Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Inflation in fractional Newtonian cosmology

S. M. M. Rasouli

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.

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 -folds and the fractional parameter , 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 -dependent normalization.
Paper Structure (19 sections, 63 equations, 1 figure)

This paper contains 19 sections, 63 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Fractional Newtonian cosmology
  3. Constructing an appropriate fractional potential for inflation
  4. Early time inflation
  5. Pre-inflationary regime
  6. Scenarios (I) and (II)
  7. Scenario (I):
  8. Scenario (II):
  9. Scenarios (III) and (IV)
  10. Scenario (III):
  11. Scenario (IV):
  12. Dynamical transition from pre-inflation to inflation
  13. Case I: $\alpha>1$
  14. Case II: $\alpha<1$
  15. Post-inflationary regime
  16. ...and 4 more sections

Figures (1)

  • Figure 1: The $\alpha$-dependent potential $\Phi_{\alpha}(a)$ (left panel) and the corresponding effective force $\mathcal{F}(a)$ (right panel) as functions of the scale factor. The solid and the dashed curves correspond to $\Phi_0=1/6$ and $\Phi_0=1/12$, respectively, and we have set $p= 4$, $a_c=1$.