B. Vakili

Noether symmetric f(R) quantum cosmology and its classical correlations

Abstract We quantize a flat FRW cosmology in the context of the f ( R ) gravity by Noether symmetry approach. We explicitly calculate the form of f ( R ) for which such symmetries exist. It is shown that the existence of a Noether symmetry yields a general solution of the Wheeler–DeWitt equation where can be expressed as a superposition of states of the form e i S . In terms of Hartle criterion, this type of wave function exhibits classical correlations, i.e. the emergent of classical universe is expected due to the oscillating behavior of the solutions of Wheeler–DeWitt equation. According to this interpretation we also provide the Noether symmetric classical solutions of our f ( R ) cosmological model.

Noether symmetric classical and quantum scalar field cosmology

We study the evolution of a two-dimensional minisuperspace cosmological model in classical and quantum levels by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a Friedmann?Robertson?Walker model and a scalar field with which the action of the model is augmented. It is shown that the minisuperspace of such a model is a two-dimensional manifold with a vanishing Ricci scalar. We present a coordinate transformation which cast the corresponding minisupermetric to a Minkowskian or Euclidean one according to the choices of an ordinary or phantom model for the scalar field. Then, the Noether symmetry of such a cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generators of the desired symmetry. We explicitly calculate the form of the scalar field potential functions for which such symmetries exist. For these potential functions, the exact classical and quantum solutions in the cases where the scalar field is an ordinary or a phantom one are presented and compared.

Spacetime singularity resolution in Snyder noncommutative space

Inspired by quantum gravity proposals, we construct a deformed phase space which supports the UV and IR cutoffs. We show that the Liouville theorem is satisfied in the deformed phase space which allows us to formulate the thermodynamics of the early universe in the semiclassical regime. Applying the proposed method to the Snyder noncommutative space, we find a temperature dependent equation of state which opens a new window for the natural realization of inflation as a phase transition from the quantum gravity regime to the standard radiation dominated era. Also, we obtain finite energy and entropy densities for the Universe when at least the weak energy condition is satisfied. We show that there is a minimum size for the Universe which is proportional to the Planck length and consequently the big bang singularity is removed.

Late time acceleration in a deformed phase space model of dilaton cosmology

The effects of noncommutativity on the phase space of a dilatonic cosmological model is investigated. The existence of such noncommutativity results in a deformed Poisson algebra between the minisuperspace variables and their momenta conjugate. For an exponential dilaton potential, the exact solutions in the commutative and noncommutative cases are presented and compared. We use these solutions to address the late time acceleration issue of cosmic evolution.

Cosmology with minimal length uncertainty relations

We study the effects of the existence of a minimal observable length in the phase space of classical and quantum de Sitter (dS) and anti-de Sitter (AdS) cosmology. Since this length has been suggested in quantum gravity and string theory, its effects in the early universe might be expected. Adopting the existence of such a minimum length results in the generalized uncertainty principle (GUP), which is a deformed Heisenberg algebra between minisuperspace variables and their momenta operators. We extend these deformed commutating relations to the corresponding deformed Poisson algebra in the classical limit. Using the resulting Poisson and Heisenberg relations, we then construct the classical and quantum cosmology of dS and AdS models in a canonical framework. We show that in classical dS cosmology this effect yields an inflationary universe in which the rate of expansion is larger than that of the usual dS universe. Also, for the AdS model it is shown that the GUP might change the oscillatory nature of the corresponding cosmology. We also study the effects of the GUP in quantized models through approximate analytical solutions to the Wheeler–DeWitt (WD) equation, in the limit of a small scale factor for the universe, and compare the results with the ordinary quantum cosmology in each case.

Natural cutoffs via compact symplectic manifolds

In the context of phenomenological models of quantum gravity, it is claimed that the ultraviolet and infrared natural cutoffs can be realized from local deformations of the Hamiltonian systems. In this paper, we scrutinize this hypothesis and formulate a cutoff-regularized Hamiltonian system. The results show that while local deformations are necessary to have cutoffs, they are not sufficient. In fact, the cutoffs can be realized from globally-deformed Hamiltonian systems that are defined on compact symplectic manifolds. By taking the universality of quantum gravity effects into account, we then conclude that quantum gravity cutoffs are global (topological) properties of the symplectic manifolds. We justify our results by considering three well-known examples: The Moyal, Snyder and polymer deformed Hamiltonian systems.

A late time accelerated FRW model with scalar and vector fields via Noether symmetry

Abstract We study the evolution of a three-dimensional minisuperspace cosmological model by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a flat Friedmann–Robertson–Walker (FRW) model, a scalar field with potential function V ( ϕ ) with which the gravity part of the action is minimally coupled and a vector field of its kinetic energy is coupled with the scalar field by a coupling function f ( ϕ ) . Then, the Noether symmetry of such a cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generator of the desired symmetry. We explicitly calculate the form of the coupling function between the scalar and the vector fields and also the scalar field potential function for which such symmetry exists. Finally, by means of the corresponding Noether current, we integrate the equations of motion and obtain exact solutions for the scale factor, scalar and vector fields. It is shown that the resulting cosmology is an accelerated expansion universe for which its expansion is due to the presence of the vector field in the early times, while the scalar field is responsible of its late time expansion.

Thermostatistics of the polymeric ideal gas

In this paper, we formulate statistical mechanics of the polymerized systems in the semiclassical regime. On the corresponding polymeric symplectic manifold, we set up a noncanonical coordinate system in which all of the polymeric effects are summarized in the density of states. Since we show that the polymeric effects only change the number of microstates of a statistical system, working in this coordinate is quite reasonable from the statistical point of view. The results show that the number of microstates decreases due to existence of an upper bound for the momentum of the test particles in the polymer framework. We obtain a corresponding canonical partition function by means of the deformed density of states. By using the partition function, we study thermodynamics of the ideal gas in the polymer framework and show that our results are in good agreement with those that arise from the full quantum consideration at high temperature, and they coincide with their usual counterpart in the limit of low temperature.

Polymer quantization versus the Snyder noncommutative space

We study a noncanonical Hilbert space representation of the polymer quantum mechanics. It is shown that Heisenberg algebra get some modifications in the constructed setup from which a generalized uncertainty principle will naturally come out. Although the extracted physical results are the same as those obtained from the standard canonical representation, the noncanonical representation may be notable in view of its possible connection with the generalized uncertainty theories suggested by string theory. In this regard, by considering an Snyder-deformed Heisenberg algebra we show that since the translation group is not deformed it can be identified with a polymer-modified Heisenberg algebra. In classical level, it is shown the noncanonical Poisson brackets are related to their canonical counterparts by means of a Darboux transformation on the corresponding phase space.

Deformed phase space in a two-dimensional minisuperspace model

We study the effects of noncommutativity and deformed Heisenberg algebra on the evolution of a two-dimensional minisuperspace cosmological model in classical and quantum regimes. The phase-space variables turn out to correspond to the scale factor of a flat FRW model with a positive cosmological constant and a dilatonic field with which the action of the model is augmented. The exact classical and quantum solutions in commutative and noncommutative cases are presented. We also obtain some approximate analytical solutions for the corresponding classical and quantum cosmology in the presence of the deformed Heisenberg relations between the phase-space variables, in the limit where the minisuperspace variables are small. These results are compared with the standard commutative and noncommutative cases, and similarities and differences of these solutions are discussed.