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Register a new userA New Representation of the Field Equations of Quadratic Metric-Affine Gravity
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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 present two conjectures on the new types of solutions of QMAG which the ansatz presented in this paper will hopefully enable us to prove.
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We give a self-contained introduction into the metric-affine gauge theory of gravity. Starting from the equivalence of reference frames, the prototype of a gauge theory is presented and illustrated by the example of Yang-Mills theory. Along the same lines we perform a gauging of the affine group and establish the geometry of metric-affine gravity. The results are put into the dynamical framework of a classical field theory. We derive subcases of metric-affine gravity by restricting the affine group to some of its subgroups. The important subcase of general relativity as a gauge theory of translations is explained in detail.
We classify the metric-affine theories of gravitation, in which the metric and the connections are treated as independent variables, by use of several constraints on the connections. Assuming the Einstein-Hilbert action, we find that the equations for the distortion tensor (torsion and non-metricity) become algebraic, which means that those variables are not dynamical. As a result, we can rewrite the basic equations in the form of Riemannian geometry. Although all classified models recover the Einstein gravity in the Palatini formalism (in which we assume there is no coupling between matter and the connections), but when matter field couples to the connections, the effective Einstein equations include an additional hyper energy-momentum tensor obtained from the distortion tensor. Assuming a simple extension of a minimally coupled scalar field in metric-affine gravity, we analyze an inflationary scenario. Even if we adopt a chaotic inflation potential, certain parameters could satisfy observational constraints. Furthermore, we find that a simple form of Galileon scalar field in metric-affine could cause G-inflation.
In this paper we review the Myrzakulov Gravity models (MG-N, with $mathrm{N = I, II, ldots, VIII}$) and derive their respective metric-affine generalizations (MAMG-N), discussing also their particular sub-cases. The field equations of the theories are obtained by regarding the metric tensor and the general affine connection as independent variables. We then focus on the case in which the function characterizing the aforementioned metric-affine models is linear and consider a Friedmann-Lema^{i}tre-Robertson-Walker background to study cosmological aspects and applications.
We set the foundation and formulate the Perfect (Ideal) Hyperfluid. The latter represents the natural generalization of the usual perfect fluid structure where now the microscopic characteristics of matter (spin, shear, dilation) are also taken into account, sourcing a non-Riemannian arena (i.e spacetime torsion and non-metricity) for Metric-Affine Gravity. We derive the energy tensors of this Hyperfluid structure and subsequently present the conservation laws obeyed by them. Finally, we consider a Cosmological application of this Perfect Hyperfluid and classify some possible forms of this fluid structure.
The intriguing choice to treat alternative theories of gravity by means of the Palatini approach, namely elevating the affine connection to the role of independent variable, contains the seed of some interesting (usually under-explored) generalizations of General Relativity, the metric-affine theories of gravity. The peculiar aspect of these theories is to provide a natural way for matter fields to be coupled to the independent connection through the covariant derivative built from the connection itself. Adopting a procedure borrowed from the effective field theory prescriptions, we study the dynamics of metric-affine theories of increasing order, that in the complete version include invariants built from curvature, nonmetricity and torsion. We show that even including terms obtained from nonmetricity and torsion to the second order density Lagrangian, the connection lacks dynamics and acts as an auxiliary field that can be algebraically eliminated, resulting in some extra interactions between metric and matter fields.
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