Cosmic microwave background and inflation in multi-fractional spacetimes
  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.
