Kasner Cosmology Research Articles

Kasner cosmology in bumblebee gravity

Kasner cosmology is a vacuum and anisotropically expanding spacetime in the general relativity context. In this work, such a cosmological model is studied in another context, the bumblebee model, where the Lorentz symmetry is spontaneously broken. By using the bumblebee context it is possible to justify the anisotropic feature of the Kasner cosmology. Thus, the origin of the anisotropy in this cosmological model could be in the Lorentz symmetry breaking. Lastly, an application in the pre-inflationary cosmology is suggested.

Probing inside a charged hairy black hole in massive gravity

In this paper, we investigate the internal structure of a charged hairy black hole solution in the non-linear massive gravity. We first consider the impact of various configurations of massive gravity on the condensate operator and then probe the black hole interior dynamics. Like a standard holographic superconductor system, just below the critical temperature, the interior evolves through several distinct epochs, including a collapse of the Einstein-Rosen bridge, Josephson oscillations of the scalar field, and finally a Kasner (or Kasner inversion) cosmology. However, for the large massive gravity parameter, we see distinguishing features for the interior dynamics. In this regime, at a given temperature, the Einstein-Rosen bridge collapse and subsequent Josephson oscillations epochs completely disappear from the interior dynamics and the final Kasner cosmology epoch starts exactly after the would-be inner horizon and the system does not experience the Kasner inversion epoch.

Anisotropic SD2 brane: accelerating cosmology and Kasner-like space-time from compactification

Starting from an anisotropic (in all directions including the time direction of the brane) non-SUSY D2 brane solution of type IIA string theory we construct an anisotropic space-like D2 brane (or SD2 brane, for short) solution by the standard trick of a double Wick rotation. This solution is characterized by five independent parameters. We show that compactification on six-dimensional hyperbolic space (H_6) of a time-dependent volume of this SD2 brane solution leads to accelerating cosmologies (for some time tsim ,t_0, with t_0 some characteristic time) where both the expansions and the accelerations are different in three spatial directions of the resultant four-dimensional universe. On the other hand at early times (t ll t_0) this four-dimensional space, in certain situations, leads to four-dimensional Kasner-like cosmology, with two additional scalars, namely, the dilaton and a volume scalar of H_6. Unlike in the standard four-dimensional Kasner cosmology here all three Kasner exponents could be positive definite, leading to expansions in all three directions.

A numerical study of the Regge calculus and smooth lattice methods on a Kasner cosmology

Two lattice based methods for numerical relativity, the Regge calculus and the smooth lattice relativity, will be compared with respect to accuracy and computational speed in a full 3+1 evolution of initial data representing a standard Kasner cosmology. It will be shown that both methods provide convergent approximations to the exact Kasner cosmology. It will also be shown that the Regge calculus is of the order of 110 times slower than the smooth lattice method.

A cosmological solution of Regge calculus

We revisit the Regge calculus model of the Kasner cosmology first considered by Lewis (1982 Phys. Rev. D 25 306 12). One of the most highly symmetric applications of lattice gravity in the literature, Lewis' discrete model closely matched the degrees of freedom of the Kasner cosmology. As such, it was surprising that Lewis was unable to obtain the full set of Kasner–Einstein equations in the continuum limit. Indeed, an averaging procedure was required to ensure that the lattice equations were even consistent with the exact solution in this limit. We correct Lewis' calculations and show that the resulting Regge model converges quickly to the full set of Kasner–Einstein equations in the limit of very fine discretization. Numerical solutions to the discrete and continuous-time lattice equations are also considered.

Dynamical conifold transitions and moduli trapping in M-theory cosmology

We study five-dimensional Kasner cosmologies in the vicinity of a conifold locus occurringin a time-dependent Calabi–Yau compactification of M-theory. The dynamics of M2-branewinding modes, which become light in this region, is taken into account using a suitablegauged supergravity action. We find cosmological solutions which interpolate between thetwo branches of the transition, establishing that conifold transitions can be realizeddynamically. However, generic solutions do not correspond to transitions, but to the modulibeing trapped close to the conifold locus. This effect results from an interplaybetween the scalar potential and Hubble friction. We show that the dynamicsdoes not depend on the details of the potential, but only on its overall shape.

Topological phase transitions in Calabi‐Yau compactifications of M‐theory

AbstractIn this thesis we construct five‐dimensional gauged supergravity actions which describe flop and conifold transitions in M‐theory compactified on Calabi‐Yau threefolds. While the vector multiplet sector is determined exactly, we use the Wolf spaces $X(1+N) = {{U(1+N,2)}\over{U(1+N) \times U(2)}}$ to model the universal hypermultiplet together with N charged hypermultiplets corresponding to winding states of M2‐branes. After specifying the hypermultiplet sector the actions are uniquely determined by M‐theory. As an application we consider five‐dimensional Kasner cosmologies. Including the dynamics of the winding modes, we find smooth cosmological solutions which undergo flop and conifold transitions. Instead of the usual runaway behavior the scalar fields of these solutions generically stabilize in the transition region where they oscillate around the transition locus. The scalar potential thereby induces short episodes of accelerated expansion in the space‐time.

M-theory cosmologies from singular Calabi–Yau compactifications*

We study five-dimensional Kasner cosmologies in a time-dependent Calabi–Yau compactificationof M-theory undergoing a flop transition. The dynamics of the additional states, which become massless at the transition point and give rise to a scalar potential, are taken into account using a recently constructed gauged supergravity action. Due to the dynamics of these states the moduli do not show the usual run-away behaviour but oscillate around the transition region. Moreover, the solutionstypically exhibit short periods of accelerated expansion.We also analyse the interplay between the geometries of moduli space and spacetime.

Behavior of Kasner cosmologies with induced matter

We extend the induced matter model, previously applied to a variety of isotropic cases, to a generalization of Bianchi type-I anisotropic cosmologies. The induced matter model is a 5D Kaluza-Klein approach in which assumptions of compactness are relaxed for the fifth coordinate, leading to extra geometric terms. One interpretation of these extra terms is to identify them as an ``induced matter'' contribution to the stress-energy tensor. In similar spirit, we construct a five dimensional metric in which the spatial slices possess Bianchi type-I geometry. We find a set of solutions for the five dimensional Einstein equations, and determine the pressure and density of induced matter. We comment on the long-term dynamics of the model, showing that the assumption of positive density leads to the contraction over time of the fifth scale factor.

An ADM 3+1 formulation for smooth lattice general relativity

A new hybrid algorithm for numerical relativity is presented. We employ a lattice in which the metric is recorded as pure scalar quantities such as the geodesic leg lengths. The dynamics of the lattice is governed by the standard ADM 3 + 1 equations, which are given as a set of second-order ordinary differential equations for the scalar data of the lattice. The only approximation introduced in this algorithm is in the approximation of a smooth metric by a lattice. No approximations are introduced into the field equations nor in their application to the lattice. An example for the Kasner cosmology is presented and the results shown to be in excellent agreement with the continuum solution.

A fully -dimensional Regge calculus model of the Kasner cosmology

We describe the first discrete-time four-dimensional numerical application of Regge calculus. The spacetime is represented as a complex of four-dimensional simplices, and the geometry interior to each 4-simplex is flat Minkowski spacetime. This simplicial spacetime is constructed so as to be foliated with a one-parameter family of spacelike hypersurfaces built from tetrahedra. We implement a novel 2-surface initial-data prescription for Regge calculus, and provide the first fully four-dimensional application of an implicit decoupled evolution scheme (the `Sorkin evolution scheme'). We benchmark this code on the Kasner cosmology - a cosmology which embodies generic features of the collapse of many cosmological models. We (i) reproduce the continuum solution with a fractional error in the 3-volume of after evolution steps; (ii) demonstrate stable evolution; (iii) preserve the standard deviation of spatial homogeneity to less than and (iv) explicitly display the existence of diffeomorphism freedom in Regge calculus. We also present the second-order convergence properties of the solution to the continuum.

THE ISSUE OF TIME EVOLUTION IN QUANTUM GRAVITY

We discuss the relation between the concept of time and the dynamic structure of quantum gravity. We briefly review the problems of time associated with the standard procedures of gravity quantization. By explicitly utilizing York’s analysis of the geometrodynamic degrees of freedom, and imposing the constraints as expectation value equations, we describe a new procedure of gravity quantization. In particular, this “minimally constrained canonical” quantization procedure leads to a linear Schrödinger equation augmented by the super-Hamiltonian and supermomentum constraints imposed on expectation values. This approach supplies a description of time evolution in quantum geometrodynamics free from the standard problems of time associated with canonical approaches. Furthermore, the theory is applicable to the full theory of general relativity, without the need to impose symmetries or reduce dimensionality. Using this method we arrive at an analytic expression for the quantum evolution of the Kasner cosmology, as well as a numerically generated solution of the quantized Taub model. The key new feature of this approach is that we impose the constraints weakly — instead of the quantum-mechanical wave function satisfying the constraints exactly, it need only satisfy them on average. Thus the constraints only constrain the observables.

Gravitational wave perturbations and gauge conditions

We numerically evolve initial data modeling gravitational wave perturbations about a background Kasner cosmology. We examine the gravitational waves present in the initial data, and show that these inhomogeneities on the initial slice are not merely gauge effects. The evolution of these gravitational waves is gauge dependent, but we are able to separate the effects of the gauge terms from the true decay rate of the perturbations.