2018/03/04 by Shun Arai, Sergey Sibiryakov, Yuko Urakawa
Physics and Astronomy · #Adiabatic process #Black Holes and Theoretical Physics #Cosmological perturbation theory #Cosmology and Gravitation Theories #Curvature #Hubble volume #Hubble's law #Inflaton #Lorentz covariance #Noncommutative and Quantum Gravity Theories #Scalar (mathematics) #Scaling #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1088/1475-7516/2019/03/034
30 pages, 2 figures
arxiv created 2018/03/04 · openalex created_date 2018/03/29 · openalex publication_date 2019/03/21 · arxiv updated 2019/04/03 · openalex updated_date 2026/08/06
Instead of Lorentz invariance, gravitational degrees of freedom may obey Lifshitz scaling at high energies, as it happens in Hořava's proposal for quantum gravity. We study consequences of this proposal for the spectra of primordial perturbations generated at inflation. Breaking of 4D diffeomorphism (Diff) invariance down to the foliation-preserving Diff in Hořava-Lifshitz (HL) gravity leads to appearance of a scalar degree of freedom in the gravity sector, khronon, which describes dynamics of the time foliation. One can naively expect that mixing between inflaton and khronon will jeopardize conservation of adiabatic perturbations at super Hubble scales. This indeed happens in the projectable version of the theory. By contrast, we find that in the non-projectable version of HL gravity, khronon acquires an effective mass which is much larger than the Hubble scale well before the Hubble crossing time and decouples from the adiabatic curvature perturbation ζ sourced by the inflaton fluctuations. As a result, at super Hubble scales the adiabatic perturbation ζ behaves as in an effectively single field system and its spectrum is conserved in time. Lifshitz scaling is imprinted in the power spectrum of ζ through the modified dispersion relation of the inflaton. We point out violation of the consistency relation between the tensor-to-scalar ratio and the spectral tilt of primordial gravitational waves and suggest that it can provide a signal of Lorentz violation in inflationary era.