Modifications of Einstein's theory of gravitation have been extensively considered in the past years, in connection to both cosmology and quantum gravity. Higher-curvature and higher-derivative gravity theories constitute the main examples of such modifications. These theories exhibit, in general, more degrees of freedom than those found in standard general relativity; counting, identifying, and retrieving the description/representation of such dynamical variables is currently an open problem, and a decidedly nontrivial one. In this work we review, via both formal arguments and custom-made examples, the most relevant methods to unveil the gravitational degrees of freedom of a given model, discussing the merits, subtleties and pitfalls of the various approaches.
- higher derivative theories
Belenchia, A., Letizia, M., di Casola, E., & Liberati, S. (2018). Higher-order theories of gravity: diagnosis, extraction and reformulation via non-metric extra degrees of freedom—a review. Reports on Progress in Physics. https://doi.org/10.1088/1361-6633/aaa4ab