arXiv subjects

Jakub Mielczarek

Publications and source records attributed to Jakub Mielczarek.

At least 37 records · Page 2Linked to original sources

arXiv2020

Quantum fluctuations of the compact phase space cosmology

In the recent article Phys. Rev. D 100, no. 4, 043533 (2019) a compact phase space generalization of the flat de Sitter cosmology has been proposed. The main advantages of the compactification is that physical quantities are bounded, and the quantum theory is characterized by finite dimensional Hilbert space. Furthermore, by considering the $\mathbb{S}^2$ phase space, quantum description is constructed with the use $SU(2)$ representation theory. The purpose of this article is to apply effective methods to extract semi-classical regime of the quantum dynamics. The analysis is performed both without prior solving of the quantum constraint and by extracting physical Hamiltonian of the model. At the effective level, the results of the two procedures are shown to be equivalent. We find a nontrivial behavior of the fluctuations around the recollapse of the universe, which is distinct from what is found after quantization with the standard flat phase space. The behavior is reflected at the level of the modified Friedmann equation with quantum back-reaction effects, which is derived. Finally, an unexpected relation between the quantum fluctuations of the cosmological sector and the holographic Bousso bound is shown.

gr-qc↗

arXiv2019

Minisuperspace model of compact phase space gravity

The kinematical phase space of classical gravitational field is flat (affine) and unbounded. Because of this, field variables may tend to infinity leading to appearance of singularities, which plague Einstein's theory of gravity. The purpose of this article is to study the idea of generalizing the theory of gravity by compactification of the phase space. We investigate the procedure of compactification of the phase space on a minisuperspace gravitational model with two dimensional phase space. In the affine limit, the model reduces to the flat de Sitter cosmology. The phase space is generalized to the spherical case, and the case of loop quantum cosmology is recovered in the cylindrical phase space limit. Analysis of the dynamics reveals that the compactness of the phase space leads to both UV and IR effects. In particular, the phase of re-collapse appears, preventing the universe from expanding to infinite volume. Furthermore, the quantum version of the model is investigated and the quantum constraint is solved. As an example, we analyze the case with the spin quantum number $s=2$, for which we determine transition amplitude between initial and final state of the classical trajectory. The probability of the transition is peaked at $Λ=0$.

gr-qc↗

arXiv2019

Spin Foam Vertex Amplitudes on Quantum Computer -- Preliminary Results

Vertex amplitudes are elementary contributions to the transition amplitudes in the spin foam models of quantum gravity. The purpose of this article is make the first step towards computing vertex amplitudes with the use of quantum algorithms. In our studies we are focused on a vertex amplitude of 3+1 D gravity, associated with a pentagram spin-network. Furthermore, all spin labels of the spin network are assumed to be equal $j=1/2$, which is crucial for the introduction of the \emph{intertwiner qubits}. A procedure of determining modulus squares of vertex amplitudes on universal quantum computers is proposed. Utility of the approach is tested with the use of: IBM's \emph{ibmqx4} 5-qubit quantum computer, simulator of quantum computer provided by the same company and QX quantum computer simulator. Finally, values of the vertex probability are determined employing both the QX and the IBM simulators with 20-qubit quantum register and compared with analytical predictions.

gr-qc↗

arXiv2019

Minisuperspace results for causal dynamical triangulations

Detailed applications of minisuperspace methods are presented and compared with results obtained in recent years by means of causal dynamical triangulations (CDTs), mainly in the form of effective actions. The analysis sheds light on conceptual questions such as the treatment of time or the role and scaling behavior of statistical and quantum fluctuations. In the case of fluctuations, several analytical and numerical results show agreement between the two approaches and offer possible explanations of effects that have been seen in causal dynamical triangulations but whose origin remained unclear. The new approach followed here suggests `CDT experiments' in the form of new simulations or evaluations motivated by theoretical predictions, testing CDTs as well as the minisuperspace approximation.

gr-qc↗

arXiv2018

Quantum Hubble horizon

The article addresses a possibility of obtaining cosmologically relevant effects from the quantum nature of the Hubble horizon. Following the observation made by E.~Bianchi and C.~Rovelli in Phys.\ Rev.\ D {\bf 84} (2011) 027502 we explore relationship between the Planck scale discreteness of the Hubble horizon and deformations of the symmetry of rotations. We show that the so-called $q$-deformations in a natural way lead to a mechanism of condensation in the very early Universe. We argue that this provides a possible resolution of the problem of initial homogeneity at the onset of inflation. Furthermore, we perform entropic analysis of the quantum Hubble horizon and show that the $Λ$CDM model may arise from linearly (in area of the horizon) corrected Bekenstein-Hawking entropy. Based on this, we have shown that the current accelerating expansion can be associated with the entropy decrease in the Hubble volume. The presented results open new ways to explore relation between the Planck scale effects and observationally relevant features of our Universe.

gr-qc↗

arXiv2018

Towards the map of quantum gravity

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between Loop Quantum Gravity, Causal Dynamical Triangulations, Hořava-Lifshitz gravity, Asymptotic Safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincaré algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers.

hep-th↗

arXiv2018

Ultralocal nature of geometrogenesis

In this article we show that the ultralocal state of gravity can be associated with the so-called crumpled phase of gravity, observed e.g. in Causal Dynamical Triangulations. By considering anisotropic scaling present in the Hořava-Lifshitz theory, we prove that in the ultralocal scaling limit ($z \rightarrow 0$) the graph representing connectivity structure of space is becoming complete. In consequence, transition from the ultralocal phase ($z=0$) to the standard relativistic scaling ($z=1$) is implemented by the geometrogensis, similar to the one considered in Quantum Graphity approach. However, the relation holds only for the finite number of nodes $N$ and in the continuous limit ($N\rightarrow \infty$) the complete graph reduces to the set of disconnected points due to the weights $w=1/N$ associated with the links. By coupling Ising spin matter to the considered graph we show that the process of geometrogensis can be associated with critical behavior. Based on both analytical and numerical analysis phase diagram of the system is reconstructed showing that (for a ring graph) symmetry broken phase occurs at $z\in [0, 0.5)$. Finally, cosmological consequences of the considered process of geometrogenesis as well as similarities with the so-called synaptic pruning are briefly discussed.

gr-qc↗

arXiv2018

Quantum Gravity on a Quantum Chip

This essay aims at emphasizing the potential of a synergy between quantum gravity and the quantum computing technologies. Such a combination would be beneficial for both understanding the Planck scale physics and the stimulation of development of the quantum technologies. This is especially important in the present early days of commercial quantum computers, when challenges originating from the basic research may catalyze the technological progress. Our attention is focused on simulations of a Planck scale system with the use of existing adiabatic quantum computers. Current possibilities, technological challenges and prospects for the future are outlined.

gr-qc↗

arXiv2018

A concept of biopharmaceutical nanosatellite

The article is a short overview of a proposal of a CubeSat type nanosatellite designed to conduct biopharmaceutical tests on the low earth orbit. Motivations behind the emerging demand for such solution nowadays and in the close future are emphasized. The possible objectives and challenges to be addressed in the planned biopharmaceutical CubeSat missions are discussed. In particular, it is hard to imagine progress of the space tourism and colonization of Mars without a wide-ranging development of pharmaceutics dedicated to be used in space. Finally, an exemplary layout of a 3U type CubeSat is presented. We stress that, thanks to recent development in both nanosatellite technologies and lab-on-a-chip type biofluidic systems the proposed idea becomes now both feasible and relatively affordable.

physics.bio-ph↗

arXiv2018

From Causal Dynamical Triangulations To Astronomical Observations

This letter discusses phenomenological aspects of dimensional reduction predicted by the Causal Dynamical Triangulations (CDT) approach to quantum gravity. The deformed form of the dispersion relation for the fields defined on the CDT space-time is reconstructed. Using the Fermi satellite observations of the GRB 090510 source we find that the energy scale of the dimensional reduction is $E_* > 0.7 \sqrt{4-d_{\rm UV}} \cdot 10^{10}$ GeV at (95 $\%$ CL), where $d_{\rm UV}$ is the value of the spectral dimension in the UV limit. By applying the deformed dispersion relation to the cosmological perturbations it is shown that, for a scenario when the primordial perturbations are formed in the UV region, the scalar power spectrum $\mathcal{P}_S \propto k^{n_S-1}$ where $n_S-1\approx \frac{3 r (d_{\rm UV}-2)}{(d_{\rm UV}-1)r-48}$. Here, $r$ is the tensor-to-scalar ratio. We find that within the considered model, the predicted from CDT deviation from the scale-invariance ($n_S=1$) is in contradiction with the up to date Planck and BICEP2 data.

gr-qc↗

arXiv2018

Spin networks on adiabatic quantum computer

The article is addressing a possibility of implementation of spin network states on adiabatic quantum computer. The discussion is focused on application of currently available technologies and analyzes a concrete example of D-Wave machine. A class of simple spin network states which can be implemented on the Chimera graph architecture of the D-Wave quantum processor is introduced. However, extension beyond the currently available quantum processor topologies is required to simulate more sophisticated spin network states, which may inspire development of new generations of adiabatic quantum computers. A possibility of simulating Loop Quantum Gravity is discussed and a method of solving a graph non-changing scalar (Hamiltonian) constraint with the use of adiabatic quantum computations is proposed.

gr-qc↗

arXiv2017

Silent initial conditions for cosmological perturbations with a change of space-time signature

Recent calculations in loop quantum cosmology suggest that a transition from a Lorentzian to an Euclidean space-time might take place in the very early Universe. The transition point leads to a state of silence, characterized by a vanishing speed of light. This behavior can be interpreted as a decoupling of different space points, similar to the one characterizing the BKL phase. In this study, we address the issue of imposing initial conditions for the cosmological perturbations at the transition point between the Lorentzian and Euclidean phases. Motivated by the decoupling of space points, initial conditions characterized by a lack of correlations are investigated. We show that the "white noise" gains some support from analysis of the vacuum state in the deep Euclidean regime. Furthermore, the possibility of imposing the silent initial conditions at the trans-Planckian surface, characterized by a vanishing speed for the propagation of modes with wavelengths of the order of the Planck length, is studied. Such initial conditions might result from a loop-deformations of the Poincaré algebra. The conversion of the silent initial power spectrum to a scale-invariant one is also examined.

gr-qc↗

arXiv2017

Nonlinear Field Space Cosmology

We consider the FRW cosmological model in which the matter content of universe (playing a role of inflaton or quintessence) is given by a novel generalization of the massive scalar field. The latter is a scalar version of the recently introduced Nonlinear Field Space Theory (NFST), where physical phase space of a given field is assumed to be compactified at large energies. For our analysis we choose the simple case of a field with the spherical phase space and endow it with the generalized Hamiltonian analogous to the XXZ Heisenberg model, normally describing a system of spins in condensed matter physics. Subsequently, we study both the homogenous cosmological sector and linear perturbations of such a test field. In the homogenous sector we find that nonlinearity of the field phase space is becoming relevant for large volumes of universe and then it can lead to a recollapse, and possibly also at very high energies, leading to the phase of a bounce. Quantization of the field is performed in the limit where nontrivial nature of its phase space can be neglected, while there is a non-vanishing contribution from the Lorentz symmetry breaking term of the Hamiltonian. As a result, in the leading order of the XXZ anisotropy parameter, we find that the inflationary spectral index remains unmodified with respect to the standard case but the total amplitude of perturbations is subject to a correction. The Bunch-Davies vacuum state also becomes appropriately corrected. The proposed new approach is bringing cosmology and condensed matter physics closer together, which may turn out to be beneficial for both disciplines.

gr-qc↗

arXiv2017

Klein-Gordon field from the XXZ Heisenberg model

We examine the recently introduced idea of Spin-Field Correspondence focusing on the example of the spin system described by the XXZ Heisenberg model with external magnetic field. The Hamiltonian of the resulting nonlinear scalar field theory is derived for arbitrary value of the anisotropy parameter $Δ$. We show that the linear scalar field theory is reconstructed in the large spin limit. For $Δ=1$ a non-relativistic scalar field theory satisfying the Born reciprocity principle is recovered. As expected, for the vanishing anisotropy parameter $Δ\rightarrow 0$ the standard relativistic Klein-Gordon field is obtained. Various aspects of the obtained class of the scalar fields are studied, including the fate of the relativistic symmetries and the properties of the emerging interaction terms. We show that, in a certain limit, the so-called polymer quantisation of the field variables is recovered. This and other discussed properties suggest a possible relevance of the considered framework in the context of quantum gravity.

hep-th↗

arXiv2017

Spectral dimension with deformed spacetime signature

Studies of the effective regime of loop quantum gravity (LQG) revealed that, in the limit of Planckian curvature scales, spacetime may undergo a transition from the Lorentzian to Euclidean signature. This effect is a consequence of quantum modifications of the hypersurface deformation algebra, which in the linearized case is equivalent to a deformed version of the Poincaré algebra. In this paper the latter relation is applied to the LQG-inspired hypersurface deformation algebra that is characterized by the above mentioned signature change. While the exact form of the deformed Poincaré algebra is not uniquely determined, the algebra under consideration is representative enough to capture a number of qualitative features. In particular, the analysis reveals that the signature change can be associated with two symmetric invariant energy scales, which separate three physically disconnected momentum subspaces. Furthermore, the invariant measure on momentum space is derived, which allows to properly define the average return probability, characterizing a fictitious diffusion process on spacetime. The diffusion is subsequently studied in the momentum representation for all possible variants of the model. Finally, the spectral dimension of spacetime is calculated in each case as a function of the scale parameter. In the most interesting case the deformation is of the asymptotically ultralocal type and the spectral dimension undergoes a reduction to $d_S = 1$ in the UV limit.

hep-th↗

arXiv2017

The Top-Down Complexity

The rising complexity of our terrestrial surrounding is an empirical fact. Details of this process evaded description in terms of physics for long time attracting attention and creating myriad of ideas including non-scientific ones. In this essay we explain the phenomenon of the growth of complexity by combining our up to date understanding of cosmology, non-equilibrium physics and thermodynamics. We argue that the observed increase of complexity is causal in nature, stands in agreement with the second law of thermodynamics and has it's origin in the cosmological expansion. Moreover, we highlight the connection between the leader of complexity growth in localized areas of space with free energy rate density, starting from the largest scales towards the smaller ones. Finally, in the light of recent advances in non-equilibrium statistical mechanics, our belief in the causal structure of modern scientific theories is transferred to biological systems. On relevant scales, adaptation and complexity growth follows a similar pattern, in which free energy rate density is provided by an external electromagnetic radiation. The presented, holistic approach, arms us with predicting power about variety of attributes of complex systems and leads to a chain of successful explanations on all scales of the Universe.

physics.pop-ph↗

arXiv2017

Spin-Field Correspondence

In the recent article Phys.\ Lett.\ B {\bf 759} (2016) 424 a new class of field theories called Nonlinear Field Space Theory has been proposed. In this approach, the standard field theories are considered as linear approximations to some more general theories characterized by nonlinear field phase spaces. The case of spherical geometry is especially interesting due to its relation with the spin physics. Here, we explore this possibility showing that classical scalar field theory with such a field space can be viewed as a perturbation of a continuous spin system. In this picture, the spin precession and the scalar field excitations are dual descriptions of the same physics. The duality is studied on the example of the Heisenberg model. It is shown that the Heisenberg model coupled to a magnetic field leads to a non-relativistic scalar field theory, characterized by quadratic dispersion relation. Finally, on the basis of analysis of the relation between the spin phase space and the scalar field theory we propose the \emph{Spin-Field correspondence} between the known types of fields and the corresponding spin systems.

hep-th↗

arXiv2016

Slow-roll approximation in loop quantum cosmology

The slow-roll approximation is an analytical approach to study dynamical properties of the inflationary universe. In this article, systematic construction of the slow-roll expansion for effective loop quantum cosmology is presented. The analysis is performed up to the fourth order in both slow-roll parameters and the parameter controlling the strength of deviation from the classical case. The expansion is performed for three types of the slow-roll parameters: Hubble slow-roll parameters, Hubble flow parameters and potential slow-roll parameters. An accuracy of the approximation is verified by comparison with the numerical phase space trajectories for the case with a massive potential term. The results obtained in this article may be helpful in the search for the subtle quantum gravitational effects with use of the cosmological data.

gr-qc↗