Hamiltonian Analysis of f(Q)f(Q) Gravity and the Failure of the Dirac-Bergmann Algorithm for Teleparallel Theories of Gravity

In recent years, $f(Q)$ gravity has enjoyed considerable attention in the literature and important results have been obtained. However, the question of how many physical degrees of freedom the theory propagates -- and how this number may depend on the form of the function $f$ -- has not been answered satisfactorily. In this article we show that a Hamiltonian analysis based on the Dirac-Bergmann algorithm -- one of the standard methods to address this type of question -- fails. We isolate the source of the failure, show that other commonly considered teleparallel theories of gravity are affected by the same problem, and we point out that the number of degrees of freedom obtained in Phys. Rev. D 106 no. 4, (2022) by K. Hu, T. Katsuragawa, and T. Qui (namely eight), based on the Dirac-Bergmann algorithm, is wrong. Using a different approach, we show that the upper bound on the degrees of freedom is seven. Finally, we propose a more promising strategy for settling this important question.Comment: 45 pages, 3 figues, Comments are welcom

Kinetic Field Theory: Higher-Order Perturbation Theory

We give a detailed exposition of the formalism of Kinetic Field Theory (KFT) with emphasis on the perturbative determination of observables. KFT is a statistical non-equilibrium classical field theory based on the path integral formulation of classical mechanics, employing the powerful techniques developed in the context of quantum field theory to describe classical systems. Unlike previous work on KFT, we perform the integration over the probability distribution of initial conditions in the very last step. This significantly improves the clarity of the perturbative treatment and allows for physical interpretation of intermediate results. We give an introduction to the general framework, but focus on the application to interacting $N$-body systems. Specializing the results to cosmic structure formation, we reproduce the linear growth of the cosmic density fluctuation power spectrum on all scales from microscopic, Newtonian particle dynamics alone.Comment: 59 pages, 4 figure

Local clustering of relic neutrinos with kinetic field theory

The density of relic neutrinos is expected to be enhanced due to clustering in our local neighbourhood at Earth. We introduce a novel analytical technique to calculate the neutrino overdensity, based on kinetic field theory. Kinetic field theory is a particle-based theory for cosmic structure formation and in this work we apply it for the first time to massive neutrinos. The gravitational interaction is expanded in a perturbation series and we take into account the first-order contribution to the local density of relic neutrinos. For neutrino masses that are consistent with cosmological neutrino mass bounds, our results are in excellent agreement with state-of-the-art calculations.Comment: 7 pages, 1 figur

Hamiltonian Analysis of f (ℚ) Gravity and the Failure of the Dirac–Bergmann Algorithm for Teleparallel Theories of Gravity

In recent years,f (Q) gravity has enjoyed considerable attention in the literature and important results have been obtained. However, the question of how many physical degrees of freedom the theory propagates-and how this number may depend on the form of the function f-has not been answered satisfactorily. In this article it is shown that a Hamiltonian analysis based on the Dirac-Bergmann algorithm-one of the standard methods to address this type of question-fails. The source of the failure is isolated and it is shown that other commonly considered teleparallel theories of gravity are affected by the same problem. Furthermore, it is pointed out that the number of degrees of freedom obtained in Phys. Rev. D 106 no. 4, (2022) by K. Hu, T. Katsuragawa, and T. Qui (namely eight), based on the Dirac-Bergmann algorithm, is wrong. Using a different approach, it is shown that the upper bound on the degrees of freedom is seven. Finally, a more promising strategy for settling this important question is proposed.ISSN:0015-8208ISSN:1521-397

First-order thermodynamics of Horndeski gravity

We extend to the Horndeski realm the irreversible thermodynamics description of gravity previously studied in “first generation” scalar-tensor theories. We identify a subclass of Horndeski theories as an out-of–equilibrium state, while general relativity corresponds to an equilibrium state. In this context, we identify an effective heat current, “temperature of gravity,” and shear viscosity in the space of theories. The identification is accomplished by recasting the field equations as effective Einstein equations with an effective dissipative fluid, with Einstein gravity as the equilibrium state, following Eckart’s first-order thermodynamics.ISSN:1550-7998ISSN:0556-2821ISSN:1550-236