Stefan Zentarra

Gravitational clustering in our cosmic vicinity is expected to lead to an enhancement of the local density of relic neutrinos. We derive expressions for the neutrino density, using a perturbative approach to kinetic field theory and perturbative solutions of the Vlasov equation up to second order. Our work reveals that both formalisms give exactly the same results and can thus be considered equivalent. Numerical evaluation of the local relic neutrino density at first and second order provides some fundamental insights into the frequently applied approach oflinear responseto neutrino clustering (also known as the Gilbert equation). Against the naive expectation, including the second-order contribution does not lead to an improvement of the prediction for the local relic neutrino density but to a dramatic overestimation. This is because perturbation theory breaks down in a momentum-dependent fashion and in particular for densities well below unity.

In recent years, 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.

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.

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.

We consider a simpler geometrical formulation of General Relativity based on non-metricity, known as Coincident General Relativity. We study the ADM formulation of the theory and perform a detailed Hamiltonian analysis. We explicitly show the propagation of two physical degrees of freedom, as it should, even though the role of boundary terms and gauge conditions is significantly altered. This might represent an alternative promising new route for numerical relativity and canonical quantum gravity. We also give an outlook on the number of propagating degrees of freedom in non-linear extension of non-metricity scalar.