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Register a new userHamiltonian formalism in Friedmann cosmology and its quantization
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We propose a Hamiltonian formalism for a generalized Friedmann-Roberson-Walker cosmology model in the presence of both a variable equation of state (EOS) parameter $w(a)$ and a variable cosmological constant $Lambda(a)$, where $a$ is the scale factor. This Hamiltonian system containing 1 degree of freedom and without constraint, gives Friedmann equations as the equation of motion, which describes a mechanical system with a variable mass object moving in a potential field. After an appropriate transformation of the scale factor, this system can be further simplified to an object with constant mass moving in an effective potential field. In this framework, the $Lambda$ cold dark matter model as the current standard model of cosmology corresponds to a harmonic oscillator. We further generalize this formalism to take into account the bulk viscosity and other cases. The Hamiltonian can be quantized straightforwardly, but this is different from the approach of the Wheeler-DeWitt equation in quantum cosmology.
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We present a superfield construction of Hamiltonian quantization with N=2 supersymmetry generated by two fermionic charges Q^a. As a byproduct of the analysis we also derive a classically localized path integral from two fermionic objects Sigma^a that can be viewed as ``square roots of the classical bosonic action under the product of a functional Poisson bracket.
An action principle that applies uniformly to any number N of supercharges is proposed. We perform the reduction to the N=0 partition function by integrating out superpartner fields. As a new feature for theories of extended supersymmetry, the canonical Pfaffian measure factor is a result of a Gaussian integration over a superpartner. This is mediated through an explicit choice of direction n^a in the theta-space, which the physical sector does not depend on. Also, we re-interpret the metric g^{ab} in the Susy algebra [D^a,D^b] = g^{ab}partial_t as a symplectic structure on the fermionic theta-space. This leads to a superfield formulation with a general covariant theta-space sector.
The unfree gauge symmetry implies that gauge variation of the action functional vanishes provided for the gauge parameters are restricted by the differential equations. The unfree gauge symmetry is shown to lead to the global conserved quantities whose on shell values are defined by the asymptotics of the fields or data on the lower dimension surface, or even at the point of the space-time, rather than Cauchy hyper-surface. The most known example of such quantity is the cosmological constant of unimodular gravity. More examples are provided in the article for the higher spin gravity analogues of the cosmological constant. Any action enjoying the unfree gauge symmetry is demonstrated to admit the alternative form of gauge symmetry with the higher order derivatives of unrestricted gauge parameters. The higher order gauge symmetry is reducible in general, even if the unfree symmetry is not. The relationship is detailed between these two forms of gauge symmetry in the constrained Hamiltonian formalism. The local map is shown to exist from the unfree gauge algebra to the reducible higher order one, while the inverse map is non-local, in general. The Hamiltonian BFV-BRST formalism is studied for both forms of the gauge symmetry. These two Hamiltonian formalisms are shown connected by canonical transformation involving the ghosts. The generating function is local for the transformation, though the transformation as such is not local, in general. Hence, these two local BRST complexes are not quasi-isomorphic in the sense that their local BRST-cohomology groups can be different. This difference in particular concerns the global conserved quantities. From the standpoint of the BRST complex for unfree gauge symmetry, these quantities are BRST-exact, while for the alternative complex, these quantities are the non-trivial co-cycles.
A Friedmann like cosmological model in Einstein-Cartan framework is studied when the torsion function is assumed to be proportional to a single $phi(t)$ function coming just from the spin vector contribution of ordinary matter. By analysing four different types of torsion function written in terms of one, two and three free parameters, we found that a model with $phi(t)=- alpha H(t) big({rho_{m}(t)}/{rho_{0c}}big)^n$ is totally compatible with recent cosmological data, where $alpha$ and $n$ are free parameters to be constrained from observations, $rho_m$ is the matter energy density and $rho_{0c}$ the critical density. The recent accelerated phase of expansion of the universe is correctly reproduced by the contribution coming from torsion function, with a deceleration parameter indicating a transition redshift of about $0.65$.
In the present paper the Yang-Mills theory in the first order formalism is studied. On classical level the first order formulation is equivalent to the standard second order description of the Yang-Mills theory. It is proven that both formulations remain equivalent on quantum level as well.
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