Hamiltonian Cosmology Research Articles

Hamiltonian cosmology of bigravity

This article is written as a review of the Hamiltonian formalism for the bigravity with de Rham–Gabadadze–Tolley (dRGT) potential, and also of applications of this formalism to the derivation of the background cosmological equations. It is demonstrated that the cosmological scenarios are close to the standard ΛCDM model, but they also uncover the dynamical behavior of the cosmological term. This term arises in bigravity regardless on the choice of the dRGT potential parameters, and its scale is given by the graviton mass. Various matter couplings are considered.

Loop quantum gravity corrections to gravitational wave dispersion

Cosmological tensor perturbations equations are derived for Hamiltonian cosmology based on Ashtekar's formulation of general relativity, including typical quantum gravity effects in the Hamiltonian constraint as they are expected from loop quantum gravity. This translates to corrections of the dispersion relation for gravitational waves. The main application here is the preservation of causality which is shown to be realized due to the absence of anomalies in the effective constraint algebra used.

Cosmological vector modes and quantum gravity effects

In contrast to scalar and tensor modes, vector modes of linear perturbations around an expanding Friedmann–Robertson–Walker universe decay. This makes them largely irrelevant for late time cosmology, assuming that all modes started out at a similar magnitude at some early stage. By now, however, bouncing models are frequently considered which exhibit a collapsing phase. Before this phase reaches a minimum size and re-expands, vector modes grow. Such modes are thus relevant for the bounce and may even signal the breakdown of perturbation theory if the growth is too strong. Here, a gauge-invariant formulation of vector mode perturbations in Hamiltonian cosmology is presented. This lays out a framework for studying possible canonical quantum gravity effects, such as those of loop quantum gravity, at an effective level. As an explicit example, typical quantum corrections, namely those coming from inverse densitized triad components and holonomies, are shown to increase the growth rate of vector perturbations in the contracting phase, but only slightly. Effects at the bounce of the background geometry can, however, be much stronger.

Third quantization formalism for Hamiltonian cosmologies

Within the ADM technique of Hamiltonian cosmology, in the case of Bianchi class A models, we introduce a Fock-like, field theoretical approach to the description of quantum cosmology. We then calculate the total transition amplitude between two quantum states of the state functional of the ADM geometry.

Hamiltonian cosmology and gravitational solitons: A variational outlook

A general procedure is applied for finding the possible variational principle of a given nonlinear system of partial differential equations. In particular, attention is focused on Hamiltonian homogeneous cosmologies and gravitational solitons. In the first case, it is found that a variational principle exists if and only if the model is of class A, thus complementing previous results of MacCallum and Taub. In the second case, it is shown that the pertinent system arises from a variational principle; furthermore, the explicit form of the Lagrangian is given. Owing to the structure of the Lagrangian an outstanding first integral is determined.

Canonical quantization of diagonal Bianchi V models filled with a perfect fluid

Diagonal Bianchi V cosmological models as well as their isotropic counterparts, the open Friedmann-Robertson-Walker (FRW) models, filled with a perfect fluid with an equation of state of the type p = (γ − 1)ϱ(γ = constant = 1, 4 3 or 2) are quantized in the framework of an ADM-type canonical quantization scheme developed by Demaret and Moncrief. Sneddon's supplementary constraint introduced to extend the methods of Hamiltonian cosmology valid for class A Bianchi models, to class B models is explicitly taken into account. Bianchi V models are non-singular apart from a set of measure of zero comprising open FRW models as well as Bianchi models filled with a fluid with a stiff equation of state ( p = ϱ), a result similar to that obtained previously for Bianchi I and IX models.

Hamiltonian cosmology: a further investigation

In a recent paper, Ryan (see J. Math. Phys., vol.15, p.812 (1974)) claimed that Hamiltonian cosmology was dead. The present paper investigates the illness and makes some attempts at reviving the subject. It is found that in certain cases, the addition of another constraint to the variational principle will enable the correct field equations to be obtained. These results are then compared with some results for asymptotically flat spaces.

Hamiltonian cosmology: Death and transfiguration

Following work of MacCallum and Taub, we show that for Bianchi-type universes of Ellis-MacCallum class B (Bianchi types II, III, IV, V, VIh≠−1, VIIh=0) Hamiltonian cosmology breaks down. We construct a quasi-Hamiltonian theory for these models.

Hamiltonian cosmology

A simple polynomial Hamiltonian is given for type VIII and IX vacuum cosmologies. This Hamiltonian also describes solutions with time-like homogeneous 3-surfaces, and so suggests quantized versions which incolce fluctuations of 3-space signature and topology.