DSR as an explanation of cosmological structure

Deformed special relativity (DSR) is one of the possible realizations of a varying speed of light (VSL). It deforms the usual quadratic dispersion relations so that the speed of light becomes energy dependent, with preferred frames avoided by postulating a non-linear representation of the Lorentz group. The theory may be used to induce a varying speed of sound capable of generating (near) scale-invariant density fluctuations, as discussed in a recent Letter. We identify the non-linear representation of the Lorentz group that leads to scale-invariance, finding a universal result. We also examine the higher order field theory that could be set up to represent it

Reappraisal of a model for deformed special relativity

We revisit one of the earliest proposals for deformed dispersion relations in the light of recent results on dynamical dimensional reduction and production of cosmological fluctuations. Depending on the specification of the measure of integration and addition rule in momentum space the model may be completed so as to merely deform Lorentz invariance, or so as to introduce a preferred frame. Models which violate Lorentz invariance have a negative UV asymptotic dimension and a very red spectrum of quantum vacuum fluctuations. Instead, models which preserve frame independence can exhibit running to a UV dimension of 2, and a scale-invariant spectrum of fluctuations. The bispectrum of the fluctuations is another point of divergence between the two casings proposed here for the original model

Life of cosmological perturbations in MDR models, and the prospect of travelling primordial gravitational waves

We follow the life of a generic primordial perturbation mode (scalar or tensor) subject to modified dispersion relations (MDR), as its proper wavelength is stretched by expansion. A necessary condition ensuring that travelling waves can be converted into standing waves is that the mode starts its life deep inside the horizon and in the trans-Planckian regime, then leaves the horizon as the speed of light corresponding to its growing wavelength drops, to eventually become cis-Planckian whilst still outside the horizon, and finally re-enter the horizon at late times. We find that scalar modes in the observable range satisfy this condition, thus ensuring the viability of MDR models in this respect. For tensor modes we find a regime in which this does not occur, but in practice it can only be realised for wavelengths in the range probed by future gravity wave experiments if the quantum gravity scale experienced by gravity waves goes down to the PeV range. In this case travelling---rather than standing---primordial gravity waves could be the tell-tale signature of MDR scenarios.Comment: 9 pages, 1 figure. v2 matches version accepted for publicatio

String theories with deformed energy momentum relations, and a possible non-tachyonic bosonic string

We consider a prescription for introducing deformed dispersion relations in the bosonic string action. We find that in a subset of such theories it remains true that the embedding coordinates propagate linearly on the worldsheet. While both the string modes and the center of mass propagate with deformed dispersion relations, the speed of light remains energy independent. We consider the canonical quantization of these strings, and find that it is possible to choose theories so that ghost modes still decouple, as usual. However the Virasoro algebra now exhibits an energy dependent central charge. We also find that there are examples where the tachyon is eliminated from the spectrum of the free bosonic string