2021/11/17 by Jinhui Wang, Wang, Jinhui, Leonardo Senatore +1
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.2111.09257
openalex publication_date 2021/11/17 · openalex created_date 2021/11/22 · openalex updated_date 2026/07/28
We study the onset of inflation in 3+1 dimensional cosmologies with an inflationary potential U satisfying 0 < Λ1 ≤ U ≤ Λ2, matter satisfying the dominant and strong energy conditions, and with spatial slices that can be foliated by 2-dimensional surfaces that are orbits under an isometry group. Assuming an initial Cauchy slice with positive mean curvature everywhere, we show, via mean curvature flow, that there exists a family of spatial slices parameterized by λ, whose volume grows between the flat slicings in de Sitter spaces with cosmological constants Λ1 and Λ2. In particular, inflationary expansion indeed occurs in this setting with inhomogeneous initial conditions. Finally, we apply this "inflationary time coordinate" λ to study asymptotics of the variation in the metric, the average stress-energy tensor, and the dynamics of an inflaton field on a spatial slice.