Noether Symmetries as a geometric criterion to select theories of gravity

Abstract

We review the {\it 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.

arXiv comment16 pages, accepted for publication in the International Journal of Geometric Methods in Modern Physics

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Cited by in corpus (37)

• Noether symmetries in Symmetric Teleparallel Cosmology
• Minisuperspace quantum cosmology in $f(Q)$ gravity
• Exact Spherically Symmetric Solutions in Modified Teleparallel gravity
• Constraining Non-local Gravity by S2 star orbits
• Early and late time cosmology: the $f(R)$ gravity perspective
• Late-time constraints on modified Gauss-Bonnet cosmology
• Spherical and cylindrical solutions in f (T) gravity by Noether Symmetry Approach
• Equivalence of non-minimally coupled cosmologies by Noether symmetries
• Classification of Teleparallel Horndeski Cosmology via Noether Symmetries
• Noether symmetries and boundary terms in extended Teleparallel gravity cosmology
• Non-Local Curvature and Gauss-Bonnet Cosmologies by Noether Symmetries
• Exact spherically symmetric solutions in modified Gauss-Bonnet gravity from Noether symmetry approach
• The Noether Bessel Hagen Symmetry Approach for Dynamical Systems
• Non-Local Curvature Gravity Cosmology via Noether Symmetries
• Ghost and Laplacian Instabilities in the Teleparallel Horndeski Gravity
• Addressing Cosmological Tensions by Non-Local Gravity
• Testing non-local gravity by clusters of galaxies
• Minisuperspace Quantum Cosmology in Metric and Affine Theories of Gravity
• Conservation laws and Exact Solutions in Brans-Dicke Cosmology with a Scalar Field
• Noether Symmetries in $f(T,T_G)$ Cosmology
• Exploring departures from Schwarzschild black hole in $f(R)$ gravity
• Quantum cosmology with symmetry analysis for quintom dark energy model
• Quantum cosmology for non-minimally coupled scalar field in FLRW space-time: A symmetry analysis
• The Noether Symmetry Approach: Foundation and applications. The case of scalar-tensor Gauss-Bonnet gravity
• A Study of the Approximate Singular Lagrangian -- Conditional Noether Symmetries and First Integrals
• Noether Symmetry analysis in Chameleon Field Cosmology
• Multiscalar-torsion Cosmology: Exact and Analytic Solutions from Noether Symmetries
• Noether Symmetry Approach in Eddington-inspired Born-Infeld gravity
• Linearized Field Equations and Extra Force in $f(R,{\mathbf{T}}^{(n)})$ Extended Gravity
• Testing non-local gravity through Ultra-Diffuse Galaxies kinematics
• Multiscalar field cosmological model and possible solutions using Noether symmetry approach
• Vacuum quantum effects on Lie groups with bi-invariant metrics
• Friedmann's Universe Controlled by Gauss-Bonnet Modified Gravity
• Exact FLRW cosmological solutions via invariants of the symmetry groups
• Dwarf galaxies in non-local gravity
• Generalized Noether Theorem for Gauss-Bonnet Cosmology
• Noether gauge symmetry approach applying for the non-minimally coupled gravity to the Maxwell field