Maximal acceleration in a Lorentz invariant non-commutative space-time

Harikumar, E.; Panja, Suman Kumar; Rajagopal, Vishnu

doi:10.1140/epjp/s13360-022-03195-4

Cited by 3 publications

(6 citation statements)

References 65 publications

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“…Since generalizing general relativity to non-commutative space-time and analyzing such models is harder [22][23][24][25][26][27], it is useful to adopt Newtonian cosmology to include non-commutative modifications and analyze the same. The effect of non-commutativity also changes the Newtonian potential [28][29][30]. In [30], it was shown that the Newtonian potential is modified in the power of radial distance, in the presence of extra dimensions, due to the non-commutativity of space-time (Doplicher-Fredenhagen-Roberts space-time).…”

Section: Introductionmentioning

confidence: 99%

“…The effect of non-commutativity also changes the Newtonian potential [28][29][30]. In [30], it was shown that the Newtonian potential is modified in the power of radial distance, in the presence of extra dimensions, due to the non-commutativity of space-time (Doplicher-Fredenhagen-Roberts space-time). In [28,29], modifications to both kinetic and potential terms due to the non-commutativity of space-time were considered.…”

Section: Introductionmentioning

confidence: 99%

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Newtonian Cosmology and Evolution of κ-Deformed Universe

Harikumar,

Sreekumar,

Panja

2023

Universe

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Considering space-time to be non-commutative, we study the evolution of the universe employing the approach of Newtonian cosmology. Generalizing the conservation of energy and the first law of thermodynamics to κ-deformed space-time, we derive the modified Friedmann equations, valid up to the first order, in the deformation parameter. Analyzing these deformed equations, we derive the time evolution of the scale factor in cases of radiation-dominated, matter-dominated, and vacuum (energy)-dominated universes. We show that the rate of change of the scale factor in all three situations is modified by the non-commutativity of space-time, and this rate depends on the sign of the deformation parameter, indicating a possible explanation for the observed Hubble tension. We undertake this investigation for two different realizations of non-commutative space-time coordinates. In both cases, we also argue for the existence of bounce in the evolution of the universe.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Newtonian Cosmology and Evolution of κ-Deformed Universe

Harikumar,

Sreekumar,

Panja

2023

Universe

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“…The existence of a maximal acceleration has been a matter of research for a long time in different contexts. Starting as a consequence of Caianiello's quantum geometry, [6], it has been a recurrent topic in field theory [5], in string field theory [8,23], loop quantum gravity [25], non-commutative spacetimes [18,19,17] or classical electrodynamics [7,26,10,12,13]. Different faces of maximal acceleration have been also reviewed in [14].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, there is no chance to have a consistent theory with both concepts being equivalent in such a setting. Of course, there are ways to avoid this incompatibility between maximal proper acceleration and minimal length scales, but these ways are based either in Lorentz invariant relativistic noncommutative geometries [19] or based in non-relativistic dispersion relations [2]. Both approaches are in difficulty when considering general covariance, since the formulation of such schemes rely on specific coordinate systems.…”

Section: Introductionmentioning

confidence: 99%

Remarks on the Notions of Maximal Proper Acceleration, Minimal Lapse of Proper Time and Entropy Rate Change

Torromé

2023

Preprint

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It is discussed the relation between maximal proper acceleration and a lower bound to the proper time during which acceleration acts to reach the maximum possible variation in speed. While maximal proper acceleration implies an upper bound on the proper time than an instantaneous inertial observer will be able to measure, this bound is not observed by the physical proper time given by the metric of maximal acceleration. The Unruh temperature formula is extended to the case of hyperbolic observers in spaces of maximal proper acceleration, implying the existence of a maximal temperature. As a consequence, it is shown the existence of a lower bound to the exchange entropy due to interaction with the ambient and an upper bound to the the energy exchanged by charged particles is upper bounded by the energy at rest of the system. We also discuss that for classical point particle, with definite worldline, the existence of a minimal coordinate lapse implies the existence of a maximal acceleration.

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“…Although the physics in NC formalism has been highly studied over the last twenty years [11][12][13][14][15][16][17][18][19][20][21][22][23][24], some aspects on the construction of NC gauge theories were not fully understood, mainly when the NC parameter is positiondependent and non-associative [25][26][27]. Some mathematical frameworks such as the correspondence between NC gauge orbits induced by classical gauge orbits, known as the Seiberg-Witten map [6,28], and the use of higher algebraic structures (L ∞ -algebras) [29][30][31][32] were developed to try to solve this puzzle.…”

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confidence: 99%

Effects of wave propagation in canonical Poisson gauge theory under an external magnetic field

Abla,

Neves

2023

EPL

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The noncommutative electrodynamics based on the canonical Poisson gauge theory is studied in this paper.For a pure spatial non-commutativity, we investigate the plane wave solutions in the presence of a constantand uniform magnetic background field for the classical electrodynamics in canonical Poisson gauge theory. We obtain theproperties of the medium ruled by the permittivity and the permeability tensors in terms of the non-commutative parameter, with theelectrodynamics equations in the momentum space. Using the plane wave solutions mentioned, the dispersion relationsare modified by the magnetic background, and the correspondent group velocity is affected by the spatial non-commutative parameter.We construct the energy-momentum tensor and discuss the conserved components of this tensor in the spatial non-commutative case.The birefringence phenomenon is showed through the modified dispersion relations, that depends directly on the non-commutative correctionsand also on the magnetic background field. Using the bound of the polarized vacuum with laser (PVLAS) experiment for the vacuum magneticbirefringence, we estimate a theoretical value for the spatial non-commutative parameter.

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Maximal acceleration in a Lorentz invariant non-commutative space-time

Cited by 3 publications

References 65 publications

Newtonian Cosmology and Evolution of κ-Deformed Universe

Newtonian Cosmology and Evolution of κ-Deformed Universe

Remarks on the Notions of Maximal Proper Acceleration, Minimal Lapse of Proper Time and Entropy Rate Change

Effects of wave propagation in canonical Poisson gauge theory under an external magnetic field

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