Aspects of the polynomial affine model of gravity in three dimensions

The polynomial affine gravity is a model that is built up without the explicit use of a metric tensor field. In this article we reformulate the three-dimensional model and, given the decomposition of the affine connection, we analyse the consistently truncated sectors. Using the cosmological ansatz for the connection, we scan the cosmological solutions on the truncated sectors. We discuss the emergence of different kinds of metrics.

Rotating Kerr-Newman space-times in metric-affine gravity

We present new rotating vacuum configurations endowed with both dynamical torsion and nonmetricity fields in the framework of Metric-Affine gauge theory of gravity. For this task, we consider scalar-flat Weyl-Cartan geometries and obtain an axisymmetric Kerr-Newman solution in the decoupling limit between the orbital and the spin angular momentum. The corresponding Kerr-Newman-de Sitter solution is also compatible with a cosmological constant and additional electromagnetic fields.

Interiors of Terrestrial Planets in Metric-Affine Gravity

Using a semiempirical approach, we show that modified gravity affects the internal properties of terrestrial planets, such as their physical characteristics of a core, mantle, and core–mantle boundary. We also apply these findings for modeling a two-layer exoplanet in Palatini f(R) gravity.

Elements of the Metric–Affine gravity I: Aspects of F(R) theories reductions and the topologically massive gravity

Some classical aspects of Metric–Affine Gravity are reviewed in the context of the [Formula: see text] type models (polynomials of degree [Formula: see text] in the Riemann tensor) and the topologically massive gravity. At the nonperturbative level, we explore the consistency of the field equations when the [Formula: see text] models are reduced to a Riemann–Christoffel (RCh) space–time, either via a Riemann–Cartan (RC) space or via an Einstein–Weyl (EW) space. It is well known for the case [Formula: see text] that any path or reduction “classes” via RC or EW leads to the same field equations with the exception of the [Formula: see text] theories for [Formula: see text]. We verify that this discrepancy can be solved by imposing nonmetricity and torsion constraints. In particular, we explore the case [Formula: see text] for the interest in expected physical solutions as those of conformally flat class. On the other hand, the symmetries of the topologically massive gravity are reviewed, as the physical content in RC and EW scenarios. The appearance of a nonlinearly modified selfdual model in RC and existence of many nonunitary degrees of freedom in EW with the suggestion of a modified model for a massive gravity which cure the unphysical propagations shall be discussed.

Maxwell-modified metric affine gravity

We present a gauge formulation of the special affine algebra extended to include an antisymmetric tensorial generator belonging to the tensor representation of the special linear group. We then obtain a Maxwell modified metric affine gravity action with a cosmological constant term. We find the field equations of the theory and show that the theory reduces to an Einstein-like equation for metric affine gravity with the source added to the gravity equations with cosmological constant $$\mu $$ μ contains linear contributions from the new gauge fields. The reduction of the Maxwell metric affine gravity to Riemann–Cartan one is discussed and the shear curvature tensor corresponding to the symmetric part of the special linear connection is identified with the dark energy. Furthermore, the new gauge fields are interpreted as geometrical inflaton vector fields which drive accelerated expansion.

Observational constraints in metric-affine gravity

We derive the main classical gravitational tests for a recently found vacuum solution with spin and dilation charges in the framework of Metric-Affine gauge theory of gravity. Using the results of the perihelion precession of the star S2 by the GRAVITY collaboration and the gravitational redshift of Sirius B white dwarf we constrain the corrections provided by the torsion and nonmetricity fields for these effects.