Dark energy in multi-fractional spacetimes. (arXiv:2004.02896v2 [gr-qc] UPDATED)

<a href="http://arxiv.org/find/gr-qc/1/au:+Calcagni_G/0/1/0/all/0/1">Gianluca Calcagni</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Felice_A/0/1/0/all/0/1">Antonio De Felice</a>

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.

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.

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