Cosmic Acceleration in a Model of Fourth Order Gravity

TL;DR

This paper explores a fourth order gravity model without dark energy, demonstrating it can replicate cosmic acceleration and address the coincidence problem by adjusting a free length parameter, matching observations similar to the standard model.

Contribution

It introduces a fourth order gravity model with a variable length parameter that explains cosmic acceleration without dark energy, offering an alternative to the standard cosmological model.

Findings

The model explains cosmic acceleration with a fixed length parameter.

A time-dependent length parameter can resolve the cosmic coincidence problem.

Predictions of redshift drift differ from the standard model.

Abstract

We investigate a fourth order model of gravity, having a free length parameter, and no cosmological constant or dark energy. We consider cosmological evolution of a flat Friedmann universe in this model for the case that the length parameter is of the order of present Hubble radius. By making a suitable choice for the present value of the Hubble parameter, and value of third derivative of the scale factor (the jerk) we find that the model can explain cosmic acceleration to the same degree of accuracy as the standard concordance model. If the free length parameter is assumed to be time-dependent, and of the order of the Hubble parameter of the corresponding epoch, the model can still explain cosmic acceleration, and provides a possible resolution of the cosmic coincidence problem. We work out the effective equation of state, and its time evolution, in our model. We also compare redshift drift in our model, with that in the standard model. The equation of state and the redshift drift serve to discriminate our model from the standard model.