Dimensional reduction in the sky

TL;DR

This paper investigates how a quantum-gravity-inspired reduction of spacetime's spectral dimension to 2 in the ultraviolet leads to a naturally scale-invariant spectrum of cosmological fluctuations without inflation, impacting early universe models.

Contribution

It demonstrates that spectral dimension reduction to 2 in quantum gravity models produces scale-invariant fluctuations independently of the equation of state, challenging inflationary paradigms.

Findings

UV spectral dimension of 2 yields scale-invariant vacuum fluctuations

The fluctuation spectrum is scale-invariant before horizon crossing

Running spectral dimensions can improve cyclic/ekpyrotic models

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.