Related papers: Selection Rules in Minisuperspace Quantum Cosmolog…
Noether symmetry of F(R) theory of gravity in vacuum or in matter dominated era yields three-half power law of R. We show that this particular curvature invariant term is very special in the context of isotropic and homogeneous cosmological…
The paper deals with a cosmological model containing two scalar fields which can be considered as an extension of the Brans-Dicke scalar field model. Due to highly coupled non linear field equations, Noether Symmetry analysis has been…
We analyze the cosmology of a general Scalar-Tensor theory which encompasses generalized Brans-Dicke theory, Gauss-Bonnet gravity, non-minimal derivative gravity, generalized Galileon gravity and also the general k-essence type models.…
In the framework of f(R) scalar-tensor cosmology, we use the Noether symmetry approach to find the cosmological models consistent with the Noether symmetry. We obtain the functions f(R) and H(a), or the corresponding differential equations,…
We consider curvature-teleparallel $F(R,T)$ gravity, where the gravitational Lagrangian density is given by an arbitrary function of the Ricci scalar $R$ and the torsion scalar $T$. Using the Noether Symmetry Approach, we show that the…
It has recently been shown that, in the vicinity of their event horizons, black holes exhibit an infinite-dimensional symmetry. This symmetry captures relevant physical information about the black hole, and in particular about its…
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 discuss the application of the Hojman's Symmetry Approach for the determination of conservation laws in Cosmology, which has been recently applied by various authors in different cosmological models. We show that Hojman's method for…
In this paper, we investigate the newly developed $f(R,\mathbf{T}^2)$ theory ($R$ is the Ricci scalar and $\mathbf{T}^2=T_{\alpha\beta}T^{\alpha\beta},~T _{\alpha\beta}$ demonstrates the energy-momentum tensor) to explore some viable…
The standard $\Lambda$CDM model of cosmology is formulated as a simple modified gravity coupled to a single scalar field ("darkon") possessing a non-trivial hidden nonlinear Noether symmetry. The main ingredient in the construction is the…
Recent developments in gravitational path integrals indicate that the nonperturbative physical Hilbert space of a closed universe is one-dimensional within each superselection sector. This raises a basic puzzle: how can a unique…
It is well known that the Noether symmetry approach proves to be very useful not only to fix physically viable cosmological models but also to reduce dynamics and achieve exact solutions. In this work, We examine a formal framework of…
A model for a spatially flat homogeneous and isotropic Universe whose gravitational sources are a pressureless matter field and a tachyon field non-minimally coupled to the gravitational field is analyzed. Noether symmetry is used to find…
Swampland conjecture has been recently proposed to connect early time cosmological models with the string landscape, and then to understand if related scalar fields and potentials can come from some fundamental theory in the high energy…
We examine the assumptions behind Noether's theorem connecting symmetries and conservation laws. To compare classical and quantum versions of this theorem, we take an algebraic approach. In both classical and quantum mechanics, observables…
This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether's theorem. It…
We extend Noether's theorem to the setting of multisymplectic geometry by exhibiting a correspondence between conserved quantities and continuous symmetries on a multi-Hamiltonian system. We show that a homotopy co-momentum map interacts…
Noether's theorem provides a powerful link between continuous symmetries and conserved quantities for systems governed by some variational principle. Perhaps unfortunately, most dynamical systems of interest in neuroscience and artificial…
We disscuss some geometric aspects of the concept of non-Noether symmetry. It is shown that in regular Hamiltonian systems such a symmetry canonically leads to a Lax pair on the algebra of linear operators on cotangent bundle over the phase…
A general approach is presented for quantizing a metric nonlinear system on a manifold of constant curvature. It makes use of a curvature dependent procedure which relies on determining Noether symmetries from the metric. The curvature of…