Diffeomorphism radiative degrees of freedom of Thomas-Whitehead gravity

The Thomas-Whitehead (TW) action embeds the projectively invariant connection into a gravitational theory that contains general relativity [S. Brensinger, K. Heitritter, V. G. J. Rodgers, and K. Stiffler, [Phys. Rev. D 103, 044060 (2021)]; and , Int. J. Mod. Phys. A 33, 1850223 (2018); V. G. J. Rodgers, in Particles, Fields and Topology, Chap. 19, pp. 201--211]. In this work, the diffeomorphism field ${\mathcal{D}}_{ab}$ is examined in Minkowski space where salient features of this field can be explored. In particular, we study the radiative degrees of freedom of this field while in a Minkowski space background. We show that it can be decomposed into irreducible representations, corresponding to tensor, vector, and scalar radiating solutions. Furthermore we examine geodesic deviation in the context of TW gravity about a Minkowski space background. We do this both at zeroth and first order in metric fluctuations ${h}_{ab}$. We discuss that response of a gravitational wave antenna to the geodesics deviations. Measurements of gravitational waves by detectors like LIGO, VIRGO, KAGRA, LISA as well as Pulsar Time Arrays (PTAs) have constrained the presence of nontransverse-traceless modes in other theories of gravity. Future work could similarly be done to constrain the diffeomorphism field modes in TW gravity.