We consider the most general 11 parameter parity even quadratic Metric-Affine Theory whose action consists of the usual Einstein-Hilbert plus the 11 quadratic terms in torsion, non-metricity as well as their mixing. By following a certain procedure and using a simple trick we are able to find the unique solution of the affine connection in terms of an arbitrary hypermomentum. Given a fairly general non-degeneracy condition our result provides the exact form of the affine connection for all types of matter. Subsequently we compute the forms of torsion and non-metricity in terms of their sources (hypermomentum tensor) and also express the metric field equations in effectively Einstein's GR with modified source terms that depend on the hypermomentum and its derivatives. We show that in the absence of matter the Theory always reduces to GR. Finally we generalize our result and find the form of the connection for a wider class of quadratic Theories.
In this work we study the stability of the four vector irreducible pieces of the torsion and the nonmetricity tensors in the general quadratic metric-affine Lagrangian in 4 dimensions. The goal will be to elucidate under which conditions the spin-1 modes associated to such vectors can propagate in a safe way, together with the graviton. This highly constrains the theory reducing the parameter space of the quadratic curvature part from 16 to 5 parameters. We also study the sub-case of Weyl-Cartan gravity, proving that the stability of the vector sector is only compatible with an Einstein-Proca …
We extend the results of antecedent literature on quadratic Metric-Affine Gravity by studying a new quadratic gravity action in vacuum which, besides the usual (non-Riemannian) Einstein-Hilbert contribution, involves all the parity even quadratic terms in torsion and non-metricity plus a Lagrangian that is quadratic in the field-strengths of the torsion and non-metricity vector traces. The theory result to be equivalent, on-shell, to a Vector-Tensor theory. We also discuss the sub-cases in which the contribution to the Lagrangian quadratic in the field-strengths of the torsion and non-metricit…
We consider the most general Quadratic Metric-Affine Gravity setup in the presence of generic matter sources with non-vanishing hypermomentum. The gravitational action consists of all $17$ quadratic invariants (both parity even and odd) in torsion and non-metricity as well as their mixings, along with the terms that are linear in the curvature namely the Ricci scalar and the totally antisymmetric Riemann piece. Adding also a matter sector to the latter we first obtain the field equations for the generalized quadratic Theory. Then, using a recent Theorem, we successfully find the exact form of …
We investigate the cosmological aspects of the most general parity preserving Metric-Affine Gravity theory quadratic in torsion and non-metricity in the presence of a cosmological hyperfluid. The equations of motion are obtained by varying the action with respect to the metric and the independent affine connection. Subsequently, considering a Friedmann-Lemaître-Robertson-Walker background, we derive the most general form of the modified Friedmann equations for the full quadratic theory. We then focus on a characteristic sub-case involving only two quadratic contributions given in terms of tors…
We derive the exact gravitational wave solutions in a general class of quadratic metric-affine gauge gravity models. The Lagrangian includes all possible linear and quadratic invariants constructed from the torsion, nonmetricity and the curvature. The ansatz for the gravitational wave configuration and the properties of the wave solutions are patterned following the corresponding ansatz and the properties of the plane-fronted electromagnetic wave.
In the general framework of Metric-Affine theories of gravity, where the metric and the connection are independent variables, we consider actions quadratic in the Ricci scalar curvature and the Holst invariant (the contraction of the Riemann curvature with the Levi-Civita antisymmetric tensor) coupled non-minimally to a scalar field. We study the profile of the equivalent effective metric theory, featuring an extra dynamical pseudoscalar degree of freedom, and show that it reduces to an effective single-field inflationary model. We analyze in detail the inflationary predictions and find that t…
In this review we consider the quadratic Metric-Affine Gauge gravity Lagrangian, which contains all the algebraic invariants up to quadratic order in torsion, nonmetricity and curvature. The goal will be to collect the known exact solutions for this theory that describe the propagation of a gravitational wave and some useful properties. We concentrate on solutions whose connections are different from the Levi-Civita one and provide also the extension of already known axial torsion solutions to more general Lagrangians. At the end, we will briefly discuss colliding waves and Riemannian solution…
We deal with quadratic metric-affine gravity (QMAG), which is an alternative theory of gravity and present a new explicit representation of the field equations of this theory. In our previous work we found new explicit vacuum solutions of QMAG, namely generalised pp-waves of parallel Ricci curvature with purely tensor torsion. Here we do not make any assumptions on the properties of torsion and write down our field equations accordingly. We present a review of research done thus far by several authors in finding new solutions of QMAG and different approaches in generalising pp-waves. We presen…
We reveal the existence of a certain hidden symmetry in general ghost-free scalar-tensor theories which can only be seen when generalizing the geometry of the spacetime from Riemannian. For this purpose, we study scalar-tensor theories in the metric-affine (Palatini) formalism of gravity, which we call scalar-metric-affine theories for short, where the metric and the connection are independent. We show that the projective symmetry, a local symmetry under a shift of the connection, can provide a ghost-free structure of scalar-metric-affine theories. The ghostly sector of the second-order deriva…
In (2+1)-dimensional pure gravity with cosmological constant, the dynamics of double torus universe with pinching parameter is investigated. Each mode of affine stretching deformation is illustrated in the context of horizontal foliation along the holomorphic quadratic differential. The formulation of the Einstein Hilbert action for the parameters of the affine stretching is developed. Then the dynamics along one holomorphic quadratic differential will be solved concretely.
Using numerical methods, we investigate the absorption properties of a family of nonsingular solutions {which arise in different metric-affine theories, such as quadratic and Born-Infeld gravity.} These solutions continuously interpolate between Schwarzschild black holes and naked solitons with wormhole topology. The resulting spectrum is characterized by a series of quasibound states excitations, associated with the existence of a stable photonsphere.
