We propose two higher order generalized uncertainty principles(GUPs) which predict a minimum uncertainty in momentum and apply the deformations that they entail of the Heisenberg algebra to one half of the phase space of the LRS Bianchi I models. After numerically solving the resultant Wheeler Dewitt equations we analyze our solutions and provide evidence that potential IR effects of quantum gravity could have played a role in selecting an overwhelmingly likely geometrical configuration that a quantum universe can possess. In addition we propose a GUP which predicts both a minimum uncertainty in momentum and a maximal measurable length scale which can be interpreted as a fixed maximum cosmological horizon. The results contained in this work provide further incentives to study what effects higher order GUP(s) have on quantum cosmology so we can obtain a better understanding of how quantum gravity could have impacted cosmological evolution.
In this work we consider particle creation by the expansion of the universe, using two Bianchi type I anisotropic models. The particles studied are of spin 0 and 1/2. The cosmological models have rotational symmetry, which allows us to solve exactly the equations of motion. The number density of the created particles is calculated with the method of Bogolubov transformations.
In this paper we present the quantum LRS Bianchi IX models or, as they may be better known, the Taub-NUT models in addition to the quantum LRS Bianchi VIII models, both coupled to a stiff matter source. We solve their Wheeler DeWitt equations for an arbitrary Hartle-Hawking ordering parameter using separation of variables. Afterwards we construct a superposition of their respective wave functions and discuss some of the interesting qualitative properties they possess.
The aim of this paper is to explore teleparallel conformal Killing vector fields (CKVFs) of locally rotationally symmetric (LRS) Bianchi type V spacetimes in the context of teleparallel gravity and compare the obtained results with those of general relativity. The general solution of teleparallel conformal Killing's equations is found in terms of some unknown functions of t and x , along with a set of integrability conditions. The integrability conditions are solved in some particular cases to get the final form of teleparallel CKVFs. It is observed that the LRS Bianchi type V spacetimes admit…
It is investigated the behaviour of the ``constants'' $G,$ $c$ and $Λ$ in the framework of a perfect fluid LRS Bianchi I cosmological model. It has been taken into account the effects of a $c-$variable into the curvature tensor. Two exact cosmological solutions are investigated, arriving to the conclusion that if $q<0$ (deceleration parameter) then $G,$ $c$ are growing functions on time $t$ while $Λ$ is a negative decreasing function on time.
In this paper, we present a complete classification of Locally Rotationally Symmetric (LRS) Bianchi type I spacetimes according to their Conformal Ricci Collineations (CRCs). When the Ricci tensor is non-degenerate, a general form of the vector field generating CRCs is found, subject to some integrability conditions. Solving the integrability conditions in different cases, it is found that the LRS Bianchi type I spacetimes admit 7, 10, 11 or 15- dimensional Lie algebra of CRCs for the choice of non-degenerate Ricci tensor. Moreover, it is found that these spacetimes admit infinite number of CR…
An LRS Bianchi type-V cosmological models representing a viscous fluid distribution with a time dependent cosmological term $Λ$ is investigated. To get a determinate solution, the viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density. It turns out that the cosmological term $Λ(t)$ is a decreasing function of time, which is consistent with recent observations of type Ia supernovae. Various physical and kinematic features of these models have also been explored.
We study the asymptotic dynamics of $f(T, B)$-theory in an anisotropic Bianchi III background geometry. We show that an attractor always exists for the field equations, which depends on a free parameter provided by the specific $f(T, B)$ functional form. The attractor is an accelerated spatially flat FLRW or non-accelerated LRS Bianchi III geometry. Consequently, the $f(T, B)$-theory provides a spatially flat and isotropic accelerated Universe.
In this paper we have investigated an LRS Bianchi I anisotropic cosmological model of the universe by taking time varying $G$ and $Λ$ in the presence of bulk viscous fluid source described by full causal non-equilibrium thermodynamics. We obtain a cosmological constant as a decreasing function of time and for $m, n > 0$, the value of cosmological ``constant'' for this model is found to be small and positive which is supported by the results from recent supernovae observations.
The general solution of the field equations in LRS Bianchi-I space-time with perfect fluid equation-of-state (EoS) is presented. The models filled with dust, vacuum energy, Zel'dovich matter and disordered radiation are studied in detail. A unified and systematic treatment of the solutions is presented, and some new solutions are found. The dust, stiff matter and disordered radiation models describe only a decelerated universe, whereas the vacuum energy model exhibits a transition from a decelerated to an accelerated phase.
In this paper we study the evolution of a LRS Bianchi I Universe, filled with a bulk viscous cosmological fluid in the presence of time varying constants "but" taking into account the effects of a c-variable into the curvature tensor. We find that the only physical models are those which ``constants'' $G$ and $c$ are growing functions on time $t$, while the cosmological constant $Λ$ is a negative decreasing function. In such solutions the energy density obeys the ultrastiff matter equation of state i.e. $ω=1$.
LRS Bianchi type-I models have been studied in the cosmological theory based on Lyra's geometry. A new class of exact solutions has been obtained by considering a time dependent displacement field for variable deceleration parameter models of the universe. We have compared our models with those of Einstein's field theory with the cosmological term $Λ$. Our frame of reference is restricted to the recent Ia observations of supernovae. Some physical behaviour of the models is also examined in the presence of perfect fluids.
Within the scope of Bianchi type-I cosmological model the role of spinor field on the evolution of the Universe is investigated. In doing so we have considered a polynomial type of nonlinearity. It is found that depending on the sign of self-coupling constant the model allows either accelerated mode of expansion or oscillatory mode of evolution. Unlike general Bianchi type-I and Bianchi type $VI_0$ models in this case neither mass term nor the nonlinear term in the Lagrangian of spinor field vanish.
A spatially homogeneous anisotropic LRS Bianchi type-I cosmological model is studied in $f(R,T)$ gravity with a special form of Hubble's parameter, which leads to constant deceleration parameter. The parameters involved in the considered form of Hubble parameter can be tuned to match, our models with the $Λ$CDM model. With the present observed value of the deceleration parameter, we have discussed physical and kinematical properties of a specific model. Moreover, we have discussed the cosmological distances for our model.
In the present work we revisit the axisymmetric Bianchi VIII and IX models. At the classical level we reproduce the known analytic solution, in a novel way making use of two quadratic integrals of motion, the constraint equation, as well as a linear non-local integral of motion. These quantities correspond to two second rank Killing tensors and a homothetic vector field existing on the relevant configuration space. On the corresponding phase space the two quadratic charges commute with the Hamiltonian constraint but not among themselves. Thus, after turning these charges into operators we obta…
In this paper we report on results in the study of spatially homogeneous cosmological models with elastic matter. We show that the behavior of elastic solutions is fundamentally different from that of perfect fluid solutions already in the case of locally rotationally symmetric (LRS) Bianchi type I models; this is true even when the elastic material resembles a perfect fluid very closely. In particular, the approach to the initial singularity is characterized by an intricate oscillatory behavior of the scale factors, while the future asymptotic behavior is described by isotropization rates tha…
The present study deals with LRS Bianchi type I cosmological model representing massive string. The energy-momentum tensor for such string as formulated by Letelier (1983) is used to construct massive string cosmological models for which we assume that the shear scalar ($σ$) is proportional to the expansion scalar ($θ$). The study reveals that massive strings dominate the early Universe. The strings eventually disappear from the Universe for sufficiently large time, which is in agreement with the current astronomical observations. Some physical and geometrical behaviour of models are also disc…
The present study deals with spatially homogeneous and anisotropic locally rotationally symmetric (LRS) Bianchi type I cosmological model with dominance of dark energy. To get the deterministic model of Universe, we assume that the shear scalar $(σ)$ in the model is proportional to expansion scalar $(θ)$. This condition leads to $A=B^{n}$, where $A$,\;$B$ are metric potential and $n$ is positive constant. It has been found that the anisotropic distribution of dark energy leads to the present accelerated expansion of Universe. The physical behavior of the Universe has been discussed in detail.
Within the scope of a LRS Bianchi type-I cosmological model we study the role of the nonlinear spinor field in the evolution of the Universe. In doing so we consider a polynomial type of nonlinearity that describes different stages of the evolution. Finally we also use the observational data to fix the problem parameters that match best with the real picture of the evolution. The assessment of the age of the Universe in case of the soft beginning of expansion (initial speed of expansion in a point of singularity is equal to zero) the age was found 15 billion years, whereas in case of the hard …
We analyze the dynamics of a class of cosmological solutions of the Einstein-Vlasov equations. These equations describe an ensemble of collisionless particles (which represent galaxies or clusters of galaxies) that interact gravitatively through Einstein's equations of general relativity. The cosmological models we consider are spatially homogeneous, of Bianchi type IX, and locally rotationally symmetric (LRS). We prove that generic solutions exhibit an oscillatory approach toward the singularities (the "big bang" in the past and the "big crunch" in the future); this is in contrast to the beha…
We have studied the locally rotationally symmetric (LRS) Bianchi type-I cosmological model in $f(R,T)$ gravity ($R$ is the Ricci scalar and $T$ is the trace of the stress energy tensor) with Bulk viscous fluid as matter content. The model is constructed for the linear form $f(R,T)=R+2f(T)$. The exact solution of field equations is obtained by using a time varying deceleration parameter $q$ for a suitable choice of the function $f(T)$. In this work, the bulk viscous pressure $\bar{p}$ is found to be negative and energy density $ρ$ is found to be positive. The obtained model is anisotropic, acce…
A model of a cloud formed by massive strings is used as a source of LRS Bianchi type II with time decaying vacuum energy density $Λ$. To construct string cosmological models we have used the energy-momentum tensor for such string as formulated by Letelier (1983). The high nonlinear field equations have been solved for two types of strings, (i) Massive string and (ii) Nambu string. The expansion $θ$ in the model is assumed to be proportional to the shear $σ$. This condition leads to $A=βB^{m}$, where $A$ and $B$ are the metric coefficients, $m$ is a constant and $β$ is an integrating constant. …
Locally rotationally symmetric (LRS) Bianchi Type I cosmological models are examined in the presence of dynamically anisotropic dark energy and perfect fluid. We assume that the dark energy (DE) is minimally interacting, has dynamical energy density, anisotropic equation of state parameter (EoS). The conservation of the energy-momentum tensor of the DE is assumed to consist of two separately additive conserved parts. A special law is assumed for the deviation from isotropic EoS, which is consistent with the assumption on the conservation of the energy-momentum tensor of the DE. Exact solutions…
A new class of LRS Bianchi type ${\rm VI}_{0}$ cosmological models with free gravitational fields and a variable cosmological term is investigated in presence of perfect fluid as well as bulk viscous fluid. To get the deterministic solution we have imposed the two different conditions over the free gravitational fields. In first case we consider the free gravitational field as magnetic type whereas in second case `gravitational wrench' of unit `pitch" is supposed to be present in free gravitational field. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass…
In this paper, we examine the (LRS) Bianchi-type-I cosmological model with holographic dark energy. The exact solutions to the corresponding field equations are obtained by using generalized hybrid expansion law (HEL). The EoS parameter $ω$ for DE is found to be time dependent and redshift dependent and its exiting range for derived model is agreeing well with the current observations. Here we likewise apply two mathematical diagnostics, the statefinder ({r, s}) and $ω_{d}-ω^{'}_{d}$ plane to segregate HDE model from the $ΛCDM$ model. Here the $ω_{d}-ω^{'}_{d}$ diagnostic trajectories is the g…
An LRS Bianchi-I space-time model is studied with constant Hubble parameter in $f(R,T)=R+2λT$ gravity. Although a single (primary) matter source is considered, an additional matter appears due to the coupling between matter and $f(R,T)$ gravity. The constraints are obtained for a realistic cosmological scenario, i.e., one obeying the null and weak energy conditions. The solutions are also extended to the case of a scalar field (normal or phantom) model, and it is found that the model is consistent with a phantom scalar field only. The coupled matter also acts as phantom matter. The study shows…
The present study deals with locally rotationally symmetric (LRS) Bianchi type II cosmological models representing massive string. The energy-momentum tensor for such string as formulated by Letelier (1983) is used to construct massive string cosmological models for which we assume that the expansion ($θ$) in the models is proportional to the shear ($σ$). This condition leads to $A = B^{m}$, where A and B are the metric coefficients and m is constant. We have derived two types of models depending on different values of m i.e. for $m\neq \sqrt{2}$ and $m = \sqrt{2}$ respectively. For suitable c…
Following up on hints of anisotropy in the cosmic microwave background radiation (CMB) data, we investigate locally rotational symmetric (LRS) Bianchi type I spacetimes with non-minimally coupled scalar fields. To single out potentially more interesting solutions, we search for Noether symmetry in this system. We then specialize to the Brans-Dicke (BD) field in such a way that the Lagrangian becomes degenerate (nontrivial) and solve the equations for Noether symmetry and the potential that allows it. Then we find the exact solutions of the equations of motion in terms of three parameters and a…
An LRS Bianchi I model is considered with constant deceleration parameter, $q=α-1$, where $α\geq0$ is a constant. The physical and kinematical behaviour of the models for $α=0$ and $α\neq0$ is studied in detail. The model with $α=0$ describes late time acceleration, but eternal inflation demands a violation of the NEC and WEC. The acceleration is caused by phantom matter which approaches a cosmological constant at late times. The solutions with a scalar field also show that the model is compatible with a phantom field only. A comparison with the observational outcomes indicates that the univer…
Locally-rotationally-symmetric Bianchi type-I viscous and non -viscous cosmological models are explored in general relativity (GR) and in f(R,T) gravity. Solutions are obtained by assuming that the expansion scalar is proportional to the shear scalar which yields a constant value for the deceleration parameter (q=2). Constraints are obtained by requiring the physical viability of the solutions. A comparison is made between the viscous and non-viscous models, and between the models in GR and in f(R,T) gravity. The metric potentials remain the same in GR and in f(R,T) gravity. Consequently, the …
We consider a Bianchi type III axisymmetric geometry in the presence of an electromagnetic field. A first result at the classical level is that the symmetry of the geometry need not be applied on the electromagnetic tensor $F_{μν}$; the algebraic restrictions, implied by the Einstein field equations to the stress energy tensor $T_{μν}$, suffice to reduce the general $F_{μν}$ to the appropriate form. The classical solution thus found contains a time dependent electric and a constant magnetic charge. The solution is also reachable from the corresponding mini-superspace action, which is strikingl…
We perform dynamical analysis of anisotropic Rastall cosmologies and, in particular Kantowski-Sachs, locally rotationally symmetric (LRS) Bianchi I and LRS Bianchi III cosmologies. Using dynamical system techniques, a qualitative analysis of cosmological equations yield physically interesting cases which are in agreement with observations such as de Sitter, accelerating, stable attractors are isotropic. Features such as isotropization and cosmological bounce are discussed in detail.
In this paper, we discuss the properties of one-parameter sequences that arise when solving the Hamiltonian constraint in Bianchi I loop quantum cosmology using a separation of variables method. In particular, we focus on finding an expression for the sequence for all real values of the parameter, and discuss the pre-classicality of this function. We find that the behavior of these preclassical sequences imply time asymmetry on either side of the classical singularity in Bianchi I cosmology.
We extend recent discussions of singularity avoidance in quantum gravity from isotropic to anisotropic cosmological models. The investigation is done in the framework of quantum geometrodynamics (Wheeler-DeWitt equation). We formulate criteria of singularity avoidance for general Bianchi class A models and give explicit and detailed results for Bianchi I models with and without matter. We find that the classical singularities can generally be avoided in these models.
This manuscript investigate the dark energy Bianchi type-I cosmological models in presence of generalized Chaplygin gas, variable gravitational and cosmological constants. In this manuscript, exact solutions of Einstein field equations are obtained under the assumption of time periodic varying deceleration parameter. The physical and dynamical behaviors of the models have been discussed with the help of graphical representations. Also we have discussed the stability and physical acceptability of the obtained solutions
We analyze the quantum Bianchi I model in the setting of the nonstandard loop quantum cosmology. Elementary observables are used to quantize the volume operator. The spectrum of the volume operator is bounded from below and discrete. The discreteness may imply a foamy structure of spacetime at semiclassical level. The results are described in terms of a free parameter specifying loop geometry to be determined in astro-cosmo observations. An evolution of the quantum model is generated by the so-called true Hamiltonian, which enables an introduction of a time parameter valued in the set of all r…
Lie symmetries are discussed for the Wheeler-De Witt equation in Bianchi Class A cosmologies. In particular, we consider General Relativity, minimally coupled scalar field gravity and Hybrid Gravity as paradigmatic examples of the approach. Several invariant solutions are determined and classified according to the form of the scalar field potential. The approach gives rise to a suitable method to select classical solutions and it is based on the first principle of the existence of symmetries.
We study a quantum Bianchi type I model in which the dynamical variables of the corresponding minisuperspace obey the generalized Heisenberg algebra. Such a generalized uncertainty principle has its origin in the existence of a minimal length suggested by quantum gravity and sting theory. We present approximate analytical solutions to the corresponding Wheeler-DeWitt equation in the limit where the scale factor of the universe is small and compare the results with the standard commutative and noncommutative quantum cosmology. Similarities and differences of these solutions are also discussed.
The exact renormalization group flow equations for gravity lead to quantum corrections of Newton's constant and cosmological constant. Using this we investigate the Bianchi-I cosmological model at late times. In particular, we obtain the scale factors in different directions, and observe that they eventually evolve into Friedmann-Lemaître-Robertson-Walker (FLRW) universe for radiation. However, for stiff matter the universe shows a Kasner like behaviour. The presentation is based on our work published in \cite{Mandal:2019xlg}.
The Chern-Simons functional $S_{\rm CS}$ is an exact solution to the Ashtekar-Hamilton-Jacobi equation of general relativity with a nonzero cosmological constant. In this paper we consider $S_{\rm CS}$ in Bianchi type IX cosmology with $S^3$ spatial surfaces. We show that among the classical solutions generated by~$S_{\rm CS}$, there is a two-parameter family of Euclidean spacetimes that have a regular NUT-type closing. When two of the three scale factors are equal, these spacetimes reduce to a one-parameter family within the Euclidean Taub-NUT-de~Sitter metrics. For a nonzero cosmological con…
We investigate the Bianchi I cosmology with the homogeneous SU(2) Yang-Mills field governed by the non-Abelian Born-Infeld action. Similar system with the standard Einstein-Yang-Mills (EYM) action is known to exhibit chaotic behavior induced by the Yang-Mills field. When the action is replaced by the Born-Infeld-type non-Abelian action (NBI), the chaos-order transition is observed in the high energy region. This is interpreted as a smothering effect due to (non-perturbative in $alpha'$) string corrections to the classical EYM action. We give a numerical evidence for the chaos-order transition,…
We consider the case of $R^n$-gravity and perform a detailed analysis of the dynamics in Bianchi I cosmologies which exhibit {\it local rotational symmetry} (LRS). We find exact solutions and study their behaviour and stability in terms of the values of the parameter $n$. In particular, we found a set of cosmic histories in which the universe is initially isotropic, then develops shear anisotropies which approaches a constant value.
We study different aspects of the Hořava-Lifshitz inspired Bianchi-II cosmology and its relations with the mixmaster universe model. First, we present exact solutions for a toy model, where only the cubic in spatial curvature terms are present in the action; then we briefly discuss some exotic singularities, which can appear in this toy model. We study also the toy model where only the quadratic in spatial curvature terms are present in the action. We establish relations between our results and those obtained by using the Hamiltonian formalism. Finally, we apply the results obtained by studyin…
The quantum cosmology of the string effective action is considered within the context of the Bianchi class A minisuperspace. An exact unified solution is found for all Bianchi types and interpreted physically as a quantum wormhole. The solution is generalized for types ${\rm VI_0}$ and ${\rm VII_0}$. The Bianchi type IX wavefunction becomes increasingly localized around the isotropic Universe at large three-geometries.
The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even for the approach to general inhomogeneous singularities. Thus, it is a popular model to test consequences of modifications to general relativity suggested by quantum theories of gravity. This paper presents a detailed proof that modifications coming from loop quantum gravity lead to a non-chaotic effective behavior. The way this is realized, independently of quantization ambiguities, suggests a new l…
Loop quantum cosmology, the symmetry reduction of quantum geometry for the study of various cosmological situations, leads to a difference equation for its quantum evolution equation. To ensure that solutions of this equation act in the expected classical manner far from singularities, additional restrictions are imposed on the solution. In this paper, we consider the Bianchi I model, both the vacuum case and the addition of a cosmological constant, and show using generating function techniques that only the zero solution satisfies these constraints. This implies either that there are technica…
Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $γ$ for Locally Rotationally Symmetric (LRS) Bianchi III metric and open Friedmann-Lemaître-Robertson-Walker (FLRW) metric are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, simple time-averaged systems determine the future asymptotic behavior. Depending on values of barotropic in…
We study the anisotropic Bianchi type-I cosmological model at late times, taking into account quantum gravitational corrections in the formalism of the exact renormalization group flow of the effective average action for gravity. The cosmological evolution equations are derived by including the scale dependence of Newton's constant $G$ and cosmological constant $Λ$. We have considered the solutions of the flow equations for $G$ and $Λ$ at next to leading order in the infrared cutoff scale. Using these scale dependent $G$ and $Λ$ in Einstein equations for the Bianchi-I model, we obtain the scal…
Loop quantization of diagonalized Bianchi class A models, leads to a partial difference equation as the Hamiltonian constraint at the quantum level. A criterion for testing a viable semiclassical limit has been formulated in terms of existence of the so-called pre-classical solutions. We demonstrate the existence of pre-classical solutions of the quantum equation for the vacuum Bianchi I model. All these solutions avoid the classical singularity at vanishing volume.
We present non-critical Bianchi type $I$ string cosmology solutions in the presence of central charge deficit term $Λ$. The leading order string frame curvature appears to be in the high curvature limit $Rα'\gtrsim1$, which underlines the necessity of including higher order $α'$-corrections. We give new solutions of two-loop (order $α'$) $β$-function equations of $σ$-model with non-zero $Λ$ and dilaton field in both cases of absence and presence of spatially homogeneous $H$-field ($H=dB$). Also, the evolution of solutions is studied in the Einstein frame, where the string effective action can …
The Wheeler-DeWitt equation is considered in the context of generalized scalar-tensor theories of gravitation for Bianchi type I cosmology. Exact solutions are found for two selfinteracting potentials and arbitary coupling function. The WKB wavefunctions are obtained and a family of solutions satisfying the Hawking-Page regularity conditions of wormholes are found.
The improved dynamics of loop quantum cosmology is extended to include the Bianchi type II model. Because these space-times admit both anisotropies and non-zero spatial curvature, certain technical difficulties arise over and above those encountered in the analysis of the (anisotropic but spatially flat) Bianchi type I space-times, and of the (spatially curved but isotropic) k=+/-1 models. We address these and show that the big-bang singularity is resolved in the same precise sense as in the recent analysis of the Bianchi I model. Bianchi II space-times are of special interest to quantum cosmo…
In this paper, new exact solutions for locally rotational symmetric (LRS) space-times are obtained within the modified Brans-Dicke theory (MBDT) (Rasouli et al 2014 Class. Quantum Grav. 31 115002). Specifically, extended five-dimensional (5D) versions of Kantowski-Sachs, LRS Bianchi type I and Bianchi type III are investigated in the context of the standard Brans-Dicke theory. We subsequently extract their corresponding dynamics on a 4D hypersurface. Our results are discussed regarding others obtained in the standard Brans-Dicke theory, induced-matter theory and general relativity. Moreover, w…
The loop quantum cosmology "improved dynamics" of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present the effective equations which provide modifications to the classical equations of motion due to quantum geometry effects.
Some cosmological solutions of massive strings are obtained in Bianchi I space-time following the techniques used by Letelier and Stachel. A class of solutions corresponds to string cosmology associated with/without a magnetic field and the other class consists of pure massive strings, obeying the Takabayashi equation of state.
A twisted ${\mathcal C}^\star $- algebra of the extended (noncommutative) Heisenberg-Weyl group has been constructed which takes into account the Uncertainty Principle for coordinates in the Planck length regime. This general construction is then used to generate an appropriate Hilbert space and observables for the noncommutative theory which, when applied to the Bianchi I Cosmology, leads to a new set of equations that describe the quantum evolution of the universe. We find that this formulation matches theories based on a reticular Heisenberg-Weyl algebra in the bouncing and expanding region…
The loop quantum cosmology of the Bianchi type II string cosmological model in the presence of a homogeneous magnetic field is studied. We present the effective equations which provide modifications to the classical equations of motion due to quantum effects. The numerical simulations confirm that the big bang singularity is resolved by quantum gravity effects.
