Thanks to Jonathan Dickau for spotting this paper http://arxiv.org/abs/arXiv:1305.3153by FQXi member Giovanni Amelino-Camelia and others.
Here's the abstract:
"We explore the cosmological implications of a mechanism found in
several approaches to quantum-gravity, whereby the spectral dimension of
spacetime runs from the standard value of 4 in the infrared (IR) to a
smaller value in the ultraviolet (UV). Specifically, we invoke the
picture where the phenomenon is associated with modified dispersion
relations. With minimal assumptions, we find that UV behaviour leading
to 2 spectral dimensions results in an exactly scale-invariant spectrum
of vacuum scalar and tensor fluctuations, regardless of the equation of
state. The fluctuation production mechanism is analogous to the one
known for varying speed of sound/light models and, unlike in inflation,
the spectrum is already scale-invariant before leaving the horizon,
remaining so after freeze-in. In the light of Planck's recent results we
also discuss scenarios that break exact scale-invariance, such as the
possibility that the spectral dimension runs down to a value slightly
higher than 2, or runs down to 2 but with an extremely slow transient.
We further show that the tensor to scalar ratio is fixed by the UV ratio
between the speed of gravity and the speed of light. Not only does our
model not require inflation, but at its most minimal it seems
incompatible with it. In contrast, we find that running spectral
dimensions can improve the outlook of the cyclic/ekpyrotic scenario,
solving the main problems present in its simplest and most appealing
realisations."
Please discuss here...