abstract

We describe a CDT-like model where breaking of \(W^{(3)}\) symmetry will lead to the emergence of time and, subsequently, of space. Surprisingly, the simplest such models which lead to higher dimensional spacetimes are based on the four “magical” Jordan algebras of \(3\times 3\) Hermitian matrices with real, complex, quaternion and octonion entries, respectively. The simplest symmetry breaking leads to universes with spacetime dimensions 3, 4, 6, and 10.

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Causal Dynamical Triangulations (CDT) is a lattice approach to quantum gravity. CDT has rich phase structure, including a semiclassical phase consistent with Einstein’s general relativity. Some of the observed phase transitions are second (or higher) order which opens a possibility of investigating the ultraviolet continuum limit. Recently, a new phase with intriguing geometric properties has been discovered and the new phase transition is also second (or higher) order.

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Causal Dynamical Triangulations (CDT) is a background-independent approach to quantum gravity which provides a lattice regularization. In the case of spherical spatial topology, a universe with geometry of a four-sphere emerges dynamically in the so-called de Sitter phase. Imposing toroidal spatial topology changes this picture significantly and the average spatial volume profile becomes constant. Although no background geometry is put in by hand, the full quantum theory of CDT is able to identify a classical background geometry with superimposed quantum fluctuations. We determine the effective action for spatial volume by measuring the covariance matrix and show how to heal the problem of uniform volume profile.

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We study a formulation of lattice gravity defined via Euclidean dynamical triangulations (EDT). After fine-tuning a non-trivial local measure term, we find evidence that four-dimensional, semi-classical geometries are recovered at long distance scales in the continuum limit. Furthermore, we find that the spectral dimension at short distance scales is consistent with 3/2, a value that is also observed in the causal dynamical triangulation (CDT) approach to quantum gravity.

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In this short, virtually equations-free note I present the basic points of our recent paper, in which, using the Loop Quantum Gravity techniques, we showed that the symmetries of flat quantum spacetime in three dimensions are described by quantum \(\kappa \)-Poincaré algebra. I am stressing the physical meaning of this result, avoiding technical details.

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The recent data on astrophysical neutrinos provided by the IceCube telescope offer a striking opportunity to test in vacuo dispersion of ultra-relativistic particles propagating in quantum spacetime scenarios inspired by phenomenological approaches to quantum gravity. We propose a novel method of investigation of these effects based on a statistical analysis of the correlation between neutrino energies, and the difference in detection times between neutrinos and candidate associated GRB trigger photons. The results we obtain show an amazingly high correlation of about 0.95, characterized by a false alarm probability of less than 0.1%.

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Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far, such phase spaces have only been considered for particles or strings. We propose an extension of the usual field theories to the framework of fields with nonlinear phase space of field values, which generally means nontrivial topology or geometry. In order to examine this idea, we construct a prototype scalar field with the spherical phase space and then study its quantized version with the help of perturbative methods. As a result, we obtain a variety of predictions that are known from the quantum gravity research, including algebra deformations, generalization of the uncertainty relation and shifting of the vacuum energy.

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We discuss relativistic particle and field theoretic models of an interaction with an environment. We show that in a Markovian approximation such models lead to a diffusion. We interpret dark energy as an environment for the dark matter.

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In this letter, we discuss a comparison between two scalar field models that have been recently introduced in the context of loop quantum gravity. The scalar fields play the role of so-called reference fields that allow to construct Dirac observables for general relativity and introduce a notion of physical spatial and time coordinates respectively. One of the models uses Dirac quantization, the other one reduced phase space quantization. We want to compare the physical sector of both quantum theories and discuss their similarities and differences with a particular focus on their quantum dynamics.

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By using a scalar field as a relational time variable for the dynamics of the gravitational field, we construct mathematically complete and well-defined models of loop quantum gravity, in which the dynamics of quantum geometry is explicitly computable, at least in certain simple examples.

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A century after their prediction by Albert Einstein, gravitational waves were registered directly on Earth for the first time by the two detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO). A short description of gravitational wave phenomenon is given and the extraordinary sensitivity of the detector required to measure gravitational radiation is pointed out. Basic principle of the laser ineterferometric detector is presented. The detection of the first signal that originated from merger of two black holes is described. Finally, results of the recent searches for other sources of gravitational waves than the binary black hole coalescence are summarized.

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We discuss the relevance of the magnetorotational instability (MRI) in core-collapse supernovae (CCSNe). Our recent numerical studies show that in CCSNe, the MRI is terminated by parasitic instabilities of the Kelvin–Helmholtz type. To determine whether the MRI can amplify initially weak magnetic fields to dynamically relevant strengths in CCSNe, we performed three-dimensional simulations of a region close to the surface of a differentially rotating proto-neutron star in non-ideal magnetohydrodynamics with two different numerical codes. We find that under the conditions prevailing in proto-neutron stars, the MRI can amplify the magnetic field by (only) one order of magnitude. This severely limits the role of MRI channel modes as an agent amplifying the magnetic field in proto-neutron stars starting from small seed fields.

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This is an introduction to the problem of how generic may be a Lagrangian replacing the \(L=R\) one of Einstein’s General Relativity. We show that if the Lagrangian explicitly depends on the Weyl tensor, it is difficult to assign degrees of freedom to the tensor. In a tenable theory of gravity, the Lagrangian should be free of the conformal tensor, only the Ricci tensor is admissible.

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Kaluza–Klein metric is considered with wet dark fluid (WDF) source in \(f(R,T)\) gravity, where \(R\) is the Ricci scalar and \(T\) is the trace of the energy-momentum tensor proposed by Harko et al. (2011). The exact solutions of the field equations are derived from a time varying deceleration parameter.

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4-dimensional spaces equipped with 2-dimensional completely integrable distributions are considered. The integral manifolds of such distributions are totally null and totally geodesics 2-dimensional surfaces (the null strings). The relations between congruences (foliations) of the null strings and SD Weyl spinor and traceless Ricci tensor is analyzed. Finally, some explicit Einstein metrics of the spaces which admit the existence of the congruences of the null strings are presented.

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The structure of vacuum Einstein’s field equations for \(n\)-dimensional Kundt’s metrics is described. Using the Bianchi identity, it is shown that if a part of these equations is satisfied, then the remaining can be reduced to linear system. This observation can be used to generate new solutions from old ones. Starting from the known solution, we construct the metric of type II. We also resolve the discrepancy in general form of type D vacuum Kundt’s spacetime which has been arisen in the literature.

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The strong antigravity effects following from the Mathisson–Papapetrou equations for a highly relativistic spinning particle are discussed.

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We have found in analytic form an exact solution with separable variables for null one-way Maxwell field \(\varphi _{AB}=\varphi _2 o_A o_B\) on the Kerr space-time background and have investigated some of its properties. Solution describes outgoing waves when \(r\gt r_{{\mathrm {cr.}} 1}\gt r_{+}\), but for some Maxwell field parameters, this solution describes ingoing, standing and outgoing waves on defined intervals in the region of \(r\gt r_{+}\).

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We propose a description of linearised vacuum perturbation of a Kottler metric in terms of four unconstrained scalar functions, invariant with respect to the infinitesimal coordinate change gauge. We present a derivation of the generalised Regge–Wheeler and Zerilli equations in this scheme.

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The Hamiltonian definition of quasi-local mass is given. It is based on the multipole decomposition on Round Sphere or Rigid Sphere. The test of our quasi-local mass is performed for the Kerr spacetime.

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Self-consistent treatment of cosmological structure formation and expansion within the context of classical general relativity may lead to “extra” expansion above that expected in a structureless universe. We argue that in comparison to an early-epoch, extrapolated Einstein–de Sitter model, about 10–15% “extra” expansion is sufficient at the present to render superfluous the “dark energy” 68% contribution to the energy density budget, and that this is observationally realistic.

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The current cosmological model (\(\mit \Lambda \)CDM) with the underlying FLRW metric relies on the assumption of local isotropy, hence, homogeneity of the Universe. Difficulties arise when one attempts to justify this model as an average description of the Universe from first principles of general relativity, since, in general, the Einstein tensor built from the averaged metric is not equal to the averaged stress-energy tensor. In this context, the discrepancy between these quantities is called “cosmological backreaction” and has been the subject of scientific debate among cosmologists and relativists for more than 20 years. Here, we present one of the methods to tackle this problem, i.e. averaging the scalar parts of the Einstein equations, together with its application, the cosmological mass function of galaxy clusters.

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We constrain the contribution of tensor-mode perturbations with free \(n_{\rm t}\) in the models with dynamical dark energy with the barotropic equation of state using Planck 2015 data on CMB anisotropy, polarization and lensing, BICEP2/Keck Array data on B-mode polarization, power spectrum of galaxies from WiggleZ and SN Ia data from the JLA compilation. We also investigate the uncertainties of reconstructed potential of the scalar field dark energy.

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The models of cyclic universes and cyclic multiverses based on the alternative gravity theories of varying constants are considered.

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An analytical solution of exact perturbation equations in the flat radiation-dominated relativistic cosmology posed by Evgeny M. Lifshitz in 1946 is found. From this, we obtain exact form for the scale-dependent growth factor function which is important in observational cosmology as a useful tool of model testing.

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Dynamical systems methods are used to investigate cosmological model with non-minimally coupled scalar field. Existence of an asymptotically unstable de Sitter state distinguishes values of the non-minimal coupling constant parameter \(\frac {3}{16}\le \xi \lt \frac {1}{4}\), which correspond to conformal coupling in higher dimensional theories of gravity.