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arXiv2007

Quantum back-reaction problems

The macroscopic behavior of many physical systems can be approximately described by classical quantities. However, quantum theory demands the existence of omnipresent quantum fluctuations on top of this classical background -- which, albeit small, should have some impact onto its dynamics. The correct treatment of this quantum back-reaction is one of the main problems in quantum gravity and related to fundamental questions such as the initial (big bang) singularity or the cosmological constant. By means of the qualitative analogy between gravity and fluid dynamics, we try to shed some light onto these problems and show some of the difficulties associated with the calculation of the quantum back-reaction starting from the classical (macroscopic) equation of motion.

gr-qc↗

arXiv2008

Constructive use of holographic projections

Revisiting the old problem of existence of interacting models of QFT with new conceptual ideas and mathematical tools, one arrives at a novel view about the nature of QFT. The recent success of algebraic methods in establishing the existence of factorizing models suggests new directions for a more intrinsic constructive approach beyond Lagrangian quantization. Holographic projection as a simplifying tool for certain aspects of QFT turn out to be an indispensible part of these new attempts.

hep-th↗

arXiv2008

Causal Set Topology

The Causal Set Theory (CST) approach to quantum gravity is motivated by the observation that, associated with any causal spacetime (M,g) is a poset (M,<), with the order relation < corresponding to the spacetime causal relation. Spacetime in CST is assumed to have a fundamental atomicity or discreteness, and is replaced by a locally finite poset, the causal set. In order to obtain a well defined continuum approximation, the causal set must possess the requisite intrinsic topological and geometric properties that characterise a continuum spacetime in the large. The continuum approximation thus sets the stage for the study of topology in CST. We review the status of causal set topology and present some new results relating poset and spacetime topologies. The hope is that in the process, some of the ideas and questions arising from CST will be made accessible to the larger community of computer scientists and mathematicians working on posets.

gr-qc↗

arXiv2008

Warp Drive: A New Approach

Certain classes of higher dimensional models suggest that the Casimir Effect is a candidate for the cosmological constant. In this paper we demonstrate that a sufficiently advanced civilization could, in principal, manipulate the radius of the extra dimension to locally adjust the value of the cosmological constant. This adjustment could be tuned to generate an expansion/contraction of spacetime around a spacecraft creating an exotic form of field-propulsion. Due to the fact that spacetime expansion itself is not restricted by relativity, a faster-than-light 'warp drive' could be created. Calculations of the energy requirements of such a drive are performed and an 'ultimate' speed limit, based on the Planckian limits on the size of the extra dimensions is found.

gr-qc↗

arXiv2007

On quantum cosmology as field theory of bosonic string mass groundstate

The Quantum Cosmology can be understand as the theory of an one object that is the Universe described in terms of fundamental mass groundstate of the free boson string, that is a tachyon - a hypothetical particle with negative mass square, which has linear velocity more than the velocity of light c. From this fact it is clear that whole information about physics of our Universe is focused on studying of this untypical particle physics. In this paper this point of view is touched up on. As the general-relativistic model of our Universe we study the Einstein-Friedmann Spacetime. Firstly, the way of canonical quantization beginning from first quantization of the Dirac Hamiltonian constraints up to the second quantization by the Von Neumann-Araki-Woods quantization in the Fock space is briefly discussed. We show that using of the Bogoliubov-Heinsenberg static operator basis leads to formulation of the second quantization of the considered free boson string in terms of the monodromy in the Fock space. Finally, we propose some specific model of the Universe - the extremal tachyon mass model, and in frames of its the Hubble evolution parameter, the equation of state for Dark Matter in the Universe, and the temperature of our Universe are concluded.

gr-qc↗

arXiv2010

Recent progress on the notion of global hyperbolicity

Global hyperbolicity is a central concept in Mathematical Relativity. Here, we review the different approaches to this concept explaining both, classical approaches and recent results. The former includes Cauchy hypersurfaces, naked singularities, and the space of the causal curves connecting two events. The latter includes structural results on globally hyperbolic spacetimes, their embeddability in Lorentz-Minkowski, and the recently revised notions of both, causal and conformal boundaries. Moreover, two criteria for checking global hyperbolicity are reviewed. The first one applies to general splitting spacetimes. The second one characterizes accurately global hyperbolicity and spacelike Cauchy hypersurfaces for standard stationary spacetimes, in terms of a naturally associated Finsler metric.

gr-qc↗

arXiv2008

Large tensor-to-scalar ratio and low scale inflation

It is plausible that the scalar density perturbations are created by a relatively low scale model of inflation which predicts the CMB anisotropy and excites Standard Model baryon and cold dark matter, but negligible gravity waves. Nevertheless a significantly large tensor perturbations can be observed if there exists a prior phase of high scale inflation separated by a matter or radiation dominated epoch. In this paper we provide a simple example when the gravity waves generated at high scales trickle through the horizon of the second phase of inflation and leave a distinct imprint in the spectrum of the tensor modes. For a high scale inflation occurring at $H\sim 10^{13}$ GeV while the second phase of inflation happening at $H\sim 1$ GeV, the largest tensor to scalar ratio is bounded by $r_{\rm observed}\leq0.8$.

astro-ph↗

arXiv2007

Decoupling of kinematical time dilation and gravitational time dilation in particular geometries

Two different forms of time dilation, namely, the kinematical time dilation of special relativity and gravitational red shift are coupled during observations of systems moving through a gravitational field. In the particular situation of free fall in a Schwarzschild geometry these two effects are decoupled and in consequence the time dilation, as observed by a distant observer, factorises. Such a factorization is not a universal feature. We define here a necessary and sufficient criterion for time dilation and gravitational red-shift decoupling. This property is manifested in a particular form of the Doppler shift in Schwarzschild geometry.

gr-qc↗

arXiv2007

Quantum mechanics of the closed collapsing Universe

Two approaches to quantization of Freedman's closed Universe are compared. In the first approach, the Shrodinger's norm of the wave function of Universe is used, and in the second approach, the Klein-Gordon's norm is used. The second one allows building the quasi-Heisenberg operators as functions of time and finding their average values. It is shown that the average value of the Universe scale factor oscillates with damping and approaches to some constant value at the end of the Universe evolution.

gr-qc↗

arXiv2012

Holography constrains quantum bounce

Recent work in quantum loop cosmology suggests the universe undergoes a bounce when evolving from a previous collapsing phase. However, with non-inflationary matter sources, the scenario appears to strongly violate the holography bound S\leq A/4 during the bounce, where A now represents the cross-sectional area of the bounce. We also give a simple argument why any inflationary phase after the bounce is unlikely due to prior dissipation of a scalar field kinetic energy phase into regular matter components.

gr-qc↗

arXiv2013

On Particle Mass Changes and GR: Space-time Topology Causes LHC Leakage

It is argued that a change in particle rest mass must involve a multiply connected space-time topology. The LHC can probe these topological effects through the particle leakage (~18%) that it experiences in particle mass changing interactions. With a probability of ~82%, this 4-space leakage causes a downward shift in the observable Higgs mass, from its physical value of 131.6 GeV to 125.2 GeV.

gr-qc↗

arXiv2013

Isotropisation of Quadratic Gravity: Scalar and Tensor Components

It is believed that soon after the Planck era, spacetime should have a semi-classical nature. Therefore, it is unavoidable to modify the theory of General Relativity or look for alternative theories of gravitation. An interesting possibility found in the literature considers two geometric counter-terms to regularize the divergences of the effective action. These counter-terms are responsible for a higher order derivative metric theory of gravitation. In the present letter we investigate how isotropisation occurs. For this reason a single solution is chosen throughout this article. We obtain perturbatively, by two different methods, that the tensor and scalar components emerge naturally during the isotropisation process. In this sense our result provides a numerical example to Stelle's well known result on classical gravity with higher derivates. Our entire analysis is restricted to the particular Bianchi type $I$ case.

gr-qc↗

arXiv2013

Revealing Non-circular beam effect in WMAP-7 CMB maps with BipoSH measures of Statistical Isotropy

Mild, unavoidable deviations from circular-symmetry of instrumental beams in current Cosmic Microwave Background (CMB) experiments now pose a significant challenge to deriving high precision inferences from the high sensitivity and resolution of CMB measurements. We present analytic results, verified by numerical simulations, that CMB maps of cosmological signal that respect underlying statistical isotropy (SI) symmetry, measured with an instrument that has mildly non-circular (NC) beam would, nevertheless, exhibit SI violation. Further, we show that appropriate observable measures constructed within the Bipolar spherical harmonic (BipoSH) representation of SI violation capture subtle NC-beam effects coupled with the scan strategy of the instrument. Accompanying their latest 7-year data release, the WMAP team published very high significance measurements of non-zero BipoSH spectra, A^{20}_{l l} and A^{20}_{l-2 l}, in the "W" and "V" band of the experiment. We present a strong case that the BipoSH measurement are primarily explained by the quadrupolar (m=2) component of the NC-beams, b_{l2}, of the respective channels. The fact that subtle levels of non-circularity, e.g., WMAP beams |b_{l2}|/b_{l0} < 0.01, lead to measurable BipoSH spectra points to the immense promise and potential of the BipoSH representation. The key result of this work is that using BipoSH measurements it is possible to estimate an equivalent single hit,'parallel transported' effective NC-beam that matches both the angular power spectrum and the non-zero BipoSH measurements of the observed maps. Hence, BipoSH analysis provides a very simple and effective characterization of CMB maps made with NC-beam. (Abridged)

astro-ph.CO↗

arXiv2013

Deformations of Fuchsian AdS representations are Quasi-Fuchsian

Let $Γ$ be a finitely generated group, and let $\op{Rep}(Γ, \SO(2,n))$ be the moduli space of representations of $Γ$ into $\SO(2,n)$ ($n \geq 2$). An element $ρ: Γ\to \SO(2,n)$ of $\op{Rep}(Γ, \SO(2,n))$ is \textit{quasi-Fuchsian} if it is faithful, discrete, preserves an acausal subset in the conformal boundary $\Ein_n$ of the anti-de Sitter space; and if the associated globally hyperbolic anti-de Sitter space is spatially compact - a particular case is the case of \textit{Fuchsian representations}, i.e. composition of a faithfull, discrete and cocompact representation $ρ_f: Γ\to \SO(1,n)$ and the inclusion $\SO(1,n) \subset \SO(2,n)$. In \cite{merigot} we proved that quasi-Fuchsian representations are precisely representations which are Anosov as defined in \cite{labourie}. In the present paper, we prove that quasi-Fuchsian representations form a connected component of $\op{Rep}(Γ, \SO(2,n))$. This is an almost direct corollary of the following result: let $Γ$ be the fundamental group of a globally hyperbolic spacetime locally modeled on $\AdS_n$, and let $ρ: Γ\to \SO_0(2,n)$ be the holonomy representation. Then, if $Γ$ is Gromov hyperbolic, the $ρ(Γ)$-invariant achronal limit set in $\Ein_n$ is acausal.

math.RT↗

arXiv2013

Equivalent Generic Forms for Metric Fields Yielded by Relativistic Positioning Systems

Relativistic positioning systems provide tensors represented in $\{\ell\ell\ell\ell\}$-frames ($\ell$ for light) dual to systems of emission coordinates. We show that any Lorentzian metric field given in such a frame is isometrically equivalent to a generic metric field defined by only four positive functions depending on another specific system of emission coordinates.

gr-qc↗

arXiv2013

Statistical Inference and String Theory

In this note we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical fitting parameters. When the agents making nearby inferences align along a d-dimensional grid, we find that the pooled probability that the collective reaches a correct inference is the partition function of a non-linear sigma model in d dimensions. Stability under perturbations to the original inference scheme requires the agents of the collective to distribute along two dimensions. Conformal invariance of the sigma model corresponds to the condition of a stable inference scheme, directly leading to the Einstein field equations for classical gravity. By summing over all possible arrangements of the agents in the collective, we reach a string theory. We also use this perspective to quantify how much an observer can hope to learn about the internal geometry of a superstring compactification. Finally, we present some brief speculative remarks on applications to the AdS/CFT correspondence and Lorentzian signature spacetimes.

hep-th↗

arXiv2013

CDT and the Search for a Theory of Quantum Gravity

Causal Dynamical Triangulations provide a non-perturbative regularization of a theory of quantum gravity. We describe how this approach connects with the asymptotic safety program and Ho\vrava-Lifshitz gravity theory, and present the most recent results from computer simulations.

gr-qc↗

arXiv2013

Finite Quantum Gravity

We hereby present a class of multidimensional higher derivative theories of gravity that realizes an ultraviolet completion of Einstein general relativity. This class is marked by a "non-polynomal" entire function (form factor), which averts extra degrees of freedom (including ghosts) and improves the high energy behavior of the loop amplitudes. By power counting arguments, it is proved that the theory is super-renormalizable in any dimension, i.e. only one-loop divergences survive. Furthermore, in odd dimensions there are no counter terms for pure gravity and the theory turns out to be "finite." Finally, considering the infinite tower of massive states coming from dimensional reduction, quantum gravity is finite in even dimension as well.

hep-th↗