Comparing metric and Palatini approaches to vector Horndeski theory

Understand

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 non-metric connection.
• In general, the exact solution in metric case coincides with the approximative solution in Palatini case.