Rainbow gravity and scale-invariant fluctuations

Abstract

We re-examine a recently proposed scenario where the deformed dispersion relations associated with a flow of the spectral dimension to a UV value of 2 leads to a scale-invariant spectrum of cosmological fluctuations, without the need for inflation. In that scenario Einstein gravity was assumed. The theory displays 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. We find that the ensuing rainbow gravity theory is such that gravity switches off at high energy (or at least leads to a universal conformal coupling). This explains why the fluctuations are scale-invariant on all scales: there is no horizon scale as such. For dispersion relations that do not lead to exact scale invariance we find instead esoteric inflation in the rainbow frame. We argue that these results shed light on the behaviour of gravity under the phenomenon of dimensional reduction.

Spectral dimensions from the spectral action

“…(11) and evaluating (31) for the corresponding return probabilities. Following the ideas of [41,42] the spectral dimension arising from (34) permits an interpretation as the Hausdorff-dimension of the theory's momentum space. Provided that the change of coordinates k 2 = F (p 2 ) is bijective, the inverse propagator in the exponential can be traded for a non-trivial measure on momentum space…”

“…The second way towards obtaining a non-trivial D S (T ) starts from a theory where the propagator of the test particle is already modified at the classical level. It is this feature that gives rise to the non-trivial spectral dimension in Hořava-Lifshitz gravity [35,39,40], general Lorentz-violating theories [41,42], or fractional quantum field theory [43,44]. Finally, D S (T ) may be modified through non-trivial quantum fluctuations of spacetime predicted by a fundamental theory of gravity.…”

Kinematics of particles with quantum-de Sitter-inspired symmetries

“…They in fact describe effects that are quite generically expected in quantum gravity research [3,4] (and in particular have been explicitly shown to characterize 3D quantum gravity [5,6]) without introducing preferred frames and so evading the strong constraints on Lorentz invariance violations. Modified dispersion relations could produce observable phenomenology in the context of astrophysics [7][8][9][10][11] and there is also increasing evidence that they could be relevant in the early Universe [12][13][14][15][16][17][18][19][20].…”

Photon gas thermodynamics in dS and AdS momentum spaces

“…Evidently, the DSR models have very different behaviors at the UV regime. For instance, some of them predict dynamical dimensional reduction at UV regime while the others do not [14]. In this paper, we consider two deformed special relativity models defined by the same coordinatizations of dS and AdS momentum spaces from the thermostatistical point of view.…”