Testing a Multi-Field Inflaton Model with Numerical Relativity

Abstract

The standard Big Bang model of cosmology requires the universe to emerge from highly specific and finely-tuned initial conditions, encapsulated by the well-known horizon and flatness problems. Inflation, a period of accelerated expansion in the early universe, was put forth to solve these problems. Since its introduction in 1981, over a hundred different models of inflation have been proposed. This zoo of inflation models, in which inflation can be driven by a thermodynamic phase transition or can be triggered by the chaotic initial conditions after the big bang, all suffer from the same inescapable problem: they require ultra-fine tuning in order to produce the right amplitude and tilt for the scalar curvature fluctuations, and the right tensor-to-scalar ratio that are consistent with observations. To make matters worse, the Planck 2013 results eliminate all but the plateau models of inflation. However, these plateau models come with their own unique problems, namely, 1) gradients and inhomogeneities can quickly grow in the time between when the universe exits the quantum gravity dominated phase and when inflation can start, and 2) the eternal inflation and multiverse problem. Recently, Kallosh and Linde have proposed a model that they think will avoid the problems above; specifically, they propose a two-field model which sums a quadratic and plateau potential. In this study, we have tested whether this model really works, i.e. with this model of the inflaton field, can inflation start despite initial gradients and can the eternal inflation problem be avoided? We have conducted the first numerical general relativity study of a multi-field model of inflation. This study is the first of its kind to include the consideration of quantum runaway and the multiverse, in addition to testing whether the gradient growth problem occurs. We have modified the tetrad formulation of the (3+1)-dimensional Einstein-scalar field equations to accommodate two canonical scalar fields, and to test initial variations along one spatial dimension. We have performed numerous tests with a wide range of initial conditions of the $\phi$ and $\chi$ field, and we find that this model fails. We find two distinct failure modes: a failure to avoid eternal inflation and the multiverse problem and a failure to smooth. Significantly, we find that our simulations are second order convergent, meaning our results satisfy the field equation constraints. Because the Kallosh-Linde model is representative of the best hope for addressing the growth of gradients and multiverse problems while also producing key observable cosmological quantities, its failure to do so has important implications for the viability of inflation models in general.