Dark energy in multi-fractional spacetimes
  We study the possibility to obtain cosmological late-time acceleration from a
geometry changing with the scale, in particular, in the so-called
multifractional theories with $q$-derivatives and with weighted derivatives. In
the theory with $q$-derivatives, the luminosity distance is the same as in
general relativity and, therefore, geometry cannot act as dark energy. In the
theory with weighted derivatives, geometry alone is able to sustain a late-time
acceleration phase without fine tuning, while being compatible with
structure-formation and big-bang nucleosynthesis bounds. This suggests to
extend the theory, in a natural way, from just small-scale to also large-scale
modifications of gravity. Surprisingly, the Hausdorff dimension of spacetime is
constrained to be close to the topological dimension 4. After arguing that this
finding might not be a numerical coincidence, we conclude that present-day
acceleration could be regarded as the effect of a new restoration law for
spacetime geometry.
