The Generalized Uncertainty Principle and the Friedmann equations

Majumder, Barun

doi:10.1007/s10509-011-0815-6

Cited by 28 publications

(34 citation statements)

References 57 publications

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“…It is worth mentioning that GUP has been studied with Friedmann equations through different frameworks in [26,27]. In this paper, we first derive the modified Friedmann equations for a general form of the entropy as a function of area using the first law of thermodynamics (dE = T dS + W dV ).…”

Section: Jhep06(2014)093mentioning

confidence: 99%

Minimal length, Friedmann equations and maximum density

Awad

Ali

2014

J. High Energ. Phys.

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Inspired by Jacobson's thermodynamic approach [4], Cai et al. [5,6] have shown the emergence of Friedmann equations from the first law of thermodynamics. We extend Akbar-Cai derivation [6] of Friedmann equations to accommodate a general entropyarea law. Studying the resulted Friedmann equations using a specific entropy-area law, which is motivated by the generalized uncertainty principle (GUP), reveals the existence of a maximum energy density closed to Planck density. Allowing for a general continuous pressure p(ρ, a) leads to bounded curvature invariants and a general nonsingular evolution. In this case, the maximum energy density is reached in a finite time and there is no cosmological evolution beyond this point which leaves the big bang singularity inaccessible from a spacetime prospective. The existence of maximum energy density and a general nonsingular evolution is independent of the equation of state and the spacial curvature k. As an example we study the evolution of the equation of state p = ωρ through its phase-space diagram to show the existence of a maximum energy which is reachable in a finite time.

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Section: Jhep06(2014)093mentioning

confidence: 99%

Minimal length, Friedmann equations and maximum density

Awad

Ali

2014

J. High Energ. Phys.

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“…In (16) and (17), the commutation relations between the several components of the quantization tensor α µ ν , (11), has been used. The squared four-momentum operator as well as the squared four-position operator are equal to the corresponding squared operators of usual quantum mechanics and thus the following commutation relations are valid:…”

Section: Quaternionic Quantization In Quantum Mechanicsmentioning

confidence: 99%

“…If this is postulated, then these generalized quantization principles have also to be transferred to the quantization of general relativity an thus the gravitational field what differs from the formulation of clasical general relativity on noncommutative space-time [10] or even usual quantum general relativity on noncommutative space-time [11], [12], [13], [14]. In [15], [16], [17], [18], [19] ideas to transfer the concept of a generalized uncertainty principle to gravity can be found, but in [20] and [21] the generalized uncertainty principle principle has really been transferred to the variables of canonical quantum gravity and quantum cosmology, whereas in [22] the concept of noncommutative geometry has been transferred to the components of the tetrad field. An extension of the field theoretic quantization principle to a nonlocal quantization principle has been considered in [23].…”

Section: Introductionmentioning

confidence: 99%

Quaternionic quantization principle in general relativity and supergravity

Kober

2016

Int. J. Mod. Phys. A

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A generalized quantization principle is considered, which incorporates nontrivial commutation relations of the components of the variables of the quantized theory with the components of the corresponding canonical conjugated momenta referring to other space-time directions. The corresponding commutation relations are formulated by using quaternions. At the beginning, this extended quantization concept is applied to the variables of quantum mechanics. The resulting Dirac equation and the corresponding generalized expression for plane waves are formulated and some consequences for quantum field theory are considered. Later, the quaternionic quantization principle is transferred to canonical quantum gravity. Within quantum geometrodynamics as well as the Ashtekar formalism the generalized algebraic properties of the operators describing the gravitational observables and the corresponding quantum constraints implied by the generalized representations of these operators are determined. The generalized algebra also induces commutation relations of the several components of the quantized variables with each other. Finally, the quaternionic quantization procedure is also transferred to N = 1 supergravity. Accordingly, the quantization principle has to be generalized to be compatible with Dirac brackets, which appear in canonical quantum supergravity.

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“…To distinguish between the linear and second order terms in the Planck length, we rewrite the GUP of equation (4) in a more general form [54] δxδp…”

Section: Generalized Uncertainty Principalmentioning

confidence: 99%