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The Noether-Bessel-Hagen theorem can be considered a natural extension of Noether Theorem to search for symmetries. Here, we develop the approach for dynamical systems introducing the basic foundations of the method. Specifically, we…
We discuss some of the issues which we encounter when we try to invoke the scalar-tensor theories of gravitation as a theoretical basis of quintessence. One of the advantages of appealing to these theories is that they allow us to implement…
Noether invariance in statistical mechanics provides fundamental connections between the symmetries of a physical system and its conservation laws and sum rules. The latter are exact identities that involve statistically averaged forces and…
We give details and derivations for the Noether invariance theory that characterizes the spatial equilibrium structure of inhomogeneous classical many-body systems, as recently proposed and investigated for bulk systems [F. Samm\"uller…
Scalar fields with inverse power-law effective potentials may provide a negative pressure component to the energy density of the universe today, as required by cosmological observations. In order to be cosmologically relevant today, the…
Phenomenological implications of the Mimetic Tensor-Vector-Scalar theory (MiTeVeS) are studied. The theory is an extension of the vector field model of mimetic dark matter, where a scalar field is also incorporated, and it is known to be…
In this paper, we present the Noether symmetries of locally rotationally symmetric Bianchi type I (LRS BI), an anisotropic model, in the context of the teleparallel gravity. We study a certain modified teleparallel theory based on the…
The present study deals with the inhomogeneous plane symmetric models in scalar - tensor theory of gravitation. We used symmetry group analysis method to solve the field equations analytically. A new class of similarity solutions have been…
We investigate cosmological models in a recently proposed geometrical theory of gravity, in which the scalar field appears as part of the space-time geometry. We extend the previous theory to include a scalar potential in the action. We…
Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…
We consider a theory of gravity with a hidden extra-dimension and metric-dependent torsion. A set of physically motivated constraints are imposed on the geometry so that the torsion stays confined to the extra-dimension and the…
Cosmological soft theorems (or consistency relations) provide a powerful probe for the physics of inflation. These relations rely on minimal assumptions and hold very generally. Consequently, any violation of these relations would rule out…
The corrections to the cosmological models induced by non-minimal coupling between scalar field and torsion are considered. To determine these corrections in explicit form, the power-law parametrization of these corrections are proposed.…
We discuss conformal issues of pure and extended teleparallel gravity. In particular, we present formulations of conformal transformation in teleparallel gravity. Furthermore, we propose conformal scalar and gauge field theories in…
In this paper we generalize our previous results on spin connection for the linear scalar cosmological perturbation in $f(T)$ theory to wider class of theories which includes a scalar field $\Phi$ non-minimally coupled to torsion, and…
The present work is devoted to investigate the Noether symmetries of the locally rotationally symmetric Bianchi type I space time in $f(T,B)$ gravity theory which depends on the torsion scalar $T$ and the boundary term $B$. In this theory,…
Teleparallel gravity theories employ a tetrad and a Lorentz spin connection as independent variables in their covariant formulation. In order to solve their field equations, it is helpful to search for solutions which exhibit certain…
We consider modified teleparallel gravity, (f(T) gravity), as a framework to explain the present accelerated expansion of the universe. The matter component is assumed to be cold dark matter. To find the explicit form of the function $f$,…
A generalized scalar-tensor theory is investigated whose cosmological term depends on both a scalar field and its time derivative. A correspondence with solutions of five-dimensional Space-Time-Matter theory is noted. Analytic solutions are…
The torsion is shown to be vitally important in the explanation of the evolution of the universe in a large class of gravitational theories containing quadratic terms of curvature and torsion. The cosmological solutions with homogeneous and…