A generic f(R,H) metric-affine gravity theory is shown to reduce on-shell to a metric scalar-tensor theory, with the kinetic function and potential given explicitly.
Of course, the third possibility is of no physical interest, so from hereinafter we shall disregard it, assuming that only the first two possibilities are valid
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On the role of the Parity Violating Hojman--Holst term in Gravity Theories
A generic f(R,H) metric-affine gravity theory is shown to reduce on-shell to a metric scalar-tensor theory, with the kinetic function and potential given explicitly.