Class of solutions of the Wheeler-DeWitt equation in the Friedmann-Robertson-Walker universe

Vieira, H. S.; Bezerra, V. B.

doi:10.1103/physrevd.94.023511

Cited by 10 publications

(9 citation statements)

References 27 publications

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“…Recently, we found a class of solutions of the Wheeler-DeWitt equation in a homogeneous and isotropic universe for the spatially closed, flat, and open geometries of the Friedmann-Robertson-Walker universe filled with different forms of energy, namely, matter, radiation, and vacuum [9]. Soon after, we have generalized our analysis and then studied the dynamical interpretation of the Wheeler-DeWitt equation by taking into account all different kinds of energy [10].…”

Section: Introductionmentioning

confidence: 90%

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Class of solutions of the Wheeler-DeWitt equation with ordering parameter

Vieira,

Bezerra,

Muniz

et al. 2020

Preprint

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In this letter, we discuss the Wheeler-DeWitt equation with an ordering parameter in the Friedmann-Robertson-Walker universe. The solutions when the universe was very small and at the end of the expansion are obtained in terms of Bessel and Heun functions, respectively. We also obtain a boundary condition which should be satisfied by the ordering parameter, namely, p ≤ 1. We investigate the minimum value of the scale factor with respect to the maximum value of the probability density.

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Section: Introductionmentioning

confidence: 90%

“…The classical evolution of the universe at different stages, valid for all forms of energy, can be obtained from the following Hamiltonian [9]…”

Section: Wheeler-dewitt Equation With Ordering Termmentioning

confidence: 99%

Class of solutions of the Wheeler-DeWitt equation with ordering parameter

Vieira,

Bezerra,

Muniz

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…(The second Friedmann equation is obtained by studying the equation of motion of L FRW together with the continuity equation, see details in [5,12,13]). As function of p and a, the Hamiltonian reads:…”

Section: Wdw Equation In Cosmologymentioning

confidence: 99%

“…For a recent description of the other possible components, such as matter and radiation, see Refs. [12,13]. Indeed, the interest on the wave function of the Universe is very strong, as the recent lively and vibrating dispute on the effect of quantum gravitational perturbations in the early universe shows [14][15][16].…”

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confidence: 99%

Wheeler--DeWitt Universe Wave Function in the Presence of Stiff Matter

Giacosa¹,

Pagliara²

2019

Acta Phys. Pol. B

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We study the Wheeler-DeWitt (WDW) equation close to the Big-Bang. We argue that an interaction dominated fluid (speed of sound equal to the speed of light), if present, would dominate during such an early phase. Such a fluid with p = ρ ∝ 1/a 6 generates a term in the potential of the wave function of the WDW equation proportional to −1/a 2 . This very peculiar quantum potential, which embodies a spontaneous breaking of dilatation invariance, has some very remarkable consequences for the wave function of the Universe: Ψ(a) vanishes at the Big-Bang: Ψ(0) = 0; the wave function Ψ(a) is always real; a superselection rule assures that the system is confined to a ≥ 0 without the need of imposing any additional artificial barrier for unphysical negative a. These results do not depend on the operator-ordering problem of the WDW equation.

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“…Such studies were further generalized to the case coupled with a scalar field [26]. In addition, the quantization of 2d Friedmann-Robertson-Walker universe was studied in [27,28].…”

Section: Introductionmentioning

confidence: 99%

Universal horizons and Hawking radiation in nonprojectable 2d Hořava gravity coupled to a nonrelativistic scalar field

Bhattacharjee

Wang

2017

Phys. Rev. D

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In this paper, we study the non-projectable 2d Hořava gravity coupled with a non-relativistic scalar field, where the coupling is in general non-minimal and of the form f (φ)R, where f (φ) is an arbitrary function of the scalar field φ, and R denotes the 2d Ricci scalar. In particular, we first investigate the Hamiltonian structure, and show that there are two-first and two-second class constraints, similar to the pure gravity case, but now the local degree of freedom is one, due to the presence of the scalar field. Then, we present various exact stationary solutions of this coupled system, and find that some of them represent black holes but now with universal horizons as their boundaries. At these horizons, the Hawking radiations are thermal with temperatures proportional to their surface gravities, which normally depend on the non-linear dispersion relations of the particles radiated, similar to the (3+1)-dimensional case. arXiv:1703.08207v3 [gr-qc]

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Class of solutions of the Wheeler-DeWitt equation in the Friedmann-Robertson-Walker universe

Cited by 10 publications

References 27 publications

Class of solutions of the Wheeler-DeWitt equation with ordering parameter

Class of solutions of the Wheeler-DeWitt equation with ordering parameter

Wheeler--DeWitt Universe Wave Function in the Presence of Stiff Matter

Universal horizons and Hawking radiation in nonprojectable 2d Hořava gravity coupled to a nonrelativistic scalar field

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