Inflation and Primordial Perturbations in Fractal Cosmology

Aarav Shah; Paulo Moniz; Maxim Khlopov; Oem Trivedi; Maxim Krasnov

doi:10.1016/j.dark.2026.102285

paper

Inflation and Primordial Perturbations in Fractal Cosmology

arXiv:2601.04691 · doi:10.1016/j.dark.2026.102285

Abstract

We study inflationary dynamics within the framework of fractal cosmology, where space is characterized by an effective non-integer dimension $D$ . In our work, fractal effects are sourced through thermodynamic modifications at the cosmological horizon. Using the modified Friedmann and continuity equations, we then derive the modified slow roll parameter and their evolution for linear, cubic, Starobinsky ( $R + R^{2}$ ) and Natural inflationary potentials, showing that the slow roll parameters get suppressed for $D < 3$ . We further derive a fractal extension of the Mukhanov-Sasaki equation by introducing an effective momentum $k_{eff}$ , which captures the modification of spatial Laplacian due to fractality. This leads to explicit corrections to the scalar power spectrum and the spectral index $n_{s}$ , depending on both $D$ and a fractional length scale $L$ . Confrontation with Planck 2018 data constrains the effective dimension to a best-fit range of $2.7 ≲ D ≲ 3$ for the Starobinsky model. Furthermore, in the case of Natural Inflation, fractal corrections relax the usual requirement of super-Planckian axion decay constants, opening a phenomenologically viable parameter space inaccessible in the standard $3 + 1$ dimensional cosmology.

This manuscript has 36 pages and 2 figures. Comments and suggestions from readers are welcome

Inflation and Primordial Perturbations in Fractal Cosmology

Abstract

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