 2nax to a small number of "hyperparameters". We consider a number of distributions, from those motivated purely by statistical considerations, to those where the structure is specified according to a class of M-theory models. Using Bayesian methods we are able to constrain the hyperparameters of the distributions. In some cases the hyperparameters can be related to string theory, e.g. constraining the number ratio of axions to moduli, or the typical decay constant scale needed to provide the correct relic densities. Our methodology incorporates the use of both random matrix theory and Bayesian networks. 1 Cosmology, of course, also presents another two huge problems for the Standard Model: the baryon asymmetry, and the generation of initial conditions (inflation). We will not discuss these problems further.

We present MultiModeCode, 1 a Fortran 95/2000 package for the numerical exploration of multifield inflation models. This program facilitates efficient Monte Carlo sampling of prior probabilities for inflationary model parameters and initial conditions and is the first publicly available code that can efficiently generate large sample-sets for inflation models with O(100) fields. The code numerically solves the equations of motion for the background and first-order perturbations of multi-field inflation models with canonical kinetic terms and arbitrary potentials, providing the adiabatic, isocurvature, and tensor power spectra at the end of inflation. For models with sum-separable potentials MultiModeCode also computes the slow-roll prediction via the δN formalism for easy model exploration and validation. We pay particular attention to the isocurvature perturbations as the system approaches the adiabatic limit, showing how to avoid numerical instabilities that affect some other approaches to this problem. We demonstrate the use of MultiModeCode by exploring a few toy models. Finally, we give a concise review of multifield perturbation theory and a user's manual for the program.

A grand challenge of the 21 st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach in estimating the cosmological parameters is to use the large scale matter distribution of the Universe. Galaxy surveys provide the means to map out cosmic large-scale structure in three dimensions. Information about galaxy locations is typically summarized in a "single" function of scale, such as the galaxy correlation function or powerspectrum. We show that it is possible to estimate these cosmological parameters directly from the distribution of matter. This paper presents the application of deep 3D convolutional networks to volumetric representation of dark-matter simulations as well as the results obtained using a recently proposed distribution regression framework, showing that machine learning techniques are comparable to, and can sometimes outperform, maximum-likelihood point estimates using "cosmological models". This opens the way to estimating the parameters of our Universe with higher accuracy.

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.