Inhomogeneous initial data and small-field inflation
Journal of Cosmology and Astroparticle Physics
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Marsh, D., Barrow, J., & Ganguly, C. (2018). Inhomogeneous initial data and small-field inflation. Journal of Cosmology and Astroparticle Physics, 2018 (5)https://doi.org/10.1088/1475-7516/2018/05/026
We consider the robustness of small-field inflation in the presence of scalar field inhomo- geneities. Previous numerical work has shown that if the scalar potential is flat only over a narrow in- terval, such as in commonly considered inflection-point models, even small-amplitude inhomogeneities present at the would-be onset of inflation at τ = τi can disrupt the accelerated expansion. In this paper, we parametrise and evolve the inhomogeneities from an earlier time τIC 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(τi) and H(τIC), 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.
J.D.B. is supported by the Science and Technology Facilities Council (STFC) of the UK. C.G. is supported by the Jawaharlal Nehru Memorial Trust Cambridge International Scholarship. D.M. is supported by a Stephen Hawking Advanced Fellowship at the Centre for Theoretical Cosmology, DAMTP, University of Cambridge.
External DOI: https://doi.org/10.1088/1475-7516/2018/05/026
This record's URL: https://www.repository.cam.ac.uk/handle/1810/278635