Ghosts, instabilities, and superluminal propagation in modified gravity models

Abstract

We consider Modified Gravity models involving inverse powers of fourth-order curvature invariants.Using these models' equivalence to the theory of a scalar field coupled to a linear combination of the invariants, we investigate the properties of the propagating modes. Even in the case for which the fourth derivative terms in the field equations vanish, we find that the second derivative terms can give rise to ghosts, instabilities, and superluminal propagation speeds. We establish the conditions which the theories must satisfy in order to avoid these problems in Friedmann backgrounds, and show that the late-time attractor solutions generically exhibit superluminally propagating tensor or scalar modes. * a. de-felice@sussex.ac.uk

A minimal set of invariants as a systematic approach to higher order gravity models

“…This question was addressed in [4] where it was shown that adding matter to the vacuum analysis will not affect the fixed points for power-law solutions. It is also reassuring that some of our results on the separatrix analysis using dynamical systems for vacuum are consistent with results from other studies [45] that used analytical derivations and showed that such separatrix are present in similar models. Nevertheless, it remains of interest to verify this assumption using our approach in future work.…”

“…As discussed in these papers, a theory with action R + f (GB) can be re-written as the Einstein-Hilbert action plus a GB-function coupled to a scalar field φ with potential U (φ), i.e. R + f (φ)GB − U (φ) [45]. In the latter frame, the theory becomes like that of a Gauss-Bonnet one where the equations of motion (EOMs) then decouple into second order equations for the metric and for each scalar field involved.…”

“…In the latter frame, the theory becomes like that of a Gauss-Bonnet one where the equations of motion (EOMs) then decouple into second order equations for the metric and for each scalar field involved. For example, [45] derived some conditions for GBlike invariants so that the EOMs do decouple into second order equations for the metric and each scalar field. It is worth clarifying that the decoupled equations are not the background field equations in the R + f (GB) frame where the Friedmann equation (the 00-field equation) contains third derivatives of the metric.…”

“…It is worth clarifying that the decoupled equations are not the background field equations in the R + f (GB) frame where the Friedmann equation (the 00-field equation) contains third derivatives of the metric. As discussed in [45], the cancellation of fourth order derivatives in the decoupled equations is a necessary condition to have a theory free from massive spin-2 gravitons (ghosts) [24,41,42,44,45]. The condition imposes for us some relations between the parameters that we can use in order to combine R and R1.…”

“…where, as discussed in [45] (see the begining of our previous section), the fourth-order derivatives in the decoupled equations are eliminated by using the combination a 2 = −4a 3 [45] of the dimensionless constants, a 1 , a 2 , and a 3 . In the previous section, we considered models with functions of the pure GB invariant where we also required a 1 = a 3 but here we relax this condition.…”