On the degrees of freedom count on singular phase space submanifolds

Abstract

I discuss singular loci in the phase spaces of theories which lack globally well-defined numbers of dynamical modes. This is a topic which appears quite often in the recent literature on modified gravity. In particular, there were discussions about $R^2$ gravity around Minkowski space. It is a relatively simple case, and still there were some confusions. It clearly shows that one should be very accurate when trying to understand a potentially problematic theory through perturbations around a simply looking background. At the same time, many modern teleparallel approaches are laden with even more severe issues. Therefore, it is a topic which is certainly worth carefully thinking about.

arXiv comment22 pages; minor changes; the final version

References in corpus (30)

• Theoretical Aspects of Massive Gravity
• Generalization of the Proca Action
• Mimetic Dark Matter
• Vector Inflation
• Degrees of freedom of $f(T)$ gravity
• Aspects of Quadratic Gravity
• On the recently proposed Mimetic Dark Matter
• Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature
• Disformal Transformations, Veiled General Relativity and Mimetic Gravity
• Beyond generalized Proca theories
• Cosmological perturbations in modified teleparallel gravity models
• Vector theories in cosmology
• Hamiltonian formalism for f(T) gravity
• Local symmetries and physical degrees of freedom in $f(T)$ gravity: a Dirac Hamiltonian constraint analysis
• Hamiltonian analysis of Poincaré gauge theory scalar modes
• Perturbations in Non-Flat Cosmology for $f(T)$ gravity
• Foundational issues in f(T) gravity theory
• Non-trivial Minkowski backgrounds in f(T) gravity
• Linear perturbations in vector inflation and stability issues
• The effective field theory approach to the strong coupling issue in $f(T)$ gravity
• On the health of a vector field with (R A^2)/6 coupling to gravity
• Noether Identities and Gauge-Fixing the Action for Cosmological Perturbations
• Revisiting the cuscuton as a Lorentz-violating gravity theory
• Lorentz gauge-invariant variables in torsion-based theories of gravity
• Disforming to Conformal Symmetry
• On the role of constraints and degrees of freedom in the Hamiltonian formalism
• The Variational principle, Conformal and Disformal transformations, and the degrees of freedom
• New Dynamical Degrees of Freedom from Invertible Transformations
• Degrees of Freedom in modified Teleparallel Gravity
• Massless Rarita-Schwinger equations: Half and three halves spin solution

Cited by in corpus (4)

• Critical reassessment of the restricted Weyl symmetry
• Weak Gravity Limit in Newer General Relativity
• More on Bianchi I spacetimes and f(T) gravity
• Testing the Starobinsky model of inflation with resonant cavities