(In)equivalence of Metric-Affine and Metric Effective Field Theories

Understand

In a geometrical approach to gravity the metric and the (gravitational) connection can be independent and one deals with metric-affine theories.

• We construct the most general action of metric-affine effective field theories, including a generic matter sector, where the connection does not carry additional dynamical fields.
• Among other things, this helps in identifying the complement set of effective field theories where there are other dynamical fields, which can have an interesting phenomenology.
• Within the latter set, we study in detail a vast class where the Holst invariant (the contraction of the curvature with the Levi-Civita antisymmetric tensor) is a dynamical pseudoscalar.