73 research outputs found
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
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