Related papers: Conformal coupling associated with the Noether sym…
We show that the simplest FLRW cosmological system consisting in the homogeneous and isotropic massless Einstein-Scalar system enjoys a hidden conformal symmetry under the 1D conformal group $SL(2,\mathbb{R})$ acting as Mobius…
The Noether Symmetry Approach is applied to interacting quintessence cosmology with the aim to search for exact solutions and select scalar-field self-interaction potentials. It turns out that the solutions found are compatible with the…
Non-minimal actions with matter represented by a scalar field coupled to gravity are considered in the context of a homogeneous and isotropic universe. The coupling is of the form $-\xi/2 \phi^2 R$. The possibility of successful inflation…
We investigate effects of noncommutativity of phase space generated by two scalar fields conformally coupled to curvature in FRW cosmology. We restrict deformation of minisuperspace to noncommutativity between scalar fields and between…
We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincar\'e-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincar\'e-Cartan form is…
We discuss the Hamiltonian dynamics for cosmologies coming from Extended Theories of Gravity. In particular, minisuperspace models are taken into account searching for Noether symmetries. The existence of conserved quantities gives…
We discuss geometric properties of non-Noether symmetries and their possible applications in integrable Hamiltonian systems. Correspondence between non-Noether symmetries and conservation laws is revisited. It is shown that in regular…
In this work we consider a scale-tensor theory in which the space-time is endowed with a Weyl integrable geometrical structure due to the Palatini variational method. Since the scalar field has a geometrical nature (related to…
The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…
The main objective of this article is to examine some physically viable solutions through the Noether symmetry technique in $f(R, T^{2})$ theory. For this purpose, we assume a generalized anisotropic and homogenous spacetime that yields…
The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely…
We examine the scenario of non-minimally coupled relativistic fluid and $k$-essence scalar field in a flat Friedmann-Lemaitre-Robertson-Walker universe. By adding a non-minimal coupling term in the Lagrangian level, we study the variation…
We consider a general theory of all possible quadratic, first-order derivative terms of the non-metricity tensor in the framework of Symmetric Teleparallel Geometry. We apply the Noether Symmetry Approach to classify those models that are…
For a family of Horndeski theories, formulated in terms of a generalized Galileon model, we study the integrability of the field equations in a Friedmann-Lema\^{\i}tre-Robertson-Walker spacetime. We are interested in point transformations…
A certain non-Noetherian connection between symmetry and integrability properties of nonlinear field equations in conservation-law form is studied. It is shown that the symmetry condition alone may lead, in a rather straightforward way, to…
The dynamic status of scalar fields is studied in the Hamiltonian approach to the General Relativity. We show that the conformal coupling of the scalar field violates the standard geometrical structure of the Einstein equations in GR and…
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…
There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…
Symmetries have proven useful in machine learning models, improving generalisation and overall performance. At the same time, recent advancements in learning dynamical systems rely on modelling the underlying Hamiltonian to guarantee the…
Several results related to flat Friedmann-Lema\^{\i}tre-Robertson-Walker models in the conformal (Einstein) frame of scalar-tensor gravity theories are extended. Scalar fields with arbitrary (positive) potentials and arbitrary coupling…