General Relativity And Quantum Cosmology
Generalized Tachyonic Teleparallel cosmology (1901.04973v1)
Sebastian Bahamonde, Mihai Marciu, Jackson Levi Said
2019-01-15
In this paper we propose a new dark energy model in the teleparallel alternative of general relativity, by considering a generalized non--minimal coupling of a tachyonic scalar field with the teleparallel boundary term. Within the framework of teleparallel gravity, the boundary coupling term is associated with the divergence of the torsion vector. Considering the linear stability technique for various potentials and couplings, we have analyzed the dynamical properties of the present tachyonic dark energy model in the phase space, uncovering the corresponding essential dynamical features. Our study of the phase space structure revealed that for a specific class of potential energy, this model exhibits various critical points which are related to different cosmological behaviors, such as accelerated expansion and scaling solutions, determining the existence conditions and the corresponding physical features.
The Wave Function of the Universe and CMB Fluctuations (1811.12892v3)
S. P. de Alwis
2018-11-30
The Hartle-Hawking and Tunneling (Vilenkin) wave functions are treated in the Hamiltonian formalism. We find that the leading (i.e. quadratic) terms in the fluctuations around a maximally symmetric background, are indeed Gaussian (rather than inverse Gaussian), for both types of wave function, when properly interpreted. However the suppression of non-Gaussianities and hence the recovery of the Bunch-Davies state is not transparent.
Dynamical Properties of the Mukhanov-Sasaki Hamiltonian in the context of adiabatic vacua and the Lewis-Riesenfeld invariant (1812.11122v2)
Max Joseph Fahn, Kristina Giesel, Michael Kobler
2018-12-28
We use the method of the Lewis-Riesenfeld invariant to analyze the dynamical properties of the Mukhanov-Sasaki Hamiltonian and, following this approach, investigate whether we can obtain possible candidates for initial states in the context of inflation. Our main interest lies in the question to which extent these already well-established methods at the classical and quantum level for finitely many degrees of freedom can be generalized to field theory. As our results show, a straightforward generalization does in general not lead to a unitary operator on Fock space that implements the corresponding time-dependent canonical transformation associated with the Lewis-Riesenfeld invariant. The action of this operator can be rewritten as a time-dependent Bogoliubov transformation and we show that its generalization to Fock space has to be chosen appropriately in order that the Shale-Stinespring condition is not violated, where we also compare our results to already existing ones in the literature. Furthermore, our analysis relates the Ermakov differential equation that plays the role of an auxiliary equation, whose solution is necessary to construct the Lewis-Riesenfeld invariant, as well as the corresponding time-dependent canonical transformation to the defining differential equation for adiabatic vacua. Therefore, a given solution of the Ermakov equation directly yields a full solution to the differential equation for adiabatic vacua involving no truncation at some adiabatic order. As a consequence, we can interpret our result obtained here as a kind of non-squeezed Bunch-Davies mode, where the term non-squeezed refers to a possible residual squeezing that can be involved in the unitary operator for certain choices of the Bogoliubov map.
Operator-algebraic construction of gauge theories and Jones' actions of Thompson's groups (1901.04940v1)
Arnaud Brothier, Alexander Stottmeister
2019-01-15
Using ideas from Jones, lattice gauge theory and loop quantum gravity, we construct 1+1-dimensional gauge theories on a spacetime cylinder. Given a separable compact group
, we construct localized time-zero fields on the spatial torus as a net of C*-algebras together with an action of the gauge group that is an infinite product of
as a replacement of the spatial diffeomorphism group. Adding a family of probability measures on the unitary dual of
the circle group together with a certain family of heat-kernel states providing the measures, we obtain hyperfinite type III factors with a normal faithful state providing a nontrivial time evolution via Tomita-Takesaki theory (KMS condition). In the latter case, we additionally have a non-singular action of the group of rotations with dyadic angles, as a subgroup of Thompson's group
Chaos in Matrix Models and Black Hole Evaporation (1602.01473v3)
Evan Berkowitz, Masanori Hanada, Jonathan Maltz
2016-02-03
Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question ---especially aspects of this question such as a black hole's negative specific heat---we consider the real-time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zero-brane) via holography. We point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of D0-branes from the black brane, which is suppressed in the large
limit. Simple arguments show that the black zero-brane, like the Schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0-branes. While the largest Lyapunov exponent grows during the evaporation, the Kolmogorov-Sinai entropy decreases. These are consequences of the generic properties of matrix models and gauge theory. Based on these results, we give a possible geometric interpretation of the eigenvalue distribution of matrices in terms of gravity. Applying the same argument in the M-theory parameter region, we provide a scenario to derive the Hawking radiation of massless particles from the Schwarzschild black hole. Finally, we suggest that by adding a fraction of the quantum effects to the classical theory, we can obtain a matrix model whose classical time evolution mimics the entire life of the black brane, from its formation to the evaporation.
Linear Stability of Mandal-Sengupta-Wadia Black Holes (1706.07877v2)
H. Gürsel, G. Tokgöz, İzzet Sakallı
2017-06-23
In this letter, the linear stability of static Mandal-Sengupta-Wadia (MSW) black holes in
-dimensional gravity against circularly symmetric perturbations is studied. Our analysis only applies to non-extremal configurations, thus it leaves out the case of the extremal (2+1) MSW solution. The associated fields are assumed to have small perturbations in these static backgrounds. We then consider the dilaton equation and specific components of the linearized Einstein equations. The resulting effective Klein-Gordon equation is reduced to the Schr"{o}dinger like wave equation with the associated effective potential. Finally, it is shown that MSW black holes are stable against to the small time-dependent perturbation
Multi-body spherically symmetric steady states of Newtonian self-gravitating elastic matter (1807.03062v2)
Artur Alho, Simone Calogero
2018-07-09
We study the problem of static, spherically symmetric, self-gravitating elastic matter distributions in Newtonian gravity. To this purpose we first introduce a new definition of homogeneous, spherically symmetric (hyper)elastic body in Euler coordinates, i.e., in terms of matter fields defined on the current physical state of the body. We show that our definition is equivalent to the classical one existing in the literature and which is given in Lagrangian coordinates, i.e., in terms of the deformation of the body from a given reference state. After a number of well-known examples of constitutive functions of elastic bodies are re-defined in our new formulation, a detailed study of the Seth model is presented. For this type of material the existence of single and multi-body solutions is established.
Testing the multipole structure of compact binaries using gravitational wave observations (1809.10465v2)
Shilpa Kastha, Anuradha Gupta, K. G. Arun, B. S. Sathyaprakash, Chris Van Den Broeck
2018-09-27
We propose a novel method to test the consistency of the multipole moments of compact binary systems with the predictions of General Relativity (GR). The multipole moments of a compact binary system, known in terms of symmetric and trace-free tensors, are used to calculate the gravitational waveforms from compact binaries within the post-Newtonian (PN) formalism. For nonspinning compact binaries, we derive the gravitational wave phasing formula, in the frequency domain, parametrizing each PN order term in terms of the multipole moments which contribute to that order. Using GW observations, this {\it{parametrized multipolar phasing}} would allow us to derive the bounds on possible departures from the multipole structure of GR and hence constrain the parameter space of alternative theories of gravity. We compute the projected accuracies with which the second generation ground-based detectors, such as Advanced Laser Interferometer Gravitational-wave Observatory (LIGO), the third generation detectors such as Einstein Telescope and Cosmic Explorer, as well as space-based detector Laser Interferometer Space Antenna (LISA) will be able to measure these multipole parameters. We find that while Advanced LIGO can measure the first two or three multipole coefficients with good accuracy, Cosmic Explorer and Einstein Telescope may be able to measure the first four multipole coefficients which enter the phasing formula. Intermediate mass ratio inspirals, with mass ratio of several tens, in the frequency band of planned space-based LISA mission should be able to measure all the seven multipole coefficients which appear in the 3.5PN phasing formula. Our finding highlights the importance of this class of sources for probing the strong-field gravity regime. The proposed test will facilitate the first probe of the multipolar structure of Einstein's general relativity.
Dirac equation in exotic spacetimes (1811.00385v3)
Javier Faba García, Carlos Sabín
2018-10-30
We find solutions of the Dirac equation in curved spacetime. In particular, we consider 1+1 dimensional sections of several exotic metrics: the Alcubierre metric, which describes a scenario that allows faster-than-light (FTL) velocity; the G"odel metric, that describes a universe containing closed timelike curves (CTC); and the Kerr metric, which corresponds to the spacetime of a rotating black hole. Moreover, we also show that the techniques that we use in these cases can be extended to nonstatic metrics.
Quasilocal horizons in inhomogeneous cosmological models (1803.11005v2)
Eliška Polášková, Otakar Svítek
2018-03-29
We investigate quasilocal horizons in inhomogeneous cosmological models, specifically concentrating on the notion of a trapping horizon defined by Hayward as a hypersurface foliated by marginally trapped surfaces. We calculate and analyse these quasilocally defined horizons in two dynamical spacetimes used as inhomogeneous cosmological models with perfect fluid source of non-zero pressure. In the spherically symmetric Lema^{i}tre spacetime we discover that the horizons (future and past) are both null hypersurfaces provided that the Misner-Sharp mass is constant along the horizons. Under the same assumption we come to the conclusion that the matter on the horizons is of special characte - a perfect fluid with negative pressure. We also find out that they have locally the same geometry as the horizons in the Lema^{i}tre-Tolman-Bondi spacetime. We then study the Szekeres-Szafron spacetime with no symmetries, particularly its subfamily with
, and we find conditions on the horizon existence in a general spacetime as well as in certain special cases.
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