A metric-affine version of the Horndeski theory
Abstract
We study the metric-affine versions of scalar-tensor theories whose connection enters the action only algebraically. We show that the connection can be integrated out, resulting in an equivalent metric theory. Specifically, we consider the metric-affine generalisations of the subset of the Horndeski theory whose action is linear in second derivatives of the scalar field. We determine the connection and find that it can describe a scalar-tensor Weyl geometry without a Riemannian frame. Still, as this connection enters the action algebraically, the theory admits the dynamically equivalent (pseudo)-Riemannian formulation in the form of an effective metric theory with an extra K-essence term. This may have interesting phenomenological applications.
- Publication:
-
International Journal of Modern Physics A
- Pub Date:
- January 2020
- DOI:
- 10.1142/S0217751X20400102
- arXiv:
- arXiv:1911.12768
- Bibcode:
- 2020IJMPA..3540010H
- Keywords:
-
- Horndeski theory;
- Palatini approach;
- 04.20.-q;
- 04.50.Kd;
- Classical general relativity;
- Modified theories of gravity;
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology
- E-Print:
- 8 pages, to appear in the thematic issue of Int. Journ. Mod. Phys. A - proceedings of the 10th Friedmann Seminar on Gravitation and Cosmology, St. Petersburg, Russia, June 23-29, 2019