Bianchi Universes Research Articles

The deceleration parameter in perturbed Bianchi universes with a peculiar-velocity “tilt”

Bianchi cosmologies are “natural” anisotropic extensions of the Friedmann universes and they have long been used to investigate the cosmological implications of anisotropy. The latter introduces new ingredients to the standard scenarios, although there are physical processes and effects that maintain their basic Friedmann features when extended to Bianchi universes. Here, we assume a perturbed Bianchi model and look into the implications of the observers’ peculiar flow for their measurement and their interpretation of the deceleration parameter. Our motivation is twofold. To begin with, relative motions have long been known to deceive the observers by “contaminating” the observations, which also still suffer from sample limitations that cloud the statistical significance of the findings. Further motivation comes from claims that observers in bulk flows that expand slightly slower than their surroundings can have the illusion of cosmic acceleration in a universe that is actually decelerating. The claim was originally based on studies of a perturbed tilted Einstein–de Sitter model, but persisted when the background cosmology was replaced by any of the three Friedmann universes. This raised the possibility that the peculiar-motion effect on the deceleration parameter may be generic and largely independent of the host spacetime. Here, we investigate this possibility by extending the earlier studies to perturbed Bianchi models. We find that the Friedmann picture remains unchanged, unless the Bianchi background has unrealistically high anisotropy. The bulk-flow observers can still be misled to the illusion of accelerated expansion by their own peculiar motion.

New phenomenology in the first-order thermodynamics of scalar-tensor gravity for Bianchi universes

New phenomenology in the first-order thermodynamics of scalar-tensor gravity for Bianchi universes

More on the first-order thermodynamics of scalar-tensor and Horndeski gravity

Two issues in the first-order thermodynamics of scalar-tensor (including “viable” Horndeski) gravity are elucidated. The application of this new formalism to FLRW cosmology is shown to be fully legitimate and then extended to all Bianchi universes. It is shown that the formalism holds thanks to the almost miraculous fact that the constitutive relations of Eckart’s thermodynamics are satisfied, while writing the field equations as effective Einstein equations with an effective dissipative fluid does not contain new physics.

WKB Approaches to Restore Time in Quantum Cosmology: Predictions and Shortcomings

In this review, we analyse different aspects concerning the possibility to separate a gravity-matter system into a part which lives close to a quasi-classical state and a “small” quantum subset. The considered approaches are all relying on a WKB expansion of the dynamics by an order parameter and the natural arena consists of the Bianchi universe minisuperspace. We first discuss how, limiting the WKB expansion to the first order of approximation, it is possible to recover for the quantum subsystem a Schrödinger equation, as written on the classical gravitational background. Then, after having tested the validity of the approximation scheme for the Bianchi I model, we give some applications for the quantum subsystem in the so-called “corner” configuration of the Bianchi IX model. We individualize the quantum variable in the small one of the two anisotropy degrees of freedom. The most surprising result is the possibility to obtain a non-singular Bianchi IX cosmology when the scenario is extrapolated backwards in time. In this respect, we provide some basic hints on the extension of this result to the generic cosmological solution. In the last part of the review, we consider the same scheme to the next order of approximation identifying the quantum subset as made of matter variables only. This way, we are considering the very fundamental problem of non-unitary morphology of the quantum gravity corrections to quantum field theory discussing some proposed reformulations. Instead of constructing the time dependence via that one of the classical gravitational variables on the label time as in previous works, we analyse a recent proposal to construct time by fixing a reference frame. This scheme can be reached both introducing the so-called “kinematical action”, as well as by the well-known Kuchar–Torre formulation. In both cases, the Schrödinger equation, amended for quantum gravity corrections, has the same morphology and we provide a cosmological implementation of the model, to elucidate its possible predictions.

Features of the primordial Universe in f(R)-gravity as viewed in the Jordan frame

We analyze some features of the primordial Universe as viewed in the Jordan frame formulation of the f(R)-gravity when the potential term is negligible. We start formulating the Hamiltonian picture using the three-metric determinant as a basic variable and we outline that its conjugated momentum appears linearly only in the scalar constraint. We construct the formalism to characterize the dynamics of a generic inhomogeneous cosmological model and specialize it to describe behaviors of the Bianchi Universes, both on a classical and a quantum regime. We demonstrate that, when the potential term of the additional scalar mode is negligible near to the initial singularity, the Bianchi IX cosmology is no longer affected by the chaotic behavior, typical in the vacuum of the Einsteinian dynamics. In fact, the presence of the Kasner stability region and its attractive character are properly characterized. Finally, we investigate the canonical quantization of the Bianchi I model, using as time variable the non-minimally coupled scalar field and showing that the existence of a conserved current is outlined for the corresponding Wheeler–DeWitt equation. The behavior of a localized wave-packet for the isotropic Universe is also evolved, demonstrating that the singularity is still present in this revised quantum dynamics.

An Overview on the Nature of the Bounce in LQC and PQM

We present a review on some of the basic aspects concerning quantum cosmology in the presence of cut-off physics as it has emerged in the literature during the last fifteen years. We first analyze how the Wheeler–DeWitt equation describes the quantum Universe dynamics, when a pure metric approach is concerned, showing how, in general, the primordial singularity is not removed by the quantum effects. We then analyze the main implications of applying the loop quantum gravity prescriptions to the minisuperspace model, i.e., we discuss the basic features of the so-called loop quantum cosmology. For the isotropic Universe dynamics, we compare the original approach, dubbed the μ0 scheme, and the most commonly accepted formulation for which the area gap is taken as physically scaled, i.e., the so-called μ¯ scheme. Furthermore, some fundamental results concerning the Bianchi Universes are discussed, especially with respect to the morphology of the Bianchi IX model. Finally, we consider some relevant criticisms developed over the last ten years about the real link existing between the full theory of loop quantum gravity and its minisuperspace implementation, especially with respect to the preservation of the internal SU(2) symmetry. In the second part of the review, we consider the dynamics of the isotropic Universe and of the Bianchi models in the framework of polymer quantum mechanics. Throughout the paper, we focus on the effective semiclassical dynamics and study the full quantum theory only in some cases, such as the FLRW model and the Bianchi I model in the Ashtekar variables. We first address the polymerization in terms of the Ashtekar–Barbero–Immirzi connection and show how the resulting dynamics is isomorphic to the μ0 scheme of loop quantum cosmology with a critical energy density of the Universe that depends on the initial conditions of the dynamics. The following step is to analyze the polymerization of volume-like variables, both for the isotropic and Bianchi I models, and we see that if the Universe volume (the cubed scale factor) is one of the configurational variables, then the resulting dynamics is isomorphic to that one emerging in loop quantum cosmology for the μ¯ scheme, with the critical energy density value being fixed only by fundamental constants and the Immirzi parameter. Finally, we consider the polymer quantum dynamics of the homogeneous and inhomogeneous Mixmaster model by means of a metric approach. In particular, we compare the results obtained by using the volume variable, which leads to the emergence of a singularity- and chaos-free cosmology, to the use of the standard Misner variable. In the latter case, we deal with the surprising result of a cosmology that is still singular, and its chaotic properties depend on the ratio between the lattice steps for the isotropic and anisotropic variables. We conclude the review with some considerations of the problem of changing variables in the polymer representation of the minisuperspace dynamics. In particular, on a semiclassical level, we consider how the dynamics can be properly mapped in two different sets of variables (at the price of having to deal with a coordinate dependent lattice step), and we infer some possible implications on the equivalence of the μ0 and μ¯ scheme of loop quantum cosmology.

Non‐Flat Universes and Black Holes in Asymptotically Free Mimetic Gravity

AbstractThe recently proposed theory of “Asymptotically Free Mimetic Gravity” is extended to the general non‐homogeneous, spatially non‐flat case. We present a modified theory of gravity which is free of higher derivatives of the metric. In this theory asymptotic freedom of gravity implies the existence of a minimal black hole with vanishing Hawking temperature. Introducing a spatial curvature dependent potential, we moreover obtain non‐singular, bouncing modifications of spatially non‐flat Friedmann and Bianchi universes.

Anisotropic mimetic cosmology

We consider a mimetic set up in which the mimetic scalar is coupled to a vector field. It is shown that such a field with a time-like component does not contribute to the background equations and yet produces healthy isocurvature perturbations with respect to ghost and gradient instabilities in spite of the absence of any propagating curvature perturbations at the level of the quadratic action. We then consider a vector field with space-like components which leads to an anisotropic Bianchi universe and show that the ghost and gradient instabilities are absent in the limit of high momenta and that the propagating curvature perturbations have healthy UV behavior.

Kantowski-Sachs and Bianchi type models with a general non-canonical scalar field

The paper deals with spatially homogeneous and anisotropic Kantowski-Sachs and Bianchi universes with a general non-canonical scalar field with the Lagrangian L = F(X) − Ω(ϕ), where $$X = \frac{1}{2}{\phi _i}{\phi ^i}$$ . We discuss a general non-canonical scalar field in three different cosmologies: (i) cosmology with a constant potential, Ω(ϕ) = Ω0 = const, (ii) cosmology with a constant equation-of-state parameter, i.e., γϕ = const, and (iii) cosmology with a constant speed of sound, i.e., c s 2 = const. For a constant potential, we have shown that the k-essence Lagrangian and the Lagrangian of the present model are equivalent. Dissipation of anisotropy, when the universe is filled with a general non-canonical scalar field, is investigated. The existence of an average bounce in Kantowski-Sachs and locally rotationally symmetric Bianchi-I and Bianchi-III models is discussed in detail.

Does GW Generation Have Semi-Classical Features?

We argue in this document that initial vacuum state values possibly responsible for GW generation in relic conditions in the initial onset of inflation may have a temporary un squeezed, possibly even coherent initial value, which would permit in certain models classical coherent initial gravitational wave states. Furthermore, several arguments pro and con as to if or not initial relic GW should be high frequency will be presented. The existence of higher dimensions, in itself if the additional dimensions are small and compact will have no capacity to influence the frequency values of relic GW, as predicted by Giovanni, and others in 1995. Furthermore, to consider are the results of Sahoo, Mishra, and Pacif (2016) which via Bianchi universes, removes the necessity of an initial space-time singularity, which may have bearing on the issue of the degree of the initial coherent states, so postulated for gravitational waves, as is brought up in the conclusion.

Spin precession in anisotropic cosmologies

We consider the precession of a Dirac particle spin in some anisotropic Bianchi universes. This effect is present already in the Bianchi-I universe. We discuss in some detail the geodesics and the spin precession for both the Kasner and the Heckmann-Schucking solutions. In the Bianchi-IX universe the spin precession acquires the chaotic character due to the stochasticity of the oscillatory approach to the cosmological singularity. The related helicity flip of fermions in the very early Universe may produce the sterile particles contributing to dark matter.

Chaotic spin precession in anisotropic universes and fermionic dark matter

We consider the precession of a Dirac particle spin in some anisotropic Bianchi universes. This effect is present already in the Bianchi-I universe. In the Bianchi-IX universe it acquires the chaotic character due to the stochasticity of the oscillatory approach to the cosmological singularity. The related helicity flip of fermions in the veryearly Universe may produce the sterile particles contributing to dark matter.

Light propagation in a homogeneous and anisotropic universe

This article proposes a comprehensive analysis of light propagation in an anisotropic and spatially homogeneous Bianchi I universe. After recalling that null geodesics are easily determined in such a spacetime, we derive the expressions of the redshift and direction drifts of light sources; by solving analytically the Sachs equation, we then obtain an explicit expression of the Jacobi matrix describing the propagation of narrow light beams. As a byproduct, we recover the old formula by Saunders for the angular diameter distance in a Bianchi I spacetime, but our derivation goes further since it also provides the optical shear and rotation. These results pave the way to the analysis of both supernovae data and weak lensing by the large-scale structure in Bianchi universes.

Towards a cosmology with minimal length and maximal energy

The Friedmann–Robertson–Walker (FRW) universe and Bianchi I, II universes are investigated in the framework of the generalized uncertainty principle (GUP) with a linear and a quadratic term in Planck length and momentum, which predicts the minimum measurable length as well as maximum measurable momentum. We obtain a dynamic cosmological bounce for the FRW universe. With the Bianchi universe, we found that the universe may still be isotropic by implementing GUP. Moreover, the wall velocity appears to be stationary with respect to the universe velocity, which means that when the momentum of the universe evolves into a maximum measurable energy, the bounce is enhanced against the wall, which means that no maximum limit angle is manifested anymore.

TwistedC⋆-algebra formulation of quantum cosmology with application to the Bianchi I model

A twisted ${\mathcal{C}}^{\ensuremath{\star}}$-algebra of the extended (noncommutative) Heisenberg-Weyl group has been constructed which takes into account the uncertainty principle for coordinates in the Planck-length regime. This general construction is then used to generate an appropriate Hilbert space and observables for the noncommutative theory which, when applied to the Bianchi I cosmology, leads to a new set of equations that describe the quantum evolution of the Universe. We find that this formulation matches theories based on a reticular Heisenberg-Weyl algebra in the bouncing and expanding regions of a collapsing Bianchi universe. There is, however, an additional effect introduced by the dynamics generated by the noncommutativity. This is an oscillation in the spectrum of the volume operator of the Universe, within the bouncing region of the commutative theories. We show that this effect is generic and produced by the noncommutative momentum exchange between the degrees of freedom in the cosmology. We give asymptotic and numerical solutions which show the above mentioned effects of the noncommutativity.

The Cosmic Microwave Background and Fundamental Physics

A brief overview of the links between the Cosmic Microwave Background (CMB) and fundamental physics is given. After a summary of the basics of the CMB, and of current observations, topics are considered including the generation of perturbations, inflation and string theory, evidence for parity violation, variation of the fundamental constants, restrictions on alternative theories of gravity, primordial non-Gaussianity, early- and late-time Bianchi universes and topological defects.

Stable isotropic cosmological singularities in quadratic gravity

We show that, in quadratic Lagrangian theories of gravity, isotropic cosmological singularities are stable to the presence of small scalar, vector, and tensor inhomogeneities. We study the effects of the quadratic Ricci term on the dynamics of the Universe at early times. Unlike in general relativity, a particular exact isotropic solution is shown to be the stable attractor on approach to the initial cosmological singularity. This solution is also known to act as an attractor in Bianchi universes of types I, II, and IX, and the results of this paper reinforce the hypothesis that small inhomogeneous and anisotropic perturbations of this attractor form part of the general cosmological solution to the field equations of quadratic gravity. Implications for the existence of a ``gravitational entropy'' are also discussed.

On the Viability of Bianchi Type VIIhModels with Dark Energy

We generalize the predictions for the cosmic microwave background (CMB) anisotropy patterns arising in Bianchi type VIIh universes to include a dark energy component. We consider these models in light of the result of Jaffe and collaborators in which a correlation was found on large angular scales between the WMAP data and the anisotropy structure in a low-density Bianchi universe. We find that by including a term ΩΛ > 0, the same best-fit anisotropy pattern is reproduced by several combinations of cosmological parameters. This subset of models can then be further constrained by current observations that limit the values of various cosmological parameters. In particular, we consider the so-called geometric degeneracy in these parameters imposed by the peak structure of the WMAP data themselves. Apparently, despite the additional freedom allowed by the dark energy component, the modified Bianchi models are ruled out at high significance.

Erratum to: “On Milnor seven dimensional sphere, El Naschie’s ε∞ theory and energy of a Bianchi universe” [Chaos, Solitons and Fractals 19 (2004) 17

Erratum to: “On Milnor seven dimensional sphere, El Naschie’s ε∞ theory and energy of a Bianchi universe” [Chaos, Solitons and Fractals 19 (2004) 17

INFLUENCE OF GRAVITY ON NONCOMMUTATIVE DIRAC EQUATION

In this paper, we investigate the influence of gravity and noncommutativity on Dirac particles. By adopting the tetrad formalism, we show that the modified Dirac equation keeps the same form. The only modification is in the expression of the covariant derivative. The new form of this derivative is the product of its counterpart given in curved spacetime with an operator which depends on the noncommutative θ-parameter. As an application, we have computed the density number of the created particles in the presence of constant strong electric field in an anisotropic Bianchi universe.