Comparing metric and Palatini approaches to vector Horndeski theory
Abstract
We compare cosmologic and spherically symmetric solutions to metric and Palatini versions of vector Horndeski theory. It appears that Palatini formulation of the theory admits more degrees of freedom. Specifically, homogeneous isotropic configuration is effectively bimetric, and static spherically symmetric configuration contains nonmetric connection. In general, the exact solution in metric case coincides with the approximative solution in Palatini case. The Palatini version of the theory appears to be more complicated, but the resulting nonlinearity may be useful: we demonstrate that it allows the specific cosmological solution to pass through singularity, which is not possible in metric approach.
 Publication:

International Journal of Modern Physics D
 Pub Date:
 2018
 DOI:
 10.1142/S0218271818500384
 arXiv:
 arXiv:1708.09796
 Bibcode:
 2018IJMPD..2750038D
 Keywords:

 Modified gravity;
 Palatini formulation;
 Horndeski theory;
 04.50.Kd;
 04.20.Fy;
 04.40.Nr;
 Modified theories of gravity;
 Canonical formalism Lagrangians and variational principles;
 EinsteinMaxwell spacetimes spacetimes with fluids radiation or classical fields;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematical Physics;
 83D;
 J.2
 EPrint:
 14 pages, to be published in Int.J.Mod.Phys.D version 2  minor changes: page format changed for a better view