On the degrees of freedom of R2 gravity in flat spacetime

Abstract

We study the degrees of freedom of R2 gravity in flat spacetime with two approaches. By rewriting the theory a la Stueckelberg, and implementing Lorentz-like gauges to the metric perturbations, we confirm that the pure theory propagates one scalar degree of freedom, while the full theory contains two tensor modes in addition. We then consider the degrees of freedom by directly examining the metric perturbations. We show that the degrees of freedom of the full theory match with those obtained with the manifestly covariant approach. In contrast, we find that the pure R2 gravity has no degrees of freedom. We show that a similar discrepancy between the two approaches appears also in a theory dual to the three-form, and appears due to the Lorentz-like gauges, which lead to the fictitious modes even after the residual gauge redundancy has been taken into account. At first sight, this implies a discontinuity between the full theory and the pure case. By studying the first-order corrections of the full R2 gravity beyond the linear regime, we show that at high-energies, both scalar and tensor degrees of freedom become strongly coupled. This implies that the apparent discontinuity of pure and full R2 gravity is just an artefact of the perturbation theory, and further supports the absence of degrees of freedom in the pure R2 gravity.

The effective field theory approach to the strong coupling issue in f(T) gravity with a non-minimally coupled scalar field

“…Around a Minkowski background, an extra dynamical scalar mode of f (T ) gravity manifests itself only in the fourth order perturbation action [52]. The absence of the scalar mode in lower-order perturbations raises concerns about a strong coupling problem [53][54][55][56][57][58][59], which can be understood from an effective point of view -if the kinetic term is considered to be small, normalizing the kinetic term by redefining the variables will inevitably induce and amplify the coupling coefficients at higher order in perturbations. Linear perturbations of f (T ) gravity in a Friedmann-Lemaître-Robertson-Walker (FLRW) universe have been explored in previous studies [60][61][62][63][64][65][66], revealing no additional DoFs at linear level.…”