On the co-existence of matter dominated and accelerating solutions in f(G)-gravity

TL;DR

This paper investigates the limitations of f(G)-gravity models in describing realistic cosmological evolution, showing that certain transitions between decelerated and accelerated expansion are mathematically incompatible within these theories.

Contribution

It demonstrates that f(G)-gravity theories cannot generally support both decelerating and accelerating solutions simultaneously, constraining their cosmological viability.

Findings

Power-law solutions only exist for special f(G) forms.

Transitions from deceleration to acceleration require passing through G=0.

Differentiability at G=0 prevents simultaneous decelerating and accelerating solutions.

Abstract

Working within the theory of modified Gauss-Bonnet gravity, we show that FLRW--like power--law solutions only exist for a very special class of f(G)theories. Furthermore, we point out that any transition from decelerated to accelerated expansion must pass through G=0, and no function f(G) that is differentiable at this point can admit both a decelerating power--law solution and any accelerating solution. This strongly constrains the cosmological viability of f(G)-gravity, since it may not be possible to obtain an expansion history of the universe which is compatible with observations. We explain why the same issue does not occur in f(R)-gravity and discuss possible caveats for the case of f(G)-gravity.