Inflation in fractional Newtonian cosmology

Abstract: In this paper, we investigate the evolution of the early universe within the framework of fractional Newtonian cosmology. By constructing a suitable fractional potential, we show that the cosmological evolution can naturally originate from a non-singular pre-inflationary regime. We find a natural transition time, separating the pre-inflationary and inflationary regimes, characterized by the balance of the corresponding forces. By analyzing the dynamics near the transition time, we show that the inflationary phase emerges as a stable dynamical attractor. We show that the fractional force vanishes and undergoes a sign change at a point very close to the end of inflation. We then determine the small separation between the force zero point and the end of inflation, and show that it leads to a meaningful relation between the number of $e$-folds and the fractional parameter $α$, ensuring consistency with observations and resolving the horizon problem. Moreover, our results demonstrate the existence of a graceful exit from inflation, followed by an exact radiation-dominated solution with the standard time dependence and an $α$-dependent normalization.