Fractional Einstein-Gauss-Bonnet scalar field cosmology

TL;DR

This paper develops a fractional calculus-based modification of Einstein-Gauss-Bonnet cosmology, deriving new equations, analyzing stability, and fitting observational data to support late-time cosmic acceleration as an alternative to Lambda-CDM.

Contribution

Introduces a novel fractional calculus framework in Einstein-Gauss-Bonnet cosmology, deriving modified equations and fitting them to observational data for late-time acceleration.

Findings

Consistent with accelerated expansion at late times.

Estimated parameters align with observational data.

Supports an alternative to Lambda-CDM for cosmic acceleration.

Abstract

Our paper introduces a new theoretical framework called the Fractional Einstein--Gauss--Bonnet scalar field cosmology, which has important physical implications. Using fractional calculus to modify the gravitational action integral, we derived a modified Friedmann equation and a modified Klein--Gordon equation. Our research reveals non-trivial solutions associated with exponential potential, exponential couplings to the Gauss--Bonnet term, and a logarithmic scalar field, which are dependent on two cosmological parameters, $m$ and $\alpha_{0}=t_{0}H_{0}$ and the fractional derivative order $\mu$. By employing linear stability theory, we reveal the phase space structure and analyze the dynamic effects of the Gauss--Bonnet couplings. The scaling behavior at some equilibrium points reveals that the geometric corrections in the coupling to the Gauss--Bonnet scalar can mimic the behavior of the dark sector in modified gravity. Using data from cosmic chronometers, type Ia supernovae, supermassive Black Hole Shadows, and strong gravitational lensing, we estimated the values of $m$ and $\alpha_{0}$, indicating that the solution is consistent with an accelerated expansion at late times with the values $\alpha_0=1.38\pm 0.05$, $m=1.44\pm 0.05$, and $\mu=1.48 \pm 0.17$ (consistent with $\Omega_{m,0}=0.311\pm 0.016$ and $h=0.712\pm 0.007$), resulting in an age of the Universe $t_{0}=19.0\pm 0.7$ [Gyr] at 1$\sigma$ CL. Ultimately, we obtained late-time accelerating power-law solutions supported by the most recent cosmological data, and we proposed an alternative explanation for the origin of cosmic acceleration other than $\Lambda$CDM. Our results generalize and significantly improve previous achievements in the literature, highlighting the practical implications of fractional calculus in cosmology.