The Hamiltonian of Asymptotically Friedmann-Lemaître-Robertson-Walker Spacetimes

Abstract

We obtain the correct hamiltonian which describes the dynamics of classes of asymptotic open Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, which includes Tolman geometries. We calculate the surface term that has to be added to the usual hamiltonian of General Relativity in order to obtain an improved hamiltonian with well defined functional derivatives. For asymptotic flat FLRW spaces, this surface term is zero, but for asymptotic negative curvature FLRW spaces it is not null in general. In the particular case of the Tolman geometries, they vanish. The surface term evaluated on a particular solution of Einstein's equations may be viewed as the "energy" of this solution with respect to the FLRW spacetime they approach asymptotically. Our results are obtained for a matter content described by a dust fluid, but they are valid for any perfect fluid, including the cosmological constant. PACS number(s): 04.20.Cv., 04.20.Me

Realistic equations of state for the primeval universe

“…The plot of ρ(kT ) is shown in Figure 1 The complete EOS for the pressure p comes from the substitution of Eqs. ( 27), (4) and (32) into (24). Figure 2 shows the plot of function p = p(kT ).…”

“…Let us admit that the proposed EOS, Eqs. (24) and (25), are valid during all the PNS period. A first application to cosmology can done through the usual parametrization…”

“…This self-interaction is chosen so as to produce just those features which are necessary to describe the early accelerated regime [10]. The phenomenological explanations for the present-day acceleration include, among others, (i) the quintessence models [14,15,16,17,18], which roughly follow the same lines of the inflationary theory; (ii) models of matter and darkenergy unification via Chapligyn-like equations of state (EOS) [19] or through equations of the Van der Walls type [20,21]; (iii) models of mass-varying-neutrino type, which couple neutrinos to a quintessence scalar field [22]; (iv) models introducing interactions in the energy conservation equation [23,24].…”

Discrete Neumann boundary value problem for a nonlinear equation with singular ϕ-Laplacian

“…For other results on the problems in some FLRW spacetimes, see [26][27][28][29] and the references therein.…”