Inflationary universe in the presence of a minimal measurable length

Mohammadi, Abolhassan; Ali, Ahmed Farag; Golanbari, T.; Aghamohammadi, Amir; Saaidi, Kh.; Faizal, Mir

doi:10.1016/j.aop.2017.08.008

Cited by 16 publications

(7 citation statements)

References 54 publications

(90 reference statements)

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“…Early applications of this principle concerned mainly black-hole thermodynamics [9][10][11], but more recently also cosmological topics, such as inflation [12,13], nonsingular universe construction [14,15] and the dark energy model [16,17]. The underlying idea is that a generalization of the principle can modify the entropy-area relation in thermodynamics, thereby introducing corrections to the cosmological evolution equation.…”

Section: Introductionmentioning

confidence: 99%

Implications of minimum and maximum length scales in cosmology

Kouwn

2018

Physics of the Dark Universe

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We investigate the cosmological implications of the generalized and extended uncertainty principle (GEUP), and whether it could provide an explanation for the dark energy. The consequence of the GEUP is the existence of a minimum and a maximum length, which can in turn modify the entropy area law and also modify the Friedmann equation. The cosmological consequences are studied by paying particular attention to the role of these lengths. We find that the theory allows a cosmological evolution where the radiation-and matter-dominated epochs are followed by a long period of virtually constant dark energy, that closely mimics the ΛCDM model. The main cause of the current acceleration arises from the maximum length scale β, governed by the relation Λ ∼ −β −1 W (−β −1 ). Using recent observational data (the Hubble parameters, type Ia supernovae, and baryon acoustic oscillations, together with the Planck or WMAP 9-year data of the cosmic microwave background radiation), we estimate constraints to the minimum length scale α 10 81 and the maximum length scale β ∼ −10 −2 .

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Section: Introductionmentioning

confidence: 99%

Implications of minimum and maximum length scales in cosmology

Kouwn

2018

Physics of the Dark Universe

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“…A similar investigation guideline is not a priori modified for the features of classical(ized) gravity (emerging) after the Planck scale, as defined by the corresponding (possibly) isotropic universe volume [74]. Also within this perspective, the effects of primordial perturbations can overlap those remaining from the anisotropic cosmological model, in the sense that a minimal length, which defines the volume (age) under which the universe is not explorable, can modify the Friedmann equation suitably also for generating inflation [75].…”

Section: Semiclassical States From Quantum Cosmologiesmentioning

confidence: 99%

Semiclassical Length Measure from a Quantum-Gravity Wave Function

Lecian

2017

Technologies

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Abstract:The definition of a length operator in quantum cosmology is usually influenced by a quantum theory for gravity considered. The semiclassical limit at the Planck age must meet the requirements implied in present observations. The features of a semiclassical wave-functional state are investigated, for which the modern measure(ment)s is consistent. The results of a length measurement at present times are compared with the same measurement operation at cosmological times. By this measure, it is possible to discriminate, within the same Planck-length expansion, the corrections to a Minkowski flat space possibly due to classicalization of quantum phenomena at the Planck time and those due to possible quantum-gravitational manifestations of present times. This analysis and the comparison with the previous literature can be framed as a test for the verification of the time at which anomalies at present related to the gravitational field, and, in particular, whether they are ascribed to the classicalization epoch. Indeed, it allows to discriminate not only within the possible quantum features of the quasi (Minkowski) flat spacetime, but also from (possibly Lorentz violating) phenomena detectable at high-energy astrophysical scales. The results of two different (coordinate) length measures have been compared both at cosmological time and as a perturbation element on flat Minkowski spacetime. The differences for the components of the corresponding classical(ized) metric tensor have been analyzed at different orders of expansions. The results of the expectation values of a length operator in the universe at the Planck time must be comparable with the same length measurements at present times, as far as the metric tensor is concerned. The comparison of the results of (straight) length measures in two different directions, in particular, can encode the pertinent information about the parameters defining the semiclassical wavefunctional for (semiclassicalized) gravitational field.

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“…Many authors have studied effects of a minimal length in cosmology using a classical approach in which the Poisson brackets are modified according to the correspondence principle [10,22,[47][48][49][50][51]. In the vast majority of the GUP formulation the parameter related to the minimal length (deformation parameter) is positive.…”

Section: Introductionmentioning

confidence: 99%

Quantum cosmology with dynamical vacuum in a minimal-length scenario

et al. 2021

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In 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.

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Inflationary universe in the presence of a minimal measurable length

Cited by 16 publications

References 54 publications

Implications of minimum and maximum length scales in cosmology

Implications of minimum and maximum length scales in cosmology

Semiclassical Length Measure from a Quantum-Gravity Wave Function

Quantum cosmology with dynamical vacuum in a minimal-length scenario

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