Inhomogeneous Initial Data and Small-Field Inflation

Abstract

We consider the robustness of small-field inflation in the presence of scalar field inhomogeneities. Previous numerical work has shown that if the scalar potential is flat only over a narrow interval, such as in commonly considered inflection-point models, even small-amplitude inhomogeneities present at the would-be onset of inflation at $\tau ={\tau }_i$ can disrupt the accelerated expansion. In this paper, we parametrise and evolve the inhomogeneities from an earlier time ${\tau }_{IC}$ at which the initial data were imprinted, and show that for a broad range of inflationary and pre-inflationary models, inflection-point inflation withstands initial inhomogeneities. We consider three classes of perturbative pre-inflationary solutions (corresponding to energetic domination by the scalar field kinetic term, a relativistic fluid, and isotropic negative curvature), and two classes of exact solutions to Einstein's equations with large inhomogeneities (corresponding to a stiff fluid with cylindrical symmetry, and anisotropic negative curvature). We derive a stability condition that depends on the Hubble scales $H({\tau }_i)$ and $H({\tau }_{IC})$, and a few properties of the pre-inflationary cosmology. For initial data imprinted at the Planck scale, the absence of an inhomogeneous initial data problem for inflection-point inflation leads to a novel, lower limit on the tensor-to-scalar ratio.

arXiv comment31 pages, 4 figures. Changes in v2: minor clarifications, some calculations moved to an appendix. This is an author-created, un-copyedited version of an article published in JCAP. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

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• Dynamics of inflation with mutually orthogonal vector fields in a closed universe
• Robustness of inflation to kinetic inhomogeneities
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• Topology of Cosmological Black Holes