The fundamental theory and the semiclassical description of loop quantum cosmology (LQC) have been studied in the Friedmann-Robertson-Walker and Bianchi I models. As an extension to include both anisotropy and intrinsic curvature, this paper investigates the cosmological model of Kantowski-Sachs spacetime with a free massless scalar field at the level of phenomenological dynamics with the LQC discreteness corrections. The LQC corrections are implemented in two different improved quantization schemes. In both schemes, the big bang and big crunch singularities of the classical solution are resolved and replaced by the big bounces when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. Symmetries of scaling are also noted and suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale. The bouncing scenarios are in an analogous fashion of the Bianchi I model, naturally extending the observations obtained previously.
We investigate existence, uniqueness, and the asymptotic properties of constant mean curvature (CMC) slicings in vacuum Kantowski-Sachs spacetimes with positive cosmological constant. Since these spacetimes violate the strong energy condition, most of the general theorems on CMC slicings do not apply. Although there are in fact Kantowski-Sachs spacetimes with a unique CMC foliation or CMC time function, we prove that there also exist Kantowski-Sachs spacetimes with an arbitrary number of (families of) CMC slicings. The properties of these slicings are analyzed in some detail.
We consider the brane Kantowski-Sachs universe when bulk space is five dimensional anti-de Sitter obeying a linear equation of state of the form $p=(γ-1)ρ+p_{0}$, where $ γ,\:p_{0}$ are a parameters. In this framework we discuss the brane Kantowski-Sachs cosmology and compare it with standard Kantowski-Sachs cosmology in Einstein theory for some specific matter choice. For several specific choice of relation between energy and pressure, the behavior of the scale factors at early time is found. It is shown that the brane Kantowski-Scahs cosmology may quickly become isotropic for some choices of…
We consider brane Kantowski-Sachs Universe when bulk space is five-dimensional Anti-deSitter space. The corresponding cosmological equations with perfect fluid are written. For several specific choices of relation between energy and pressure it is found the behavior of scale factors at early time. In particulary, for $γ=3/2$ Kantowski-Sachs brane cosmology is modified to become the isotropic one, while for $γ=1$ it remains the anisotropic cosmology in the process of evolution.
We investigate proper conformal vector fields in non conformally flat Kantowski-Sachs and Bianchi type III space-times using direct integration technique. Using the above mentioned technique we show that very special classes of the above space-times admit proper conformal vector fields.
A study of proper Weyl collineations in Kantowski-Sachs and Bianchi type III space-times is given by using the rank of the 6X6 Weyl matrix and direct integration techniques. Studying proper Weyl collineations in each of the above space-times, it is shown that there exists no such possibility when the above space-times admit proper Weyl collineations.
The action functional of the anisotropic Kantowski--Sachs cosmological model is turned into that of an ordinary gauge system. Then a global phase time is identified for the model by imposing canonical gauge conditions, and the quantum transition amplitude is obtained by means of the usual path integral procedure of Fadeev and Popov.
We investigate proper affine symmetry for the Kantowski-Sachs and Bianchi type III space-times by using holonomy and decomposability, the rank of the 6X6 Riemann matrix and direct integration techniques. It is shown that the very special classes of the above space-times admit proper affine vector fields.
A complete study of Kantowski-Sachs and Bianchi type III space-times according to their proper homothetic vector fields is given by using direct integration technique. Using the above mentioned technique we have shown that very special classes of the above space-times admit proper homothetic vector fields. The dimension of homothetic vector fields is five.
We present a counter example to paper \cite{P71} and show that the result obtained is correct for a class of metric but not general. We calculate the total energy of the Kantowski-Sachs space-time by using the energy-momentum definitions of Møller in the theory of general relativity and the tetrad theory of gravity.
We briefly discuss the Hamiltonian formalism of Kantowski-Sachs space-times with vacuum, anisotropic fluid and two cross-streaming radiation field sources. For these models a cosmological time is introduced. New constraints are found in which the fluid momenta are separated from the rest of the variables. In consequence their Poisson brackets give an Abelian algebra.
We show that the classification of Kantowski-Sachs, Bianchi Types I and III spacetimes admitting Matter Collineations (MCs) presented in a recent paper by Camci et al. [Camci, U., and Sharif, M. {Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes}, 2003 Gen. Relativ. Grav. vol. 35, 97-109] is incomplete. Furthermore for these spacetimes and when the Einstein tensor is non-degenerate, we give the complete Lie Algebra of MCs and the algebraic constraints on the spatial components of the Einstein tensor.
We use the Einstein, Bergmann-Thomson, Landau-Lifshitz and Papapetrou energy-momentum complexes to calculate the energy and momentum distributions of Kantowski and Sachs space-time. We show that the Einstein and Bergmann-Thomson definitions furnish a consistent result for the energy distribution, but the definition of Landau-Lifshitz do not agree with them. We show that a signature switch should affect about everything including energy distribution in the case of Einstein and Papapetrou prescriptions but not in Bergmann-Thomson and Landau-Lifshitz prescriptions.
We investigate perturbations of Kantowski-Sachs models with a positive cosmological constant, using the gauge invariant 1+3 and 1+1+2 covariant splits of spacetime together with a harmonic decomposition. The perturbations are assumed to be vorticity-free and of perfect fluid type, but otherwise include general scalar, vector and tensor modes. In this case the set of equations can be reduced to six evolution equations for six harmonic coefficients.
In the context of modified tele-parallel theory of gravity, we undertake cosmological anisotropic models and search for their solutions. Within a suitable choice of non-diagonal tetrads, the decoupled equations of motion are obtained for Bianchi-I, Bianchi-III and Kantowski-Sachs models, from which we obtain the correspondent solutions. By the way, energy density and pressures are also obtained, showing, as an important result, that our universe may live a quintessence like universe even still anisotropic models are considered.
Perturbations of Kantowski-Sachs models with a positive cosmological constant are considered in a harmonic decomposition, in the framework of gauge invariant 1+3 and 1+1+2 covariant splits of spacetime. Scalar, vector and tensor modes are allowed, however they remain vorticity-free and of perfect fluid type. The dynamics is encompassed in six evolution equations for six harmonic coefficients.
The Wheeler-DeWitt equation for a class of Kantowski-Sachs like models is completely solved. The generalized models include the Kantowski-Sachs model with cosmological constant and pressureless dust. Likewise contained is a joined model which consists of a Kantowski-Sachs cylinder inserted between two FRW half--spheres. The (second order) WKB approximation is exact for the wave functions of the complete set and this facilitates the product structure of the wave function for the joined model. In spite of the product structure the wave function can not be interpreted as admitting no correlations…
The emergent universe scenario is a proposal for resolving the Big Bang singularity problem in the standard Friedmann-Lemaitre-Robertson-Walker cosmology. In the context of this scenario, the Universe originates from a nonsingular static state. In the present work, considering the realization of the emergent universe scenario, we address the possibility of having a nonsingular Kantowski-Sachs type static state. Considering four and five dimensional models (with and without brane), it is shown that both the existence and stability of a nonsingular state depend on the dimensions of the spacetime…
The purpose of this paper is to find conformal vector fields of some perfect fluid Kantowski-Sachs and Bianchi type III space-times in the f(R) theory of gravity using direct integration technique. In this study there exists only eight cases. Studying each case in detail, we found that in two cases proper conformal vector fields exist while in the rest of six cases conformal vector fields become Killing vector fields. The dimension of conformal vector fields is either 4 or 6.
This paper intends to obtain concircular vector fields of Kantowski Sachs and Bianch type III spacetimes. For this purpose, ten conformal Killing equations and their general solution in the form of conformal Killing vector fields are derived along with their conformal factors. The obtained conformal Killing vector fields are then placed in Hessian equations to obtain the final form of concircular vector fields. The existence of concircular symmetry imposes restrictions on the metric functions. The conditions imposing restrictions on these metric functions are obtained as a set of integrability…
In this work the growth of density perturbations in Kantowski-Sachs cosmologies with a positive cosmological constant is studied, using the 1+3 and 1+1+2 covariant formalisms. For each wave number we obtain a closed system for scalars formed from quantities that are zero on the background and hence are gauge-invariant. The solutions to this system are then analyzed both analytically and numerically. In particular the effects of anisotropy and the behaviour close to a bounce in the cosmic scale factor are considered. We find that typically the density gradient in the bouncing directions experie…
The forms of coupling of the scalar field with gravity, appearing in the induced theory of gravity, and the potential are found in the Kantowski-Sachs model under the assumption that the Lagrangian admits Noether symmetry. The form thus obtained makes the Lagrangian degenerate. The constrained dynamics thus evolved due to such degeneracy has been analysed and a solution has also been presented which is inflationary in behaviour. It has further been shown that there exists other technique to explore the dynamical symmetries of the Lagrangian and that is simply by inspecting the field equations.…
Although it is not a fundamental question, to determine exact and general solutions for a given theory has advantages over a numerical integration in many specific cases. Of course, respecting the peculiarities of the problem. Revisiting the integration of the General Relativity Theory field equations for the Kantowski-Sachs spacetime, that describes a homogeneous but anisotropic universe whose spatial section has the topology of $R \times S^2$, we integrate the equations for arbitrary curvature parameter, and writing the solutions considering the process of gravitational collapse. We took the…
The Noether symmetry approach is useful tool to restrict the arbitrariness in a gravity theory when the equations of motion are underdetermined due to the high number of functions to be determined in the ansatz. We consider two scalar-coupled theories of gravity, one motivated by induced gravity, the other more standard; in Bianchi I, Bianchi III and Kantowski-Sachs cosmological models. For these models, we present a full set of Noether gauge symmetries, which are more general than those obtained by the strict Noether symmetry approach in our recent work. Some exact solutions are derived using…
In this paper the interior of the Schwarzschild black hole, which is presented as a vacuum homogeneous and anisotropic Kantowski-Sachs minisuperspace cosmological model, is considered. Lagrangian of the model is reduced by a suitable coordinate transformation to Lagrangian of two decoupled oscillators with the same frequencies and with zero energy in total (an oscillator-ghost-oscillator system). The model will be presented in a classical, a p-adic and a noncommutative case. Then, within the standard quantum approach Wheeler-DeWitt equation and its general solutions, i.e. a wave function of th…
Ricci collineations of the Bianchi types I and III, and Kantowski-Sachs space- times are classified according to their Ricci collineation vector (RCV) field of the form (i)-(iv) one component of $ξ^a (x^b)$ is nonzero, (v)-(x) two components of $ξ^a (x^b)$ are nonzero, and (xi)-(xiv) three components of $ξ^a (x^b)$ are nonzero. Their relation with isometries of the space-times is established. In case (v), when $det(R_{ab}) = 0$, some metrics are found under the time transformation, in which some of these metrics are known, and the other ones new. Finally, the family of contracted Ricci colline…
A general treatment of vorticity-free, perfect fluid perturbations of Kantowski-Sachs models with a positive cosmological constant are considered within the framework of the 1+1+2 covariant decomposition of spacetime. The dynamics is encompassed in six evolution equations for six harmonic coefficients, describing gravito-magnetic, kinematic and matter perturbations, while a set of algebraic expressions determine the rest of the variables. The six equations further decouple into a set of four equations sourced by the perfect fluid, representing forced oscillations and two uncoupled damped oscil…
We illustrate the recently proposed generalized unimodular gravity using simple examples of the Friedmann, Kantowski-Sachs and Schwarzschild geometries and show that it can be further generalized and reveal some unexpected and interesting effects.
Many cosmological scenarios envisage either a bounce of the universe at early times, or collapse of matter locally to form a black hole which re-expands into a new expanding universe region. Energy conditions preclude this happening for ordinary matter in general relativistic universes, but scalar or dilatonic fields can violate some of these conditions, and so could possibly provide bounce behaviour. In this paper we show that such bounces cannot occur in Kantowski-Sachs models without violating the {\it reality condition} $\dotϕ^2\geq 0$. This also holds true for other isotropic spatially ho…
The $f(T)$ theory is recently proposed to explain the present cosmic accelerating expansion of the universe. $f(T)$ theory is an extension of Teleparallel theory of gravity, where $T$ is the torsion scalar. This paper contains the construction of $f(T)$ models within the Kantowski-Sachs universe. For this purpose, we use conservation equation and equation of state parameter, which represents the different phases of the universe. We discuss possible cases for the matter dominated era, radiation dominated era, present dark energy phase and their combinations. Particularly, a constant solution ha…
We extend the ideas introduced in the previous work to a more general space-time. In particular we consider the Kantowski-Sachs space time with space section with topology $R \times S^2$. In this way we want to study a general space time that we think to be the space time inside the horizon of a black hole. In this case the phase space is four dimensional and we simply apply the quantization procedure suggested by Loop Quantum Gravity and based on an alternative to the Schroedinger representation introduced by H. Halvorson. Through this quantization procedure we show that the inverse of the vo…
Resolution of singularities in the Kantowski-Sachs model due to non-perturbative quantum gravity effects is investigated. Using the effective spacetime description for the improved dynamics version of loop quantum Kantowski-Sachs spacetimes, we show that even though expansion and shear scalars are universally bounded, there can exist events where curvature invariants can diverge. However, such events can occur only for very exotic equations of state when pressure or derivatives of energy density with respect to triads become infinite at a finite energy density. In all other cases curvature inv…
I present quantum wormhole solutions in the Kantowski--Sachs spacetime generated from coupling the gravitational field to the axion and EM fields. These solutions correspond to the classical ones found by Keay and Laflamme and by Cavaglià et al.
It is shown that growing-entropy stiff-fluid Kantowski-Sachs universes become time-symmetric (if they start with time-asymmetric phase) and isotropize. Isotropization happens without any inflationary era during the evolution since there is no cosmological term here. It seems that this approach is an alternative to inflation since the universe gets bigger and bigger approaching 'flatness'.
We consider a cosmological model based upon a non-canonical noncommutative extension of the Heisenberg-Weyl algebra to address the thermodynamical stability and the singularity problem of both the Schwarzschild and the Kantowski-Sachs black holes. The interior of the black hole is modelled by a noncommutative extension of the Wheeler-DeWitt equation. We compute the temperature and entropy of a Kantowski-Sachs black hole and compare our results with the Hawking values. Again, the noncommutativity in the momenta sector allows us to have a minimum in the potential, which is relevant in order to a…
Using effective dynamics, we investigate the behavior of expansion and shear scalars in different proposed quantizations of the Kantowski-Sachs spacetime with matter in loop quantum cosmology. We find that out of the various proposed choices, there is only one known prescription which leads to the generic bounded behavior of these scalars. The bounds turn out to be universal and are determined by the underlying quantum geometry. This quantization is analogous to the so called 'improved dynamics' in the isotropic loop quantum cosmology, which is also the only one to respect the freedom of the r…
The dynamics of the vacuum Kantowski-Sachs space-time are studied in the so-called limiting curvature mimetic gravity theory. It is shown that in this theory the vacuum Kantowski-Sachs space-time is always singular. While the departures from general relativity due to the limiting curvature mimetic theory do provide an upper bound on the magnitude of the expansion scalar, both its rate of oscillations and the magnitude of the directional Hubble rates increase without bound and cause curvature invariants to diverge. Also, since the radial scale factor does not vanish in finite (past) time, in th…
We analyse the Kantowski-Sachs cosmologies with Vlasov matter of massive and massless particles using dynamical systems analysis. We show that generic solutions are past and future asymptotic to the non-flat locally rotationally symmetric Kasner vacuum solution. Furthermore, we establish that solutions with massive Vlasov matter behave like solutions with massless Vlasov matter towards the singularities.
In the context of scalar-torsion theory we investigate the evolution of the cosmological anisotropies for a Kantowski-Sachs background geometry. We study the phase-space of the gravitational field equations by determining the admitted stationary points and study their stability properties. For the potential function of the non-minimally coupled scalar field we assume the exponential and the power-law functions. Finally, we make use of Poincare variables in order to investigate the existence of stationary points at the infinity regime of the dynamics.
Exact and analytic solutions in Einstein-Aether scalar field theory with Kantowski-Sachs background space are determined. The theory of point symmetries is applied to determine the functional form of the unknown functions which defines the gravitational model. Conservation laws are applied to reduce the order of the field equations and write the analytic solution. Moreover, in order to understand the physical behaviour of the cosmological model a detailed analysis of the asymptotic behaviour for the gravitational field equations is performed.
In this paper, by analyzing the instability against spatially homogeneous and anisotropic perturbations of the Kantowski-Sachs-type during different cosmological epoch, we show that it is a theoretical consequence of the general relativity that the KS universe must be open or flat if it underwent the matter dominated and/or radiation dominated era in its past evolution, which theoretically confirms the flatness of our observable universe.
In this paper we study the quantum cosmological Kantowski-Sachs model and solve the Wheeler-DeWitt equation in minisuperspace to obtain the wave function of the corresponding universe. The perfect fluid is described by the Schutz's canonical formalism, which allows to attribute dynamical degrees of freedom to matter. The time is introduced phenomenologically using the fluid's degrees of freedom. In particular, we adopt a stiff matter fluid. The viability of this model is analyzed and discussed.
The paper deals with a non--minimally coupled scalar field in the background of homogeneous but anisotropic Kantowski--Sachs space--time model. The form of the coupling function of the scalar field with gravity and the potential function of the scalar field are not assumed phenomenologically, rather they are evaluated by imposing Noether symmetry to the Lagrangian of the present physical system. The physical system gets considerable mathematical simplification by a suitable transformation of the augmented variables $(a, b, ϕ)\rightarrow (u, v, w)$ and by the use of the conserved quantities due…
The Kantowski-Sachs cosmological model sourced by a Skyrme field and a cosmological constant is considered in the framework of General Relativity. Assuming a constant radial profile function for the hedgehog ansatz, the Skyrme contribution to Einstein equations is shown to be equivalent to an anisotropic fluid. Using dynamical system techniques, a qualitative analysis of the cosmological equations is presented. Physically interesting features of the model such as isotropization, bounce and recollapse are discussed.
A class of positive curvature spatially homogeneous but anisotropic cosmological models within an Einstein-aether gravitational framework are investigated. The matter source is assumed to be a scalar field which is coupled to the expansion of the aether field through a generalized exponential potential. The evolution equations are expressed in terms of expansion-normalized variables to produce an autonomous system of ordinary differential equations suitable for a numerical and qualitative analysis. An analysis of the local stability of the equilibrium points indicates that there exists a range…
We study quantum cosmology of the $2D$ Jackiw-Teitelboim (JT) gravity with $Λ>0$ and calculate the Hartle-Hawking (HH) wave function for this model in the minisuperspace framework. Our approach is guided by the observation that the JT dynamics can be mapped exactly onto that of the Kantowski-Sachs (KS) model describing a homogeneous universe with spatial sections of $S^1\times S^2$ topology. This allows us to establish a JT-KS correspondence between the wave functions of the models. We obtain the semiclassical Hartle-Hawking wave function by evaluating the path integral with appropriate bounda…
A consisten quantization with a clear notion of time and evolution is given for the anisotropic Kantowski-SDachs cosmological model. It is shown that a suitable coordinate choice allows to obtain a solution of the Wheeler-DeWitt equation in the form of definite energy states, and that the results can be associated to two disjoint equivalent theories, one for each sheet of the constraint surface.
It is shown that like Bianchi I, V and IX models, a Kantowski-Sachs cosmological model also allows a unitary evolution on quantization. It has also been shown that this unitarity is not at the expense of the anisotropy. Non-unitarity, if there is any, cannot escape notice in this as the evolution is studied against a properly oriented time parameter fixed by the evolution of the fluid. Furthermore, we have constructed a wave-packet by superposing different energy eigenstates, thereby establishing unitarity in a non-trivial way, which is a stronger result than an energy eigenstate trivially giv…
We present new exact solutions of the low-energy-effective-action string equations with both dilaton $ϕ$ and axion $H$ fields non-zero. The background universe is of Kantowski-Sachs type. We consider the possibility of a pseudoscalar axion field $h$ ($H=e^ϕ(dh)^{*}$) that can be either time or space dependent. The case of time-dependent $h$ reduces to that of a stiff perfect-fluid cosmology. For space-dependent $h$ there is just one non-zero time-space-space component of the axion field $H$, and this corresponds to a distinguished direction in space which prevents the models from isotropising.…
We study the Einstein-Klein-Gordon equations for a convex positive potential in a Bianchi I, a Bianchi III and a Kantowski-Sachs universe. After analysing the inherent properties of the system of differential equations, the study of the asymptotic behaviors of the solutions and their stability is done for an exponential potential. The results are compared with those of Burd and Barrow. In contrast with their results, we show that for the BI case isotropy can be reached without inflation and we find new critical points which lead to new exact solutions. On the other hand we recover the result o…
