Modified dispersion relations, inflation, and scale invariance

Stefano Bianco, Victor Nicolai Friedhoff, and Edward Wilson-Ewing
Phys. Rev. D 97, 046006 – Published 15 February 2018

Abstract

For a certain type of modified dispersion relations, the vacuum quantum state for very short wavelength cosmological perturbations is scale-invariant and it has been suggested that this may be the source of the scale-invariance observed in the temperature anisotropies in the cosmic microwave background. We point out that for this scenario to be possible, it is necessary to redshift these short wavelength modes to cosmological scales in such a way that the scale-invariance is not lost. This requires nontrivial background dynamics before the onset of standard radiation-dominated cosmology; we demonstrate that one possible solution is inflation with a sufficiently large Hubble rate, for this slow roll is not necessary. In addition, we also show that if the slow-roll condition is added to inflation with a large Hubble rate, then for any power law modified dispersion relation quantum vacuum fluctuations become nearly scale-invariant when they exit the Hubble radius.

  • Received 11 August 2017

DOI:https://doi.org/10.1103/PhysRevD.97.046006

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Stefano Bianco1,*, Victor Nicolai Friedhoff1,†, and Edward Wilson-Ewing1,2,‡

  • 1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Golm, Germany
  • 2Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick E3B 5A3, Canada

  • *stefano.bianco@aei.mpg.de
  • nicolai.friedhoff@aei.mpg.de
  • edward.wilson-ewing@unb.ca

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Issue

Vol. 97, Iss. 4 — 15 February 2018

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