A f(R) gravity without cosmological constant

TL;DR

This paper demonstrates that a specific f(R) gravity model can replicate the universe's accelerated expansion without requiring a cosmological constant or dark energy, challenging the standard cosmological paradigm.

Contribution

It introduces an analytical f(R) gravity action that reproduces Einstein-Hilbert behavior with a cosmological constant without actually including one.

Findings

The f(R) action matches the Einstein-Hilbert action with a cosmological constant.

The model admits Minkowski and Schwarzschild solutions.

The f(R) function involves hypergeometric functions, showing a non-trivial alternative to dark energy.

Abstract

In this work we consider the possibility of describing the current evolution of the universe, without the introduction of any cosmological constant or dark energy (DE), by modifying the Einstein-Hilbert (EH) action. In the context of the f(R) gravities within the metric formalism, we show that it is possible to find an action without cosmological constant which exactly reproduces the behavior of the EH action with cosmological constant. In addition the f(R) action is analytical at the origin having Minkowski and Schwarzschild as vacuum solutions. The found f(R) action is highly non-trivial and must be written in terms of hypergeometric functions but, in spite of looking somewhat artificial, it shows that the cosmological constant, or more generally the DE, is not a logical necessity.