scholarly journals COSMOLOGY WITH MINIMAL LENGTH UNCERTAINTY RELATIONS

2009 ◽  
Vol 18 (07) ◽  
pp. 1059-1071 ◽  
Author(s):  
BABAK VAKILI
Keyword(s):  
Quantum Cosmology ◽  
Generalized Uncertainty Principle ◽  
Poisson Algebra ◽  
Heisenberg Algebra ◽  
Small Scale ◽  
Minimum Length ◽  
Uncertainty Relations ◽  
Inflationary Universe ◽  
De Sitter ◽  
Approximate Analytical Solutions

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.

scholarly journals Quantum cosmology with dynamical vacuum in a minimal-length scenario

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
M. F. Gusson ◽  
A. Oakes O. Gonçalves ◽  
R. G. Furtado ◽  
J. C. Fabris ◽  
J. A. Nogueira
Keyword(s):  
Wave Function ◽  
Commutation Relation ◽  
Uncertainty Principle ◽  
Quantum Cosmology ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Minimum Length ◽  
Position Space ◽  
Infinite Norm ◽  
The Universe

AbstractIn this work, we consider effects of the dynamical vacuum in quantum cosmology in presence of a minimum length introduced by the GUP (generalized uncertainty principle) related to the modified commutation relation $$[{\hat{X}},{\hat{P}}] := \frac{i\hbar }{ 1 - \beta {\hat{P}}^2 }$$ [ X ^ , P ^ ] : = i ħ 1 - β P ^ 2 . We determine the wave function of the Universe $$ \psi _{qp}(\xi ,t)$$ ψ qp ( ξ , t ) , which is solution of the modified Wheeler–DeWitt equation in the representation of the quasi-position space, in the limit where the scale factor of the Universe is small. Although $$\psi _{qp}(\xi ,t)$$ ψ qp ( ξ , t ) is a physically acceptable state it is not a realizable state of the Universe because $$ \psi _{qp}(\xi ,t)$$ ψ qp ( ξ , t ) has infinite norm, as in the ordinary case with no minimal length.

scholarly journals Generalized Uncertainty Principle in Quantum Cosmology

2019 ◽  
Vol 64 (11) ◽  
pp. 1050
Author(s):  
V. E. Kuzmichev ◽  
V. V. Kuzmichev
Keyword(s):  
Simultaneous Measurement ◽  
Quantum Cosmology ◽  
Degrees Of Freedom ◽  
Generalized Uncertainty Principle ◽  
Spacelike Hypersurface ◽  
Matter Field ◽  
Quantum States ◽  
Uncertainty Relations ◽  
Planck Constant ◽  
Quantum Equations

The effects of gravity which manifest themselves when performing the simultaneous measurement of two non-commuting observables in the quantum theory are discussed. Matter and gravity are considered as quantum fields. The Schr¨odinger-type time equation is given for the case of a finite number of degrees of freedom: one for the matter field and one for geometry. For a spatially closed system filled with dust and radiation being in definite quantum states, the solutions to the quantum equations are found, and the existence of the minimum measurable length and the minimum momentum is shown. It appears that the simultaneous measurement of fluctuations of the intrinsic and extrinsic curvatures of the spacelike hypersurface in spacetime cannot be performed with an accuracy exceeding the Planck constant. Unruh’s and Bronstein’s uncertainty relations are discussed.

scholarly journals Minimum Length Uncertainty Relations in the Presence of Dark Energy

Galaxies ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 11 ◽  
Author(s):  
Matthew J. Lake
Keyword(s):  
Dark Energy ◽  
High Energy ◽  
Electron Neutrino ◽  
Minimum Length ◽  
Uncertainty Relations ◽  
Electron Mass ◽  
De Sitter ◽  
Order Of Magnitude ◽  
Near Future ◽  
The Universe

We introduce a dark energy-modified minimum length uncertainty relation (DE-MLUR) or dark energy uncertainty principle (DE-UP) for short. The new relation is structurally similar to the MLUR introduced by Károlyházy (1968), and reproduced by Ng and van Dam (1994) using alternative arguments, but with a number of important differences. These include a dependence on the de Sitter horizon, which may be expressed in terms of the cosmological constant as l dS ∼ 1 / Λ . Applying the DE-UP to both charged and neutral particles, we obtain estimates of two limiting mass scales, expressed in terms of the fundamental constants G , c , ℏ , Λ , e . Evaluated numerically, the charged particle limit corresponds to the order of magnitude value of the electron mass ( m e ), while the neutral particle limit is consistent with current experimental bounds on the mass of the electron neutrino ( m ν e ). Possible cosmological consequences of the DE-UP are considered and we note that these lead naturally to a holographic relation between the bulk and the boundary of the Universe. Low and high energy regimes in which dark energy effects may dominate canonical quantum behaviour are identified and the possibility of testing the model using near-future experiments is briefly discussed.

scholarly journals GENERALIZED QUANTIZATION PRINCIPLE IN CANONICAL QUANTUM GRAVITY AND APPLICATION TO QUANTUM COSMOLOGY

2012 ◽  
Vol 27 (20) ◽  
pp. 1250106 ◽  
Author(s):  
MARTIN KOBER
Keyword(s):  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Dynamical Behavior ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Polynomial Method ◽  
Canonical Approach ◽  
Canonical Quantum Gravity ◽  
Canonical Quantum ◽  
Quantization Principle

In this paper, a generalized quantization principle for the gravitational field in canonical quantum gravity, especially with respect to quantum geometrodynamics is considered. This assumption can be interpreted as a transfer from the generalized uncertainty principle in quantum mechanics, which is postulated as generalization of the Heisenberg algebra to introduce a minimal length, to a corresponding quantization principle concerning the quantities of quantum gravity. According to this presupposition there have to be given generalized representations of the operators referring to the observables in the canonical approach of a quantum description of general relativity. This also leads to generalized constraints for the states and thus to a generalized Wheeler–DeWitt equation determining a new dynamical behavior. As a special manifestation of this modified canonical theory of quantum gravity, quantum cosmology is explored. The generalized cosmological Wheeler–DeWitt equation corresponding to the application of the generalized quantization principle to the cosmological degree of freedom is solved by using Sommerfelds polynomial method.

scholarly journals A Solution to the Soccer Ball Problem for Generalized Uncertainty Relations

2019 ◽  
Vol 64 (11) ◽  
pp. 1036 ◽  
Author(s):  
M. J. Lake
Keyword(s):  
Uncertainty Principle ◽  
Equivalence Principle ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Total Momentum ◽  
Uncertainty Relations ◽  
Relativistic Limit ◽  
Soccer Ball ◽  
Ball Problem ◽  
Extended Uncertainty

We propose a new method for generating generalized uncertainty relations (GURs) including the generalized uncertainty principle (GUP), extended uncertainty principle (EUP), and extended generalized uncertainty principle (EGUP), previously proposed in the quantum gravity literature, without modifying the Heisenberg algebra. Our approach is compatible with the equivalence principle, and with local Poincar´e invariance in the relativistic limit, thus circumventing many of the problems associated with GURs derived from modified commutation relations. In particular, it does not require the existence of a nonlinear additional law for momenta. This allows sensible multi-particle states to be constructed in which the total momentum is macroscopic, even if the momentum of an individual particle is bounded by the Planck momentum, thus providing a resolution of the “soccer ball problem” that plagues current approaches to GURs.

PRIMORDIAL BLACK HOLE PAIR CREATION IN R2 THEORY

1998 ◽  
Vol 13 (28) ◽  
pp. 2289-2293 ◽  
Author(s):  
B. C. PAUL ◽  
S. MUKHERJEE ◽  
G. P. SINGH ◽  
A. BEESHAM
Keyword(s):  
Black Holes ◽  
Semiclassical Approximation ◽  
Pair Creation ◽  
Quadratic Term ◽  
Inflationary Universe ◽  
Primordial Black Hole ◽  
Primordial Black Holes ◽  
De Sitter ◽  
Gravitational Action ◽  
Spatial Section

The probability for quantum creation of an inflationary universe with a pair of black holes has been studied in semiclassical approximation with Hartle–Hawking boundary conditions, assuming a gravitational action which includes a quadratic term in the scalar curvature αR2, α being a constant. The action of the instanton responsible for creating such a universe, with a spatial section with S1×S2 topology, is seen to be less than that of a de Sitter S3 instanton, unless α<-1/(8Λ), where Λ is the cosmological constant. Since negative α implies a classical instability, the probability for production of primordial black holes seems to be suppressd in R2-theory.

scholarly journals Emergent GUP from modified Hawking radiation in Einstein–NED theory

2020 ◽  
Vol 98 (8) ◽  
pp. 801-809
Author(s):  
S. Hamid Mehdipour
Keyword(s):  
Hawking Radiation ◽  
Lagrangian Density ◽  
General Procedure ◽  
Generalized Uncertainty Principle ◽  
Energy Condition ◽  
Intrinsic Property ◽  
Hawking Temperature ◽  
Nonlinear Electrodynamics ◽  
Uncertainty Relations ◽  
Schwarzschild Solution

We present a general procedure for constructing exact black hole (BH) solutions with a magnetic charge in the context of nonlinear electrodynamics (NED) theory as well as in the coherent state approach to noncommutative geometry (NCG). In this framework, the Lagrangian density for a noncommutative Hayward BH is obtained and the weak energy condition is satisfied. The noncommutative Hayward solution depends on two kind of charges, without which the Schwarzschild solution is applicable. Moreover, to find a link between the BH evaporation and uncertainty relations, we may calculate the Hawking temperature and find the effect of the Lagrangian density of BHs on the Hawking radiation. Therefore, a generalized uncertainty principle (GUP) emerges from the modified Hawking temperature in Einstein–NED theory. The origin of this GUP is the combined influence of a nonlinear magnetic source and an intrinsic property of the manifold associated with a fictitious charge. Finally, we find that there is an upper bound on the Lagrangian uncertainty of the BHs that is caused by the NED field and (or) the fictitious charge.

scholarly journals p-ADIC AND ADELIC MINISUPERSPACE QUANTUM COSMOLOGY

2002 ◽  
Vol 17 (10) ◽  
pp. 1413-1433 ◽  
Author(s):  
GORAN S. DJORDJEVIĆ ◽  
BRANKO DRAGOVICH ◽  
LJUBIŠA D. NEŠIĆ ◽  
IGOR V. VOLOVICH
Keyword(s):  
Quantum Mechanics ◽  
Cosmological Constant ◽  
Quantum Cosmology ◽  
Quantum Effects ◽  
De Sitter Space ◽  
Cosmological Models ◽  
De Sitter ◽  
Adelic Quantum Mechanics ◽  
Matter Fields

We consider the formulation and some elaboration of p-adic and adelic quantum cosmology. The adelic generalization of the Hartle–Hawking proposal does not work in models with matter fields. p-adic and adelic minisuperspace quantum cosmology is well defined as an ordinary application of p-adic and adelic quantum mechanics. It is illustrated by a few cosmological models in one, two and three minisuperspace dimensions. As a result of p-adic quantum effects and the adelic approach, these models exhibit some discreteness of the minisuperspace and cosmological constant. In particular, discreteness of the de Sitter space and its cosmological constant is emphasized.

scholarly journals Effect of GUP on the Kepler problem and a variable minimal length

2014 ◽  
Vol 92 (6) ◽  
pp. 484-487 ◽  
Author(s):  
Fatemeh Ahmadi ◽  
Jafar Khodagholizadeh
Keyword(s):  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Kepler Problem ◽  
Rotational Symmetry ◽  
Generalized Uncertainty Principle ◽  
Space Time ◽  
Minimal Length ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Perihelion Shift

Various approaches to quantum gravity, such as string theory, predict a minimal measurable length and a modification of the Heisenberg uncertainty principle near the Plank scale, known as the generalized uncertainty principle (GUP). Here we study the effects of GUP, which preserves the rotational symmetry of the space–time, on the Kepler problem. By comparing the value of the perihelion shift of the planet Mercury in Schwarzschild – de Sitter space–time with the resultant value of GUP, we find a relation between the minimal measurable length and the cosmological constant of the space–time. Now, if the cosmological constant varies with time, we have a variable minimal length in the space–time. Finally, we investigate the effects of GUP on the stability of circular orbits.

Tomographic analysis of quantum and classical de Sitter cosmological models

2019 ◽  
Vol 28 (16) ◽  
pp. 2040009 ◽  
Author(s):  
Cosimo Stornaiolo
Keyword(s):  
Quantum Cosmology ◽  
Classical Limit ◽  
Initial Conditions ◽  
Quantum Tomography ◽  
Wave Functions ◽  
Hamiltonian Constraint ◽  
De Sitter ◽  
Quantum Universe ◽  
Tomographic Analysis ◽  
The Universe

In this work, we show the importance of introducing the quantum tomography formalism to analyze the properties of wave functions in quantum cosmology. In particular, we examine the initial conditions of the universe proposed by various authors in the context of de Sitter’s cosmology studying their classical limit and comparing it with the classical tomogram obtained from the Hamiltonian constraint in General Relativity. This comparison gives us the opportunity to find under which conditions there is a transition from the quantum universe to the classical one. A relevant result is that in these models the decay of the cosmological constant is a sufficient condition for this transition.

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