Cosmic microwave background and inflation in multi-fractional spacetimes

TL;DR

This paper uses CMB data to constrain inflationary models in multi-fractional spacetimes, providing the first observational bounds on oscillatory features and geometric parameters of such theories.

Contribution

It introduces observational constraints on multi-fractional spacetime models with q- and weighted derivatives, especially on oscillatory measures and fractal dimensions.

Findings

Constraints on multi-fractal measure parameters from CMB black-body spectrum.

First observational bounds on oscillation amplitudes in discrete fractal spacetimes.

Limits on the multi-scale geometry and spatial dimension derived from data.

Abstract

We use FIRAS and Planck 2015 data to place observational bounds on inflationary scenarios in multi-fractional spacetimes with $q$-derivatives. While a power-law expansion in the geometric time coordinate is subject to the usual constraints from the tensor-to-scalar ratio, model-independent best fits of the black-body and scalar spectra yield upper limits on the free parameters of the multi-fractal measure of the theory. When the measure describing the fractal spacetime geometry is non-oscillating, information on the CMB black-body spectrum places constraints on the theory independent from but weaker than those obtained from the Standard Model, astrophysical gravitational waves and gamma-ray bursts (GRBs). When log oscillations are included and the measure describes a discrete fractal spacetime at microscopic scales, we obtain the first observational constraints on the amplitudes of such oscillations and find, in general, strong constraints on the multi-scale geometry and on the dimension of space. These results complete the scan and reduction of the parameter space of the theory. Black-body bounds are obtained also for the theory with weighted derivatives.