PIRSA:13110059 Scientific Series Quantum Gravity

DOI10.48660/13110059

Series: Quantum Gravity

(2013). Dimensional reduction in the sky. Perimeter Institute. https://pirsa.org/13110059

Dimensional reduction in the sky. Perimeter Institute, Nov. 21, 2013, https://pirsa.org/13110059 

@misc{ pirsa_PIRSA:13110059,
  doi = {10.48660/13110059},
  url = {https://pirsa.org/13110059},
  author = {},
  keywords = {Quantum Gravity},
  language = {en},
  title = {Dimensional reduction in the sky},
  publisher = {Perimeter Institute},
  year = {2013},
  month = {nov},
  note = {PIRSA:13110059 see, \url{https://pirsa.org}}
}

Abstract

In several approaches to quantum-gravity, the spectral dimension of spacetime runs from the standard value of 4 in the infrared (IR) to a smaller value in the ultraviolet (UV). Describing this running in terms of deformed dispersion relations, I show that a striking cosmological implication is that that UV behavior leading to 2 spectral dimensions results in an exactly scale-invariant spectrum of vacuum scalar and tensor fluctuations. I discuss scenarios that break exact scale-invariance and show that the tensor to scalar ratio is fixed by the UV ratio between the speed of gravity and the speed of light. Cosmological perturbations in this framework display a wavelength-dependent speed of light, but by transforming to a suitable "rainbow frame" this feature can be removed, at the expense of modifying gravity. In particular it turns out that the following concepts are closely connected: scale-invariance of vacuum fluctuations, conformal invariance of the gravitational coupling, UV reduction to spectral dimension 2 in position space and UV reduction to Hausdorff dimension 2 in energy-momentum space.

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