Noether currents in theories with higher derivatives and theories with differential field transformation in action (DFTA)

Abstract

The article is devoted to the investigation of the Noether currents and integrals of motion in the special subclass of theories with higher field derivatives -- theories under differential field transformations in action (DFTA). Under fairly general assertions, we derive a simple representation for the integrals as sums of "old" integrals of motion, terms, that vanishes on the "old" equations of motion and surface integrals. We show that for some cosmological theories of that kind with high order derivatives the last contribution can violate gauge invariance, specifically, diffeomorphisms. Then we investigate ambiguity of the Noether procedure for higher derivative theories and fix it in the way the problem resolves in quite general setting. The obtained results are discussed for the several extensions of the General Relativity, which are obtained by DFTA, in particular, for mimetic, disformal and Regge-Teitelboim theories of gravity.

References in corpus (18)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• Cosmology with Mimetic Matter
• Mimetic $F(R)$ gravity: inflation, dark energy and bounce
• Disformal Transformations, Veiled General Relativity and Mimetic Gravity
• Ghost-Free $F(R)$ Gravity with Lagrange Multiplier Constraint
• On the quantisation of gravity by embedding spacetime in a higher dimensional space
• New Modified Mimetic Gravity
• Embeddings for Schwarzschild metric: classification and new results
• Cosmology in Mimetic SU(2) Gauge Theory
• On covariant phase space methods
• Forms of action for perfect fluid in General Relativity and mimetic gravity
• Non-relativistic limit of embedding gravity as General Relativity with dark matter
• Modifications of gravity via differential transformations of field variables
• Energy-Momentum of the Gravitational Field: Crucial Point for Gravitation Physics and Cosmology
• Hamilton-Jacobi approach for Regge-Teitelboim cosmology
• Gravitational energy in the framework of embedding and splitting theories
• Energy-momentum pseudotensor and superpotential for generally covariant theories of gravity of general form