Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration

TL;DR

The work tackles the cosmic acceleration problem by proposing a single f(R) gravity model that replaces dark energy with curvature-dependent terms. It employs a scalar-tensor formulation in both Jordan and Einstein frames to analyze early-time inflation driven by positive curvature powers and late-time acceleration from negative powers, and demonstrates de Sitter solutions and power-law behaviors. The key contributions include a stability analysis showing improved behavior over simple 1/R models, an outline of how the model can satisfy solar-system constraints, and a discussion of branching potentials that support a unified cosmological evolution. The paper also highlights a connection between inflationary potentials and modified gravity with fractional curvature powers, suggesting broader theoretical ties between scalar-field inflation and f(R) gravity.

Abstract

The modified gravity, which eliminates the need for dark energy and which seems to be stable, is considered. The terms with positive powers of the curvature support the inflationary epoch while the terms with negative powers of the curvature serve as effective dark energy, supporting current cosmic acceleration. The equivalent scalar-tensor gravity may be compatible with the simplest solar system experiments.

Figures (3)

• Figure 1: $V(A)b$ versus $Ab$ for $ab^2={1 \over 10}$.
• Figure 2: $V(A)b$ versus $Ab$ for $ab^2={1 \over 10}$. The behavior in the region $Ab\sim 0.5$.
• Figure 3: $V(A)b$ versus $Ab$ for $ab^2={1 \over 3}$.