Future singularities and teleparallelism in loop quantum cosmology

Bamba, Kazuharu; Haro, Jaume de; Odintsov, Sergei D.

doi:10.1088/1475-7516/2013/02/008

Cited by 116 publications

(83 citation statements)

References 141 publications

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“…It was the main result obtained in [3,4]. This can be appreciated by observing the Hamiltonian operator (35), which can be split asĤ(a, c, , )Ψ =Ĥ g (a, c)Ψ + H m ( , )Ψ = 0, whereĤ g yĤ m represents the Hamiltonian for gravitational sector and the moduli fields, respectively, and the scale factors have the transformations = , = .…”

Section: − 16 11mentioning

confidence: 85%

“…An example is the Chaplygin gas, where a proper time, characteristic to this matter, leads to the presence of singularities types I, II, III, and IV (generalizations to these models are presented in [35][36][37]) which also appear in the phantom scenario to dark/energy matter. In our case, since the matter we are considering is barotropic, initial singularities of these types do not emerge from our analysis, implying also that phantom fields are absent.…”

Section: Final Remarksmentioning

confidence: 99%

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Cosmologies with Scalar Fields from Higher Dimensions Applied to Bianchi Type VIh=-1 Model: Classical and Quantum Solutions

Socorro

Sesma

Pimentel

2018

Advances in High Energy Physics

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We construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus. The corresponding action in four dimensions is similar to the action of K-essence theories. This approach is applied to anisotropic cosmological Bianchi type (ℎ=−1) model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. The classical Einstein field equations give us a hidden symmetry, corresponding to the equality between two radii B=C, which permits us to solve exactly the equations of motion. One relation between the scale factors (A,C) via the solutions is found. With this hidden symmetry, then we solve the FRW model, finding that the scale factor goes to B radii. Also the corresponding Wheeler-DeWitt (WDW) equation in the context of Standard Quantum Cosmology is solved, building a wavepacket when the scalar fields have a hyperbolic behavior, obtaining some qualitative results when we analyze the projection plane to the wall formed by the probability density. Bohm's formalism for this cosmological model is revisited too.

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Section: − 16 11mentioning

confidence: 85%

Section: Final Remarksmentioning

confidence: 99%

Cosmologies with Scalar Fields from Higher Dimensions Applied to Bianchi Type VIh=-1 Model: Classical and Quantum Solutions

Socorro

Sesma

Pimentel

2018

Advances in High Energy Physics

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“…Examples of teleparallel theories.-In this Section we will study three important examples of teleparallel theories: Einstein cosmology, loop quantum cosmology [19] and the teleparallel version of the F (R) = R 2 − µ 4 2R model [20,21].…”

Section: General Features In Teleparallel Theories-for the Flat Flrwmentioning

confidence: 99%

Nonsingular Models of Universes in Teleparallel Theories

Haro

Amorós

2013

Phys. Rev. Lett.

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Different models of universes are considered in the context of teleparallel theories. Assuming that the universe is filled by a fluid with equation of state (EoS) P = −ρ − f (ρ), for different teleparallel theories and different EoS we study its dynamics. Two particular cases are studied in detail: in the first one we consider a function f with two zeros (two de Sitter solutions) that mimics a huge cosmological constant at early times and a pressureless fluid at late times. In the second one, in the context of loop quantum cosmology with a small cosmological constant, we consider a pressureless fluid (P = 0 ⇔ f (ρ) = −ρ) which means that there are a de Sitter and an anti de Sitter solution. In both cases one obtains a non-singular universe that at early times is in an inflationary phase, after leaving this phase it passes trough a matter dominated phase and finally at late times it expands in an accelerated way.PACS numbers: 04.50. Kd, 98.80. Jk 1. Introduction.-Teleparallel theories (F (T ) theories) [1][2][3][4] are built from the scalar torsion T = −6H 2 , where H is the Hubble parameter. The field equations are second-order, which is a great advantage to F (R) theories, whose fourthorder equations lead to pathologies like instabilities or large corrections to Newton's law [5,6]. This entails that the modified Friedmann equation depicts a curve in the plane (H, ρ), that is, the universe moves along this curve an its dynamics is given by the modified Raychaudhuri equation and the conservation equation.This opens the possibility to built non-singular models of universes filled by a fluid with equation of state (EoS) P = −ρ − f (ρ), being P the pressure and ρ the energy density. For this EoS, the zeros of the function f give de Sitter and anti de Sitter solutions. Then, choosing a function f with two zeros one obtains a non-singular model of universe.As examples of teleparallel theories we study Einstein Cosmology (EC) with and without a small cosmological constant, loop quantum cosmology (LQC) with and without a small cosmological constant, and the teleparallel version of the model F (R) = R 2 − µ 4 2R , R being the scalar curvature. For these teleparallel examples we consider models of EoS, which mimic a huge cosmological constant at early times and a pressureless fluid at late times, like P = − ρ 2 ρi , ρ i being the initial energy density of the universe.We will see how these simple models could solve the socalled coincidence problem due to periods of acceleration of our universe, that is, they could mimic the evolution of a universe that begins in an inflationary phase, after leaving it passes trough a matter dominated one, and at late times enters in an accelerated phase.We also study the specific case of a universe filled by a pressureless fluid (P = 0) in the context of LQC with a small cosmological constant. In that case, at early times the universe is in an anti de Sitter phase, after leaving this phase it starts to

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“…Teleparallel theories in flat FRW cosmology are defined via a Lagrangian of the form L T = V F (T ) − V ρ (see [50][51][52] for a review of the topic), where V is the volume of the spatial part and T = −6H 2 is the so-called scalar torsion [49,53]. From this Lagrangian we can see that the conjugate momentum of V is given by p V = ∂L ∂V = −4HF ′ (T ), and thus the Hamiltonian is…”

Section: State-finder Parameters In Teleparallel Theoriesmentioning

confidence: 99%

Brane cosmology from observational surveys and its comparison with standard FRW cosmology

Astashenok

Elizalde

Haro

et al. 2013

Astrophys Space Sci

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Several dark energy models on the brane are investigated. They are compared with corresponding theories in the frame of 4d Friedmann-Robertson-Walker cosmology. To constrain the parameters of the models considered, recent observational data, including SNIa apparent magnitude measurements, baryon acoustic oscillation results, Hubble parameter evolution data and matter density perturbations are used. Explicit formulas of the so-called state-finder parameters in teleparallel theories are obtained that could be useful to test these models and to establish a link between Loop Quantum Cosmology and Brane Cosmology. It is concluded that a joint analysis as the one developed here allows to estimate, in a very convenient way, possible deviation of the real universe cosmology from the standard Friedmann-Robertson-Walker one.

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Future singularities and teleparallelism in loop quantum cosmology

Cited by 116 publications

References 141 publications

Cosmologies with Scalar Fields from Higher Dimensions Applied to Bianchi Type VIh=-1 Model: Classical and Quantum Solutions

Cosmologies with Scalar Fields from Higher Dimensions Applied to Bianchi Type VIh=-1 Model: Classical and Quantum Solutions

Nonsingular Models of Universes in Teleparallel Theories

Brane cosmology from observational surveys and its comparison with standard FRW cosmology

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