Cosmic microwave background and inflation in multi-fractional spacetimes

Gianluca Calcagni, Sachiko Kuroyanagi, Shinji Tsujikawa

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


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.

Original languageEnglish
Article number039
JournalJournal of Cosmology and Astroparticle Physics
Issue number8
Publication statusPublished - 2016 Aug 18
Externally publishedYes


  • cosmological parameters from CMBR
  • cosmology of theories beyond the SM
  • physics of the early universe

ASJC Scopus subject areas

  • Astronomy and Astrophysics


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