Minisuperspace Approach Research Articles

The semi-classical saddles in three-dimensional gravity via holography and mini-superspace approach

We determine the complex geometries dual to the semi-classical saddles in three-dimensional gravity with positive or negative cosmological constant. We examine the semi-classical saddles in Liouville field theory and interpret them in terms of gravity theory. For this, we describe the gravity theory by Chern-Simons theory and classify the possible saddles based on the homotopy group argument. We further realize the semi-classical saddles using the mini-superspace model of quantum gravity and explicitly determine the integral contour. In the case of positive cosmological constant, we recovered the geometry used for no-boundary proposal of Hartle and Hawking. In the case of negative cosmological constant, the geometry can be identified with Euclidean anti-de Sitter space attached with imaginary radius spheres. The geometry should be unphysical and several arguments on this issue are provided. Partial results were already presented in our earlier letter, and more detailed derivations and explanations on the results are given along with additional results. In particular, we reproduce the classical Liouville action from the Chern-Simons formulation of dual gravity theory.

Rotating cosmologies: classical and quantum

We revisit spatially flat, anisotropic cosmologies within the framework of mini-superspace. Putting special emphasis on the symmetries of the mini-superspace action and on the associated conservation laws, we unveil a new class of rotating cosmologies driven by solid matter. Their rotating is physical, in that it is characterized in an invariant way in terms of a conserved angular momentum. Along the way, we confirm the results of Bartolo et al. regarding the slow decay of anisotropies for solid inflation. We then use our minisuperspace approach as a laboratory to address certain puzzles of quantum cosmology — among these, how to characterize the spacetime symmetries of a quantum state at the level of the wavefunction of the universe. For the case of a solid driven cosmology, this question seems better defined than in more standard cases. Other questions remain unanswered, though; in particular, the general question of how to operate a minisuperspace-like truncation of degrees of freedom that is consistent at the quantum level.

Constraints on self-dual black hole in loop quantum gravity with S0-2 star in the galactic center

One of remarkable features of loop quantum gravity (LQG) is that it can provide resolutions to both the black hole and big bang singularities. In the mini-superspace approach based on the polymerization procedure in LQG, a quantum corrected black hole metric is constructed. This metric is also known as self-dual spacetime since the form of the metric is invariant under the exchange r ⟶ a 0/r with a 0 being proportional to the minimum area in LQG and r is the standard radial coordinate at asymptotic infinity. It modifies the Schwarzschild spacetime by the polymeric function P, purely due to the geometric quantum effects from LQG. Here P is related to the polymeric parameter δ which is introduced to define the paths one integrates the connection along to define the holonomies in the quantum corrected Hamiltonian constraint in the polymerization procedure in LQG. In this paper, we consider its effects on the orbital signatures of S0-2 star orbiting Sgr A* in the central region of our Milky Way, and compare it with the publicly available astrometric and spectroscopic data, including the astrometric positions, the radial velocities, and the orbital precession for the S0-2 star. We perform Monte Carlo Markov Chain (MCMC) simulations to probe the possible LQG effects on the orbit of S0-2 star. No significant evidence of the self-dual spacetime arisIng from LQG is found. We thus place an upper bounds at 95% confidence level on the polymeric function P < 0.043 and P < 0.056, for Gaussian and uniform priors on orbital parameters, respectively.

Wave function of the universe in the presence of trans-Planckian censorship

The wave function for a closed de Sitter universe has been computed, demanding consistency with the recently proposed Trans-Planckian Censorship Conjecture (TCC). We extend the Einstein-Hilbert action to contain a complex-valued term which provides an exponentially decaying weight for the geometries violating TCC in the Lorentzian path integral sum while working in the minisuperspace approach to quantum cosmology. This postulated modification suppresses the probability of evolution of the universe into configurations that violate TCC. We show that due to the presence of this suppression factor, the Hubble rate of the universe at the end of the inflation gets subdued and assumes a value less than what is expected classically. Moreover, the consequences of this quantum gravity motivated correction in the primordial power spectrum are discussed as well.

Observational tests of the self-dual spacetime in loop quantum gravity

The self-dual spacetime was derived from the mini-superspace approach, based on the polymerization quantization procedure in loop quantum gravity (LQG). Its deviation from the Schwarzschild spacetime is characterized by the polymeric function $P$, purely due to the geometric quantum effects from LQG. In this paper, we consider the observational constraints imposed on $P$ by using the solar system experiments and observations. For this purpose, we calculate in detail the effects of $P$ on astronomical observations conducted in the Solar system, including the deflection angle of light by the Sun, gravitational time delay, perihelion advance, and geodetic precession. The observational constraints are derived by confronting the theoretical predictions with the most recent observations. Among these constraints, we find that the tightest one comes from the measurement of the gravitational time delay by the Cassini mission, which yields $0<P<5.5\times 10^{-6}$. In addition, we also discuss the potential constraint that can be obtained in the near future by the joint European-Japanese BepiColombo project and show that it could significantly improve the current constraints.

Analytic solutions in Einstein-aether scalar field cosmology

In the context of Einstein-aether scalar field cosmology we solve the field equations and determine exact and analytic solutions. In particular, we consider a model proposed by Kanno and Soda where the aether and the scalar fields interact through the aether coefficient parameters, which are promoted to be functions of the scalar field. For this model, we write the field equations by using the minisuperspace approach and we determine the scalar field potentials which leads to Liouville-integrable systems. We solve the field equations for five families of scalar field potentials and, whether it is feasible, we write down the analytic solutions by using closed-form functions.

Quantum fields in the background spacetime of a polymeric loop black hole

The description of black holes in loop quantum gravity is a hard and tricky task. In this article, we focus on a minisuperspace approach based on a polymerization procedure. We consider the resulting effective metric and study the propagation of quantum fields in this background. The cross sections for scalar particles and fermions are explicitly calculated. The Teukolsky–Chandrasekhar procedure used to derived the fermionic radial equation of motion for usual spacetimes is entirely generalized to a much larger class. The resulting radial equation can be used in quite a lot of other contexts.

Cosmological time crystal: Cyclic universe with a small cosmological constant in a toy model approach

A new form Time Crystal has been proposed and some of its consequences have been studied. The model is a generalization of the Friedmann-Robertson-Walker (FRW) cosmology endowed with noncommutative geometry corrections. In the mini-superspace approach the scale factor undergoes the time periodic behavior, or Sisyphus dynamics, which allows us to interpret this Cosmological Time Crystal as a physically motivated toy model to simulate cyclic universe. Analyzing our model purely from Time Crystal perspective reveals many novelties such as a complex singularity structure (more complicated than the previously encountered swallowtail catastrophe) and a richer form of Sisyphus dynamics. In the context of cosmology, the system can serve as a toy model in which, apart from inducing a form of cyclic universe feature, it is possible to generate an arbitrarily small positive effective Cosmological Constant. We stress that the model is purely geometrical without introduction of matter degrees of freedom.

Cosmological constant from a deformation of the Wheeler–DeWitt equation

In this paper, we consider the Wheeler–DeWitt equation modified by a deformation of the second quantized canonical commutation relations. Such modified commutation relations are induced by a Generalized Uncertainty Principle. Since the Wheeler–DeWitt equation can be related to a Sturm–Liouville problem where the associated eigenvalue can be interpreted as the cosmological constant, it is possible to explicitly relate such an eigenvalue to the deformation parameter of the corresponding Wheeler–DeWitt equation. The analysis is performed in a Mini-Superspace approach where the scale factor appears as the only degree of freedom. The deformation of the Wheeler–DeWitt equation gives rise to a Cosmological Constant even in absence of matter fields. As a Cosmological Constant cannot exist in absence of the matter fields in the undeformed Mini-Superspace approach, so the existence of a non-vanishing Cosmological Constant is a direct consequence of the deformation by the Generalized Uncertainty Principle. In fact, we are able to demonstrate that a non-vanishing Cosmological Constant exists even in the deformed flat space. We also discuss the consequences of this deformation on the big bang singularity.

Quantum cosmology of multifield scalar matter: Some exact solutions

We consider the gravity interacting with matter scalar fields and quantized in the minisuperspace approach in which the wave functional is described by the Wheeler-DeWitt equations (WdW). Assuming the domination of the homogeneous and isotropic geometry the leading contributions to the wave functional in the approximation of the minisuperspace with Friedmann-Robertson-Walker metric (FRW) and spatially uniform scalar fields are considered. The model of several scalar fields with exponential potentials and kinetic terms admitting such a special mixing that ultimately it is possible to separate the variables in the WdW equation and to find its exact solution in terms of the special functions is proposed. The semiclassical approximation is thoroughly investigated and the boundary conditions permitting the physical solution selection for classical cosmologies are chosen.

Static gauge and energy spectrum of single-mode strings in AdS5 × S5

Motivated by the notorious difficulties in determining the first quantum corrections to the spectrum of short strings in AdS5 × S5 from first principles, we study closed bosonic strings in this background employing a static gauge. In this gauge the world-sheet Hamiltonian density is constant along the extension of the string and directly proportional to the square of the spacetime energy. We quantize this system in a minisuperspace approach, in which we consider only a single AdS5 string-mode excitation next to an arbitrary particle like zero-mode contribution in the full AdS5 × S5 background. We determine the quantum spectrum using this method to the next-to-next-to-leading order in the large 't Hooft coupling expansion. We argue for an ordering prescription which should arise from supersymmetrization and indeed recover the integrability based predictions for the spectrum of the lightest excitation, dual to the Konishi field scaling dimensions. The higher excitations fail to agree, but this is shown to be a consequence of the string-mode truncation employed. Despite this simple setup, our system reveals intriguing features, such as a close connection to particles in AdS6, classical integrability and preservation of the isometries of AdS5 × S5 at the quantum level.

Particle creation by loop black holes

We study the black hole particle production in a regular spacetime metric obtained in a minisuperspace approach to loop quantum gravity. In different previous papers the static solution was obtained and shown to be singularity-free and self-dual. In this paper expanding a previous study of the black hole dynamics we repeat the Hawking analysis which leads to a thermal flux of particles at the future infinity. The evaporation time is infinite and the unitarity is recovered due to the regularity of the spacetime and to the characteristic behavior of the surface gravity.

Hawking radiation from Loop Black Holes

We review a recent black hole particle production analisys in a regular spacetime metric obtained in a minisuperspace approach to loop quantum gravity. Repeating the Hawking analysis, which leads to a thermal flux of particles at the future infinity, one finds an infinite evaporation time and unitarity recovered due to the regularity of the singularity free spacetime and to the characteristic behavior of the surface gravity.

Model for nonsingular black hole collapse and evaporation

We study the formation of a black hole and its subsequent evaporation in a model employing a minisuperspace approach to loop quantum gravity. In previous work the static solution was obtained and shown to be singularity-free. Here, we examine the more realistic dynamical case by generalizing the static case with help of the Vaidya metric. We track the formation and evolution of trapped surfaces during collapse and evaporation and examine the buildup of quantum gravitationally caused stress-energy preventing the formation of a singularity.

On the Stability of a Class of Modified Gravitational Models

Motivated by the dark energy issue, a minisuperspace approach to the stability for modified gravitational models in a four dimensional cosmological setting is investigated. Specifically, after revisiting the f(R) case, R being the Ricci curvature, we present a stability condition around a de Sitter solution valid for modified gravitational models of generalized type F(R,G,Q), G and Q being the Gauss-Bonnet and quadratic Riemann invariants respectively. A generalization to higher order invariants is presented.

Generalized Uncertainty Principle in a Simple Varying Speed of Light Model

In this paperwewill derive a generalized uncertainty principle (GUP) in a simple varying speed of light (VSL) model. First we will show that VSL is an immediate consequence of GUP. Then, within the framework of a simple VSL model, we will show that GUP can be expressed as a function of cosmological scale factor. This expression gives two main results: uncertainties in position and momentum are actually cosmological models dependent and these uncertainties depend on mass and momentum of the particle under consideration. The relationship between matter content of the Universe and the values of uncertainties in early stages of the evolution of the Universe will be discussed in a mini-superspace approach.

THE SCHRÖDINGER WAVE FUNCTIONAL AND CLOSED STRING ROLLING TACHYON

In this paper we apply a Schrödinger picture description of the minisuperspace approach to the closed string tachyon condensation. We will calculate the rate of produced closed string and we will show that the density of high massive closed string modes reaches the string density in time of order one in string units.

The Schrödinger wave functional and S-branes

In this paper, we will consider the minisuperspace approach to S-branes dynamics in the Schrödinger picture description. Time evolution of the vacuum wave functional for quantum field theory on a S-brane is studied. Open string pair production is calculated. Analysis of the density matrix for mixed states is also performed.

Effective action and thermodynamics of radiating shells in general relativity

An effective action is obtained for the area and mass aspect of a thin shell of radiating self-gravitating matter. On following a mini-superspace approach, the geometry of the embedding space-time is not dynamical but fixed to be either Minkowski or Schwarzschild inside the shell and Vaidya in the external space filled with radiation. The Euler-Lagrange equations of motion are discussed and shown to entail the expected invariance of the effective Lagrangian under time reparametrization. They are equivalent to the usual junction equations and suggest a macroscopic quasi-static thermodynamic description.

Classical and quantum shell dynamics, and vacuum decay

Following a minisuperspace approach to the dynamics of a spherically symmetric shell, a reduced Lagrangian for the radial degree of freedom is derived directly from the Einstein - Hilbert action. The key feature of this new Lagrangian is its invariance under time reparametrization. Indeed, all classical and quantum dynamics is encoded in the Hamiltonian constraint that follows from that invariance. Thus, at the classical level, we show that the Hamiltonian constraint reproduces, in a simple gauge, Israel's matching condition which governs the evolution of the shell. In the quantum case, the vanishing of the Hamiltonian (in a weak sense) is interpreted as the Wheeler - DeWitt equation for the physical states, in analogy to the corresponding case in quantum cosmology. Using this equation, quantum tunnelling through the classical barrier is then investigated in the WKB approximation, and the connection to vacuum decay is elucidated.