Antonino Marciano
This brief article sums up results obtained in arXiv:0911.2653, which develops a constrained SU(2) lattice gauge theory in the "dipole" approximation. This is a further step toward the issue of a (inhomogeneous) loop quantum cosmology and its merging into loop quantum gravity.
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We have investigated an inhomogeneous Bianchi type-I cosmological model with electromagnetic field based on Lyra geometry. A new class of exact solutions have been obtained by considering the potentials of metric and displacement field are functions of coordinates t and x. The physical behavior of the obtained model is discussed.
There are investigated such cosmological models which instead of the usual spatial homogeneity property only fulfil the condition that in a certain synchronized system of reference all spacelike sections t = const. are homogeneous manifolds. This allows time-dependent changes of the BIANCHI type. Discussing differential geometrical theorems it is shown which of them are permitted. Besides the trivial case of changing into type I there exist some possible changes between other types. However, physical reasons like energy inequalities partially exclude them.
Inhomogeneous Bianchi type-I cosmological model with electro-magnetic field based on Lyra geometry is investigated. Using separated method, the Einstein field equations have been solved analytically with the aid of Mathematica programm. A new class of exact solutions have been obtained by considering the potentials of metric and displacement field are functions of coordinates t and x. We have assumed that F(12) is the only non-vanishing component of electro-magnetic field tensor F(ij). The Maxwells equations show that F(12) is the function of x alone whereas the magnetic permeability is the fu…
We develop the "triangulated" version of loop quantum cosmology, recently introduced in the literature. We focus on the "dipole" cosmology, where space is a three-sphere and the triangulation is formed by two tetrahedra. We show that the discrete fiducial connection has a simple and appealing geometrical interpretation and we correct the ansatz on the relation between the model variables and the Friedmann-Robertson-Walker scale factor. The modified ansatz leads to the convergence of the Hamiltonian constraint to the continuum one. We then ask which degrees of freedom are captured by this model…
The quantization scheme is suggested for a spatially inhomogeneous 1+1 Bianchi I model. The scheme consists in quantization of the equations of motion and gives the operator (so-called quasi-Heisenberg) equations describing an explicit evolution of a system. Some particular gauge suitable for quantization is proposed. The Wheeler-DeWitt equation is considered in the vicinity of zero scale factor and it is used to construct a space, where the quasi-Heisenberg operators act. Spatial discretization as a UV regularization procedure is suggested for the equations of motion.
Space-times which allow a slicing into homogeneous spatial hypersurfaces generalize the usual Bianchi models. One knows already that in these models the Bianchi type may change with time. Here we show which of the changes really appear. To this end we characterize the topological space whose points are the 3-dimensional oriented homogeneous Riemannian manifolds; locally isometric manifolds are considered as same.
Non-variational scalar field cosmology: Exact Bianchi I solutions for near-minimal scalar fields
本研究针对非变分近最小标量场耦合爱因斯坦方程，推导出四个精确Bianchi I解，涵盖多种奇点及循环行为，并发现大撕裂解在空间非均匀扰动下稳定，而振荡解不稳定。
The Gowdy cosmologies provide a suitable arena to further develop Loop Quantum Cosmology, allowing the presence of inhomogeneities. For the particular case of Gowdy spacetimes with the spatial topology of a three-torus and a content of linearly polarized gravitational waves, we detail a hybrid quantum theory in which we combine a loop quantization of the degrees of freedom that parametrize the subfamily of homogeneous solutions, which represent Bianchi I spacetimes, and a Fock quantization of the inhomogeneities. Two different theories are constructed and compared, corresponding to two differe…
Using a qualitative analysis based on the Hamiltonian formalism and the orthonormal frame representation we investigate whether the chaotic behaviour which occurs close to the initial singularity is still present in the far future of Bianchi VIII models. We describe some features of the vacuum Bianchi VIII models at late times which might be relevant for studying the nature of the future asymptote of the general vacuum inhomogeneous solution to the Einstein field equations.
A detailed study of an inhomogeneous dust cosmology contained in a $γ$-law family of perfect-fluid metrics recently presented by Mars and Senovilla is performed. The metric is shown to be the most general orthogonally transitive, Abelian, $G_2$ on $S_2$ solution admitting an additional homothety such that the self-similar group $H_3$ is of Bianchi type VI and the fluid flow is tangent to its orbits. The analogous cases with Bianchi types I, II, III, V, VIII and IX are shown to be impossible thus making this metric privileged from a mathematical viewpoint. The differential equations determining…
The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even for the approach to general inhomogeneous singularities. Thus, it is a popular model to test consequences of modifications to general relativity suggested by quantum theories of gravity. This paper presents a detailed proof that modifications coming from loop quantum gravity lead to a non-chaotic effective behavior. The way this is realized, independently of quantization ambiguities, suggests a new l…
We obtain exact solutions for the Einstein equations with an exponential-potential scalar field (\(V=Λe^{kϕ}\)) which represent simple inhomogeneous generalizations of Bianchi I cosmologies. Studying these equations numerically we find that in most of the cases there is a certain period of inflationary behaviour for \(k^2<2\). We as well find that for \(k^2>2\) the solutions homogenize generically at late times. Yet, {\em none of the solutions} isotropize. For some particular values of the integration constants we find a multiple inflationary behaviour for which the deceleration and the inflat…
Families of anisotropic and inhomogeneous string cosmologies containing non-trivial dilaton and axion fields are derived by applying the global symmetries of the string effective action to a generalized Einstein-Rosen metric. The models exhibit a two-dimensional group of Abelian isometries. In particular, two classes of exact solutions are found that represent inhomogeneous generalizations of the Bianchi type VI_h cosmology. The asymptotic behaviour of the solutions is investigated and further applications are briefly discussed.
In this paper we introduce a LTB-Bianchi I (plane symmetric) model of Universe. We study and solve Einstein field equations. We investigate the effects of such model of Universe in particular these results are important in understanding the effect of the combined presence of an inhomogeneous and anisotropic Universe. The observational magnitude-redshift data deviated from UNION 2 catalog has been analyzed in the framework of this LTB-anisotropic Universe and the fit has been achieved without the inclusion of any dark energy.
The linearly polarized Gowdy $T^3$ model can be regarded as compact Bianchi I cosmologies with inhomogeneous modes allowed to travel in one direction. We study a hybrid quantization of this model that combines the loop quantization of the Bianchi I background, adopting the improved dynamics scheme put forward by Ashtekar and Wilson-Ewing, with a Fock quantization for the inhomogeneities. The Hamiltonian constraint operator provides a resolution of the cosmological singularity and superselects separable sectors. We analyze the complicated structure of these sectors. In any of them the Hamiltoni…
Recently it was shown that the exact cosmological solutions known as the vacuum plane-wave solutions are late-time attractors for an open set of the spatially homogeneous Bianchi universes containing a non-inflationary $γ$-law perfect fluid. In this paper we study inhomogeneous perturbations of these plane-wave spacetimes. By using expansion-normalised scale-invariant variables we show that these solutions are unstable to generic inhomogeneous perturbations. The crucial observation for establishing this result is a divergence of the expansion-normalised frame variables which ultimately leads t…
Anisotropic Cosmology with Inhomogeneous $SU(2) $ and $SL(2,\mathbb{R})$ Nonlinear $σ$-Models
该研究在 Bianchi V 背景下探讨非齐次 $SU(2)$ 和 $SL(2,\mathbb{R})$ 非线性 $\sigma$-模型的宇宙动力学，发现非齐次性阻碍慢滚及双曲暴胀，并需宇宙学常数以实现加速膨胀。
We develop approximation methods in the hybrid quantization of the Gowdy model with linear polarization and a massless scalar field, for the case of three-torus spatial topology. The loop quantization of the homogeneous gravitational sector of the Gowdy model (according to the improved dynamics prescription) and the presence of inhomogeneities lead to a very complicated Hamiltonian constraint. Therefore, the extraction of physical results calls for the introduction of well justified approximations. We first show how to approximate the homogeneous part of the Hamiltonian constraint, correspondi…
We discuss the asymptotic dynamical evolution of spatially homogeneous brane-world cosmological models close to the initial singularity. We find that generically the cosmological singularity is isotropic in Bianchi type IX brane-world models and consequently these models do not exhibit Mixmaster or chaotic-like behaviour close to the initial singularity. We argue that this is typical of more general cosmological models in the brane-world scenario. In particular, we show that an isotropic singularity is a past-attractor in all orthogonal Bianchi models and is a local past-attractor in a class o…
We introduce a new framework for loop quantum gravity: mimicking the spinfoam quantization procedure we propose to study the symmetric sectors of the theory imposing the reduction weakly on the full kinematical Hilbert space of the canonical theory. As a first application of Quantum-Reduced Loop Gravity we study the inhomogeneous Bianchi I model. The emerging quantum cosmological model represents a simplified arena on which the complete canonical quantization program can be tested. The achievements of this analysis could elucidate the relationship between Loop Quantum Cosmology and the full th…
We demonstrate the scale invariance of the vacuum Bianchi type IX equations and use this to argue for the possibility of multifractal turbulence as a realisation of the suggestion by Belinski that there will be a fragmentation of local regions of inhomogeneous Mixmaster chaos on approach to an initial inhomogeneous cosmological singularity. Differences between the gravitational and hydrodynamical situations are outlined. Various potential obstacles to this picture of gravitational turbulence are discussed.
Why is the Universe so homogeneous and isotropic? We summarize a general study of a $γ$-law perfect fluid alongside an inhomogeneous, massless scalar gauge field (with homogeneous gradient) in anisotropic spaces with General Relativity. The anisotropic matter sector is implemented as a $j$-form (field-strength level), where $j\,\in\,\{1,3\}$, and the spaces studied are Bianchi space-times of solvable type. Wald's no-hair theorem is extended to include the $j$-form case. We highlight three new self-similar space-times: the Edge, the Rope and Wonderland. The latter solution is so far found to ex…
We present a new cosmological model derived from Loop Quantum Gravity. The formulation is based on a projection of the kinematical Hilbert space of the full theory down to a subspace representing the proper arena for an inhomogeneous Bianchi I model. This procedure gives a direct link between the full theory and its cosmological sector. The emerging quantum cosmological model represents a simplified arena on which the complete canonical quantization program can be tested. The achievements of this analysis could also shed light on Loop Quantum Cosmology and its relation with the full theory.
In homogeneous and isotropic Friedmann-Robertson-Walker cosmology, the topology of the universe determines its ultimate fate. If the Weak Energy Condition is satisfied, open and flat universes must expand forever, while closed cosmologies can recollapse to a Big Crunch. A similar statement holds for homogeneous but anisotropic (Bianchi) universes. Here, we prove that $arbitrarily$ inhomogeneous and anisotropic cosmologies with "flat" (including toroidal) and "open" (including compact hyperbolic) spatial topology that are initially expanding must continue to expand forever at least in some regi…
It has recently been suggested that an isotropic singularity may be a generic feature of brane cosmologies, even in the inhomogeneous case. Using the covariant and gauge-invariant approach we present a detailed analysis of linear perturbations of the isotropic model ${\cal F}_b$ which is a past attractor in the phase space of homogeneous Bianchi models on the brane. We find that for matter with an equation of state parameter $γ> 1$, the dimensionless variables representing generic anisotropic and inhomogeneous perturbations decay as $t\to 0$, showing that the model ${\cal F}_b$ is asymptotical…
We present a review on basic aspects of quantum cosmology in the presence of cut-off physics. We first analyze how the Wheeler-DeWitt equation in a pure metric approach describes the quantum Universe, showing how the singularity is not removed. We then discuss basic features of loop quantum cosmology. For the isotropic Universe, we compare the original $μ_0$ scheme and the most commonly accepted formulation, the $\barμ$ scheme. Some results concerning the Bianchi Universes are also discussed. Finally, we consider some relevant criticisms on the real link between full loop quantum gravity and i…
Light propagation in inhomogeneous and anisotropic cosmologies
本论文系统研究了宇宙小尺度非均匀性和大尺度各向异性对光传播及宇宙学参数推断的影响，提出基于随机过程的引力透镜新框架，并排除多数标量-矢量各向异性模型。
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