International Journal of Geometric Methods in Modern Physics

Inflationary scenarios motivated by the minimal supersymmetric standard model (MSSM) where five scalar fields are non-minimally coupled to gravity are considered. The potential of the model and the function of non-minimal coupling are polynomials of two Higgs doublet convolutions. We show that the use of the strong coupling approximation allows to obtain inflationary parameters in the case when a combination of the four scalar fields plays a role of inflaton. Numerical calculations show that the cosmological evolution leads to inflationary scenarios fully compatible with observational data for different values of the MSSM mixing angle $\beta$.

The premetric formalism is an alternative representation of a classical field theory in which the field equations are formulated without the spacetime metric. Only the constitutive relations between the basic field variables can involve the metric of the underlying manifold. In this paper, we present a brief pedagogical review of the premetric formalism in mechanics, electromagnetism, and gravity.

We describe the freedom of choosing a square root in massive gravity from algebraic point of view. This contribution is based on the talk given by one of us (AG) at the Geometric Foundations of Gravity conference in Tartu in August 2017.

It has been suggested that single and double jets observed emanating from certain astrophysical objects may have a purely gravitational origin. We discuss new classes of pulsed gravitational wave solutions to the equation for perturbations of Ricci-flat spacetimes around Minkowski metrics, as models for the genesis of such phenomena. We discuss how these solutions are motivated by the analytic structure of spatially compact finite energy pulse solutions of the source-free Maxwell equations generated from complex chiral eigen-modes of a chirality operator. Complex gravitational pulse solutions to the linearized source-free Einstein equations are classified in terms of their chirality and generate a family of non-stationary real spacetime metrics. Particular members of these families are used as backgrounds in analyzing time-like solutions to the geodesic equation for test particles. They are found numerically to exhibit both single and double jet-like features with dimensionless aspect ratios suggesting that it may be profitable to include such backgrounds in simulations of astrophysical jet dynamics from rotating accretion discs involving electromagnetic fields.

We review the basics and the current status of the Poincaré gauge theory of gravity. The general dynamical scheme of Poincaré gauge gravity (PG) is formulated, and its physical consequences are outlined. In particular, we discuss exact solutions with and without torsion, highlight the cosmological aspects, and consider the probing of the spacetime geometry.

In a talk at the conference Geometrical Foundations of Gravity at Tartu$,$ 2017, it was suggested that the affine spacetime connection could be associated with purely fictitious forces. This leads to gravitation in a flat and smooth geometry. Fermions are found to nevertheless couple with the metrical connection and a phase gauge field. The theory is reviewed in this proceeding in a Palatini, and in a metric-affine gauge formulation.

We review the Noether Symmetry Approach as a geometric criterion to select theories of gravity. Specifically, we deal with Noether Symmetries to solve the field equations of given gravity theories. The method allows to find out exact solutions, but also to constrain arbitrary functions in the action. Specific cosmological models are taken into account.

Torsion-based modified theories of gravity, such as $f(T)$ gravity, are arguably one of the very few “true” modified gravities based on well-defined geometric structures. However, the original formulation explicitly works in a specific choice of frame, which has led to considerable amount of confusion in the literature about these theories breaking local Lorentz invariance. Pathological properties such as superluminal propagation and the lack of well-posedness of Cauchy problem were found to plague $f(T)$ gravity. Recent effort to “covariantize” $f(T)$ gravity has, however, renewed interests in this subject. In this proceeding paper, we review and discuss issues concerning the actual number of degrees of freedom in $f(T)$ gravity, and how this might relate to the aforementioned pathologies.

We derive the gravitational energy–momentum pseudotensor ${\tau }_{\lambda }^{\sigma }$ in metric $f(R)$ gravity and in teleparallel $f(T)$ gravity. In the first case, $R$ is the Ricci curvature scalar for a torsionless Levi-Civita connection; in the second case, $T$ is the curvature-free torsion scalar derived by tetrads and Weitzenböck connection. For both classes of theories the continuity equations are obtained in presence of matter. $f(R)$ and $f(T)$ are non-equivalent, but differ for a quantity $\omega (T,B)$ containing the torsion scalar $T$ and a boundary term $B$. It is possible to obtain the field equations for $\omega (T,B)$ and the related gravitational energy–momentum pseudotensor ${\tau }_{\lambda }^{\sigma }|\omega$. Finally we show that, thanks to this further pseudotensor, it is possible to pass from $f(R)$–$f(T)$ and vice versa through a simple relation between gravitational pseudotensors.

We give an overview on the status and on the perspectives of Finsler gravity, beginning with a discussion of various motivations for considering a Finslerian modification of General Relativity. The subjects covered include Finslerian versions of Maxwell’s equations, of the Klein–Gordon equation and of the Dirac equation, and several experimental tests of Finsler gravity.

The energy–momentum tensor for a particular matter component summarises its local energy–momentum distribution in terms of densities and current densities. We re-investigate under what conditions these local distributions can be integrated to meaningful global quantities. This leads us directly to a classic theorem by Max von Laue concerning integrals of components of the energy–momentum tensor, whose statement and proof we recall. In the first half of this paper, we do this within the realm of Special Relativity (SR) and in the traditional mathematical language using components with respect to affine charts, thereby focusing on the intended physical content and interpretation. In the second half, we show how to do all this in a proper differential-geometric fashion and on arbitrary spacetime manifolds, this time focusing on the group-theoretic and geometric hypotheses underlying these results. Based on this we give a proper geometric statement and proof of Laue’s theorem, which is shown to generalise from Minkowski space (which has the maximal number of isometries) to spacetimes with significantly less symmetries. This result, which seems to be new, not only generalizes but also clarifies the geometric content and hypotheses of Laue’s theorem. A series of three appendices lists our conventions and notation and summarises some of the conceptual and mathematical background needed in the main text.