Exact Solutions and Cosmological Constraints in Fractional Cosmology

This paper investigates exact solutions of cosmological interest in fractional cosmology. Given mu, the order of Caputo's fractional derivative, and w, the matter equation of state, we present specific exact power-law solutions. We discuss the exact general solution of the Riccati Equation, where the solution for the scale factor is a combination of power laws. Using cosmological data, we estimate the free parameters. An analysis of type Ia supernovae (SNe Ia) data and the observational Hubble parameter data (OHD), also known as cosmic chronometers, and a joint analysis with data from SNe Ia + OHD leads to best-fit values for the free parameters calculated at 1 sigma, 2 sigma and 3 sigma confidence levels (CLs). On the other hand, these best-fit values are used to calculate the age of the Universe, the current deceleration parameter (both at 3 alpha CL) and the current matter density parameter at 1 sigma CL. Finding a Universe roughly twice as old as the one of Lambda CDM is a distinction of fractional cosmology. Focusing our analysis on these results, we can conclude that the region in which mu > 2 is not ruled out by observations. This parameter region is relevant because fractional cosmology gives a power-law solution without matter, which is accelerated for mu > 2. We present a fractional origin model that leads to an accelerated state without appealing to Lambda or dark energy.

Automated summary

This paper investigates exact solutions of cosmological interest in fractional cosmology. Given mu and w, specific exact power-law solutions are presented. The general solution of the Riccati Equation is discussed and the free parameters are estimated using cosmological data. Best-fit values for the free parameters are obtained through analyses with type Ia supernova data and observational Hubble parameter data. The results suggest that the parameter region with mu > 2 is not ruled out by observations, indicating the potential of fractional cosmology in providing accelerated solutions without matter.