2016/09/30 by Stefano Bianco, Victor Nicolai Friedhoff, Edward Wilson-Ewing
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Dispersion (optics) #Econometrics #Economics #Inflation (cosmology) #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Scale (ratio) #Scale invariance #Statistics #Theoretical physics #astro-ph.CO #gr-qc
paper · pdf · doi:10.1103/physrevd.97.046006
published as Phys. Rev. D 97, 046006 (2018) · 9 pages. v2: Clarifications and references added
arxiv created 2018/02/08 · openalex publication_date 2018/02/15 · arxiv updated 2018/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.