Noether Symmetry

This research area investigates the application of Noether symmetry principles to modified gravity theories such as f(T) gravity, Eddington-inspired Born–Infeld gravity, and non-minimal derivative coupling models. The aim is to leverage Noether (and Noether gauge) symmetries to identify conserved quantities, reduce the dynamical system’s complexity, and determine plausible forms of functional potentials and couplings. This methodology aids in constructing exact cosmological solutions consistent with observed cosmic acceleration and provides a systematic framework to single out physically viable models within extended gravity setups.

This field focuses on the determination and classification of Noether (gauge) symmetries admitted by geodesic Lagrangians corresponding to various spacetime geometries, such as plane waves, non-static plane symmetric metrics, and Bianchi models within classical general relativity. The identification of these symmetries facilitates the derivation of conserved quantities, reducing the complexity of geodesic equations and providing avenues for exact integrations. It also connects continuous symmetries to fundamental geometric properties such as Killing vectors and homothetic vectors, enriching the understanding of spacetime symmetries beyond isometries.

This thematic area encompasses comprehensive reviews and pedagogical presentations aimed at clarifying the implications and applications of Noether’s first and second theorems, particularly in global and local gauge symmetries, the algebra of asymptotic symmetries, and the generation of associated conserved densities. These works demystify the geometric and algebraic underpinnings of symmetries in classical and quantum field theories, expose subtleties such as boundary contributions, and build foundational understanding that supports the effective use of Noether symmetry methods across physics disciplines.