arXiv subjects

Ewa Czuchry

Publications and source records attributed to Ewa Czuchry.

At least 19 recordsLinked to original sources

arXiv2026

Finite-resolution measurement induces topological curvature defects in spacetime

We show that regularizing $(2+1)$-dimensional Minkowski spacetime with a finite-resolution Gaussian probe, analogous to Weyl-Heisenberg (Gabor) signal analysis and related quantization, induces a curved geometry with a topological defect. The regularized metric replaces $r^2$ by $r^2+σ^2$ in the angular part, where $σ$ is the resolution scale from the width of the Gaussian probe. The resulting Gaussian curvature integrates to $-2π$, independently of $σ$. This curvature defines an effective stress-energy source with universal total energy $E_{\text{eff}}=-1/(4G)$. The limit $σ\to0$ leads to distributional Dirac-delta curvature and to appearance of topological defect at the origin. These results show that finite spatial resolution measurement does not merely smooth singularities but can shape spacetime geometry.

gr-qc↗

arXiv2023

On the energy flow of $λ$ in Hořava-Lifshitz cosmology

Hořava-Lifshitz gravity has been proposed as a ghost-free quantum gravity model candidate with an anisotropic UV-scaling between space and time. We present here a cosmological background analysis of two different formulations of the theory, with particular focus on the running of the parameter $λ$. Using a large dataset consisting of Cosmic Microwave Background data from {\it Planck}, Pantheon+ supernovae catalogue, SH0ES Cepheid variable stars, Baryon acoustic oscillations (BAO), Cosmic Chronometers, and gamma-ray bursts (GRB), we arrive at new bounds on the cosmological parameters, in particular $λ$, which describes deviation from classical general relativity. For the detailed balance scenario we arrive at the bound $λ=1.02726\pm0.00012$, and for beyond detailed balance the limit reads $λ=0.9949^{+0.0045}_{-0.0046}$. We also study the influence of different data sets and priors, and we find that removing low-redshift data generally moves $λ$ closer towards UV values, whilst simultaneously widening the error bars. In the detailed balance scenario, this effect is more noticeable, and $λ$ takes on values that are significantly below unity, which corresponds to the infrared limit of the theory.

astro-ph.CO↗

arXiv2023

Resolution of cosmological singularity in Hořava-Lifshitz cosmology

The standard $Λ$CDM model despite its agreement with observational data still has some issues unaddressed, lie the problem of initial singularity. Solving that problem usually requires modifications of general relativity. However, there appeared the Hořava-Lifshitz (HL) theory of gravity, in which equations governing cosmological evolution include a new term scaling similarly as dark radiation term in the Friedmann equations, enabling a bounce of the universe instead of initial singularity. This review describes past works on a stability of such a bounce in different formulations of HL theory, initial detailed balance scenario and further projectable versions containing higher than quadratic term to the original action.

gr-qc↗

arXiv2023

Semi-Classical quantisation of 3-particles Toda lattice augmented; Application to the Mixmaster anisotropy Hamiltonian

Usual approaches to quantisation of a 3-Toda lead to numerical calculations requiring many steps that can be time consuming to insure their reliability. In order to reduce as much as possible the numerical part of the EKB quantisation procedure, and then to ease numerical calculations, we propose a reformulation of the mathematical framework with more adapted variables. The resulting equations and procedure might be easily implemented in a short Mathematica code. This more explicit framework will be useful for studying quantum Toda-Bianchi IX models in quantum cosmology where the true Bianchi IX anisotropy Hamiltonian can be approximated by a 3-particle Toda system.

gr-qc↗

arXiv2019

Quantum Mixmaster as a model of the Primordial Universe

The Mixmaster solution to Einstein field equations was examined by C. Misner in an effort to better understand the dynamics of the early universe. We highlight the importance of the quantum version of this model for early universe. This quantum version and its semi-classical portraits are yielded through affine and standard coherent state quantizations and more generally affine and Weyl-Heisenberg covariant integral quantizations. The adiabatic and vibronic approximations widely used in molecular physics can be employed to qualitatively study the dynamics of the model on both quantum and semi-classical levels. Moreover, the semi-classical approach with the exact anisotropy potential can be effective in numerical integration of some solutions. Some promising physical features such as the singularity resolution, smooth bouncing, the excitation of anisotropic oscillations and a substantial amount of post-bounce inflation as the backreaction to the latter are pointed out. Finally, a realistic cosmological scenario based on the quantum mixmaster model, which includes the formation and evolution of local structures is outlined.

gr-qc↗

arXiv2018

Hořava-Lifshitz cosmology in light of new data

We present new observational constraints on Lorentz violating Hořava-Lifshitz cosmological scenarios using an updated cosmological data set from Cosmic Microwave Background (Planck CMB), expansion rates of elliptical and lenticular galaxies, JLA compilation (Joint Light-Curve Analysis) data for Type Ia supernovae (SneIa), Baryon Acoustic Oscillations (BAO) and priors on the Hubble parameter with an alternative parametrisation of the equations. Unlike in other approaches we consider the curvature parameter $Ω_k$ as a free parameter in the analysis we considered the parameters $Ω_k$ and $ΔN_ν$ as completely free, which helped to place new, updated bounds on several of the theory parameters. Remarkably, the detailed balance scenario exhibits positive spatial curvature to more than 3$σ$, whereas for further theory generalizations we found evidence for positive spatial curvature at 1$σ$. This could create circumstantial evidence from observations and could be used to single out distinct formulations and scenarios.

gr-qc↗

arXiv2018

Comparing the dynamics of diagonal and general Bianchi IX spacetime

We make comparison of the dynamics of the diagonal and nondiagonal Bianchi IX models in the evolution towards the cosmological singularity. Apart from the original variables, we use the Hubble normalized ones commonly applied in the examination of the dynamics of homogeneous models. Applying the dynamical systems method leads to the result that in both cases the continuous space of critical points is higher dimensional and they are of the nonhyperbolic type. This is a generic feature of the dynamics of both cases and seems to be independent on the choice of phase space variables. The topologies of the corresponding critical spaces are quite different. We conjecture that the nondiagonal case may carry a new type of chaos different from the one specific to the usually examined diagonal one.

gr-qc↗

arXiv2017

Coherent states quantization and affine symmetry in quantum models of gravitational singularities

We employ the framework of affine covariant quantization and associated semiclassical portrait to address two main issues in the domain of quantum gravitational systems: (i) the fate of singularities and (ii) the lack of external time. Our discussion is based on finite-dimensional, symmetry-reduced cosmological models. We show that the affine quantization of the cosmological dynamics removes the classical singularity and univocally establishes a unitary evolution. The semiclassical portrait based on the affine coherent states exhibits a big bounce replacing the big-bang singularity. As a particularly interesting application, we derive and study a unitary quantum dynamics of the spatially homogenous, closed model, the Mixmaster universe. At the classical level it undergoes an infinite number of oscillations before collapsing into a big-crunch singularity. At the quantum level the singularity is shown to be replaced by adiabatic and nonadiabatic bounces. As another application, we consider the problem of time. We derive semiclassical portraits of quantum dynamics of the Friedman universe with respect to various internal degrees of freedom. Next we compare them and discuss the nature of quantum evolution of the gravitational field.

gr-qc↗

arXiv2017

Spectral properties of the quantum Mixmaster universe

We study the spectral properties of the anisotropic part of Hamiltonian entering the quantum dynamics of the Mixmaster universe. We derive the explicit asymptotic expressions for the energy spectrum in the limit of large and small volumes of the universe. Then we study the threshold condition between both regimes. Finally we prove that the spectrum is purely discrete for any volume of the universe. Our results validate and improve the known approximations to the anisotropy potential. They should be useful for any approach to the quantization of the Mixmaster universe.

gr-qc↗

arXiv2017

Do spikes persist in a quantum treatment of spacetime singularities?

The classical approach to spacetime singularities leads to a simplified dynamics in which spatial derivatives become unimportant compared to time derivatives, and thus each spatial point essentially becomes uncoupled from its neighbors. This uncoupled dynamics leads to sharp features (called "spikes") as follows: particular spatial points follow an exceptional dynamical path that differs from that of their neighbors, with the consequence that, in the neighborhood of these exceptional points, the spatial profile becomes ever more sharp. Spikes are consequences of the BKL-type oscillatory evolution towards generic singularities of spacetime. Do spikes persist when the spacetime dynamics is treated using quantum mechanics? To address this question, we treat a Hamiltonian system that describes the dynamics of the approach to the singularity and consider how to quantize that system. We argue that this particular system is best treated using an affine quantization approach (rather than the more familiar methods of canonical quantization) and we set up the formalism needed for this treatment. Our investigation, based on this affine approach, shows the nonexistence of quantum spikes.

gr-qc↗

arXiv2016

Nonadiabatic bounce and an inflationary phase in the quantum mixmaster universe

Following our previous paper, Bergeron et al, Smooth quantum dynamics of the mixmaster universe, Phys. Rev. D 92, 061302(R) (2015), concerning the quantization of the vacuum Bianchi IX model and the Born-Huang-Oppenheimer framework, we present a further analysis of the dynamical properties of the model. Consistently with the deep quantum regime, we implement the harmonic approximation of the anisotropy potential. We thus obtain manageable dynamical equations. We study the quantum anisotropic oscillations during the bouncing phase of the universe. Neglecting the backreaction from transitions between quantum anisotropy states we obtain analytical results. In particular, we identify a parameter which is associated with dynamical properties of the quantum model and describes a sort of phase transition. Once the parameter exceeds its critical value, the Born-Huang-Oppenheimer approximation breaks down. The application of the present result to a simple model of the Universe indicates that the parameter indeed exceeds its critical value and that there takes place a huge production of anisotropy at the bounce. This in turn must lead to a sustained phase of accelerated expansion, an inflationary phase. The quantitative inclusion of backreaction shall be examined in a follow-up paper based on the vibronic approach.

gr-qc↗

arXiv2015

Singularity avoidance in a quantum model of the Mixmaster universe

We present a quantum model of the vacuum Bianchi-IX dynamics. It is based on four main elements. First, we use a compound quantization procedure: an affine coherent state quantization for isotropic variables and a Weyl quantization for anisotropic ones. Second, inspired by standard approaches in molecular physics, we make an adiabatic approximation (Born-Oppenheimer-like approximation). Third, we expand the anisotropy potential about its minimum in order to deal with its harmonic approximation. Fourth, we develop an analytical treatment on the semiclassical level. The resolution of the classical singularity occurs due to a repulsive potential generated by the affine quantization. This procedure shows that during contraction the quantum energy of anisotropic degrees of freedom grows much slower than the classical one. Furthermore, far from the quantum bounce, the classical recollapse is reproduced. Our treatment is put in the general context of methods of molecular physics, which can include both adiabatic and nonadiabatic approximations.

gr-qc↗

arXiv2015

Vibronic framework for quantum mixmaster universe

Following our previous papers concerning the quantization of the vacuum Bianchi-IX model within or beyond the Born-Oppenheimer and adiabatic approximation, we develop a more elaborate analysis of the dynamical properties of the model based the vibronic approach utilized in molecular physics. As in the previous papers, we restrict our approach to the harmonic approximation of the anisotropy potential in order to obtain resoluble analytical expressions.

gr-qc↗

arXiv2015

Smooth Quantum Dynamics of Mixmaster Universe

We present a quantum version of the vacuum Bianchi IX model by implementing affine coherent state quantization combined with a Born-Oppenheimer-like adiabatic approximation. The analytical treatment is carried out on both quantum and semiclassical levels. The resolution of the classical singularity occurs by means of a repulsive potential generated by our quantization procedure. The quantization of the oscillatory degrees of freedom produces a radiation energy density term in the semiclassical constraint equation. The Friedmann-like lowest energy eigenstates of the system are found to be dynamically stable.

gr-qc↗

arXiv2013

Bianchi IX model: Reducing phase space

The mathematical structure of higher-dimensional physical phase spaces of the nondiagonal Bianchi IX model is analyzed in the neighborhood of the cosmological singularity by using dynamical system methods. Critical points of the Hamiltonian equations appear at infinities and are of a nonhyperbolic type, which is a generic feature of the considered singular dynamics. The reduction of the kinematical symplectic 2-form to the constraint surface enables the determination of the physical Hamiltonian. This procedure lowers the dimensionality of the dynamics arena. The presented analysis of the phase space is based on canonical transformations. We test our method for the specific subspace of the physical phase space. The obtained results encourage further examination of the dynamics within our approach.

gr-qc↗

arXiv2011

Bounce scenarios in the Sotiriou-Visser-Weinfurtner generalization of the projectable Horava-Lifshitz gravity

The occurrence of a bounce in the FRW cosmology requires modifications of General Relativity. An example of such a modification is the recently proposed Horava-Lifshitz theory of gravity, which includes a "dark radiation" term with a negative coefficient in the analog of the Friedmann equation. A modification of the HL gravity, relaxing the "detailed balance" condition, brings additional terms to the equations of motion, corresponding to stiff matter. This paper presents comparison of the phase structure of the original and modified Horava cosmology. Special attention is paid to the analysis of a wide range of bouncing solution, appearing in both versions of the Horava theory.

hep-th↗

arXiv2010

Dynamics of a self gravitating light-like matter shell with spherical symmetry

A novel Hamiltonian description of the dynamics of a spherically symmetric, light-like, self-gravitating shell is presented. It is obtained via the systematic reduction of the phase space with respect to the Gauss-Codazzi constraints, model and rare procedure in the Canonical Gravity. The Hamiltonian of the system (numerically equal to the value of the ADM mass) is explicitly calculated in terms of the gauge-invariant "true degrees of freedom", i.e. as a function on the reduced phase space. A geometric interpretation of the momentum canonically conjugate to the shell's radius is given. Models of matter compatible with the shell dynamics are found. A transformation between the different time parameterizations of the shell is calculated. The presented model may become a new toy model of quantum gravity.

gr-qc↗

arXiv2010

The phase portrait of a matter bounce in Horava-Lifshitz cosmology

The occurrence of a bounce in FRW cosmology requires modifications of general relativity. An example of such a modification is the recently proposed Horava-Lifshitz theory of gravity, which includes a ``dark radiation'' term with a negative coefficient in the analog of the Friedmann equation. This paper describes a phase space analysis of models of this sort with the aim of determining to what extent bouncing solutions can occur. A simplification, valid in the relevant region, allows a reduction of the dimension of phase space so that visualization in three dimensions is possible. It is found that a bounce is possible, but not generic in models under consideration. Apart from previously known bouncing solutions some new ones are also described. Other interesting solutions found include ones which describe a novel sort of oscillating universes.

hep-th↗