We discuss theories of gravity with independent metric and affine connection.
We count the parity-even Lagrangian terms of dimension up to four and give explicit bases for the independent terms that contribute to the two-point function.
We then give the decomposition of the linearised action
on a complete basis of spin projectors and consider various subclasses of MAGs.
We show that teleparallel theories can be dynamically equivalent to any metric theory of gravity and give the particle content
of those whose Lagrangian contains only dimension-two terms.
We point out the existence of a class of MAGs whose EOMs do not
admit propagating degrees of freedom.
Finally, we construct simple MAGs that contain only
a massless graviton and a state of spin/parity $2^-$ or $3^-$.
As a side result, we write the relativistic wave equation
for a spin/parity $2^-$ state.
Additionally, we perform an irreducible decomposition of torsion and nonmetricity with respect to the group of permutations and show how the basis of independent terms in the classical action can be rewritten via decomposed fields.
Poincar\'e gauge theories are a class of metric-affine theories with a metric-compatible (i.e. Lorentz) connection and with an action quadratic in curvature and torsion.
We show by an explicit one-loop calculation that this class of theories is not closed under renormalisation off-shell.
This statement extends to more general classes of metric-affine theories.
We, therefore, generalise them to include other necessary terms.
We discuss how their spectrum can be affected by quantum corrections.
We prove that at the perturbative level, all local counterterms that may affect the flat-space propagator can be reabsorbed into appropriate invertible field redefinitions.
We formally prove the existence of a quantisation procedure that makes the path integral of a general diffeomorphism-invariant theory of gravity, with fixed total spacetime volume, equivalent to that of its unimodular version. This is achieved by means of
a partial gauge fixing of diffeomorphisms together with a careful definition of the unimodular measure. The statement holds also in the presence of matter. As an explicit example, we consider scalar-tensor theories and compute the corresponding logarithmic divergences in both settings. In spite of significant differences in the coupling of
the scalar field to gravity, the results are equivalent for all couplings, including non-minimal ones.
