Built on

P. Aschieri and L. Castellani, “Noncommutative gauge fields coupled to noncommutative gravity,” Gen. Rel. Grav. 45
Original
1911
Earlier work this paper cites.
P. Aschieri, M. Dimitrijevic, F. Meyer and J. Wess, “Noncommutative geometry and gravity,” Class. Quant. Grav. 23
1912
Earlier work this paper cites.
G. Amelino-Camelia, J. R. Ellis, N. E. Mavromatos, D. V. Nanopoulos, “Distance measurement and wave dispersion in a Liouville string approach to quantum gravity”, Int. J. Mod. Phys. A 12, 607 (1997) [hep-th/9605211]
1997
Earlier work this paper cites.
G. Amelino-Camelia, J. R. Ellis, N. E. Mavromatos, D. V. Nanopoulos, S. Sarkar, “Tests of quantum gravity from observations of gamma-ray bursts”, Nature 393 (1998) 763 [astro-ph/9712103]
1998
Earlier work this paper cites.
A. Giaquinto, J. J. Zhang “Bialgebra actions, twists, and universal deformation formulas”, J. Pure Appl. Alg. 128, 133 (1998) [arXiv:hep-th/9411140]
1998
Earlier work this paper cites.
G. Amelino-Camelia, S. Majid, “Waves on noncommutative space-time and gamma-ray bursts”, Int. J. Mod. Phys. A 15, 4301 (2000) [hep-th/9907110]
2000
Earlier work this paper cites.
V. A. Acciari et al
Original
2001
Earlier work this paper cites.
G. Amelino-Camelia, “Testable scenario for relativity with minimum length,” Phys. Lett. B 510
2001
Earlier work this paper cites.
J. Kowalski-Glikman, “Observer-independent quantum of mass,” Phys. Lett. A 286
2001
Earlier work this paper cites.
G. Amelino-Camelia, “Relativity in space-times with short distance structure governed by an observer independent (Planckian) length scale,” Int. J. Mod. Phys. D 11
2002
Earlier work this paper cites.
J. Magueijo and L. Smolin, “Lorentz invariance with an invariant energy scale”, Phys. Rev. Lett. 88, 190403 (2002) [hep-th/0112090]
2002
Earlier work this paper cites.

Similar

J. Magueijo and L. Smolin, “Generalized Lorentz invariance with an invariant energy scale”, Phys. Rev. D 67, 044017 (2003) [gr-qc/0207085]
2003
Cited alongside, same era.
T. Jacobson, “Introduction to quantum fields in curved space-time and the Hawking effect”, in Lectures on Quantum Gravity, A. Gomberoff, D. Marolf (eds). Series of the Centro De Estudios Científicos, Springer (2005) doi:10.1007/0-387-24992-3 ¯ \underline{~} 2 [gr-qc/0308048]
2005
Cited alongside, same era.
V. Mukhanov, S. Winitzki, “Introduction to quantum effects in gravity”, Cambridge University Press (2007), ISBN: 9780521868341
2007
Cited alongside, same era.
U. Jacob, T. Piran, “Lorentz-violation-induced arrival delays of cosmological particles”, JCAP 0801, 031 (2008), [arXiv:0712.2170]
Original
2008
Cited alongside, same era.
A. Borowiec, A. Pachoł, “kappa-Minkowski spacetime as the result of Jordanian twist deformation”, Phys. Rev. D 79

Then

S. Hossenfelder, “Minimal Length Scale Scenarios for Quantum Gravity,” Living Rev. Rel. 16
Original
2013
Later among the works it cites.
P. Aschieri, A. Schenkel, “Noncommutative connections on bimodules and Drinfeld twist deformation”, Adv. Theor. Math. Phys. 18 3 (2014) 513-612 [arXiv:1210.0241]
Original
2014
Later among the works it cites.
G. Rosati, G. Amelino-Camelia, A. Marciano, M. Matassa, “Planck-scale-modified dispersion relations in FRW spacetime”, Phys. Rev. D 92, 124042 (2015) [arxiv:1507.02056]
Original
2015
Later among the works it cites.
G. Amelino-Camelia, G. D’Amico, G. Rosati and N. Loret, “In-vacuo-dispersion features for GRB neutrinos and photons,” Nature Astron. 1
Original
2017
Later among the works it cites.
L. Barcaroli, L. K. Brunkhorst, G. Gubitosi, N. Loret and C. Pfeifer, “Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes,” Phys. Rev. D 95

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2020

Dispersion Relations in $\kappa$-Noncommutative Cosmology

Aschieri, Paolo, Borowiec, Andrzej, Pachoł, Anna

Understand

We study noncommutative deformations of the wave equation in curved backgrounds and discuss the modification of the dispersion relations due to noncommutativity combined with curvature of spacetime.

Our noncommutative differential geometry approach is based on Drinfeld twist deformation, and can be implemented for any twist and any curved background.
We discuss in detail the Jordanian twist $-$giving $\kappa$-Minkowski spacetime in flat space$-$ in the presence of a Friedman-Lema\^{i}tre-Robertson-Walker (FLRW) cosmological background.
We obtain a new expression for the variation of the speed of light, depending linearly on the ratio $E_{ph}/E_{LV}$ (photon energy / Lorentz violation scale), but also linearly on the cosmological time, the Hubble parameter and inversely proportional to the scale factor.

Built on

P. Aschieri and L. Castellani, “Noncommutative gauge fields coupled to noncommutative gravity,” Gen. Rel. Grav. 45
Original
1911
Earlier work this paper cites.
P. Aschieri, M. Dimitrijevic, F. Meyer and J. Wess, “Noncommutative geometry and gravity,” Class. Quant. Grav. 23
1912
Earlier work this paper cites.
G. Amelino-Camelia, J. R. Ellis, N. E. Mavromatos, D. V. Nanopoulos, “Distance measurement and wave dispersion in a Liouville string approach to quantum gravity”, Int. J. Mod. Phys. A 12, 607 (1997) [hep-th/9605211]
1997
Earlier work this paper cites.
G. Amelino-Camelia, J. R. Ellis, N. E. Mavromatos, D. V. Nanopoulos, S. Sarkar, “Tests of quantum gravity from observations of gamma-ray bursts”, Nature 393 (1998) 763 [astro-ph/9712103]
1998
Earlier work this paper cites.
A. Giaquinto, J. J. Zhang “Bialgebra actions, twists, and universal deformation formulas”, J. Pure Appl. Alg. 128, 133 (1998) [arXiv:hep-th/9411140]
1998
Earlier work this paper cites.
G. Amelino-Camelia, S. Majid, “Waves on noncommutative space-time and gamma-ray bursts”, Int. J. Mod. Phys. A 15, 4301 (2000) [hep-th/9907110]
2000
Earlier work this paper cites.
V. A. Acciari et al
Original
2001
Earlier work this paper cites.
G. Amelino-Camelia, “Testable scenario for relativity with minimum length,” Phys. Lett. B 510
2001
Earlier work this paper cites.
J. Kowalski-Glikman, “Observer-independent quantum of mass,” Phys. Lett. A 286
2001
Earlier work this paper cites.
G. Amelino-Camelia, “Relativity in space-times with short distance structure governed by an observer independent (Planckian) length scale,” Int. J. Mod. Phys. D 11
2002
Earlier work this paper cites.
J. Magueijo and L. Smolin, “Lorentz invariance with an invariant energy scale”, Phys. Rev. Lett. 88, 190403 (2002) [hep-th/0112090]
2002
Earlier work this paper cites.

Similar

J. Magueijo and L. Smolin, “Generalized Lorentz invariance with an invariant energy scale”, Phys. Rev. D 67, 044017 (2003) [gr-qc/0207085]
2003
Cited alongside, same era.
T. Jacobson, “Introduction to quantum fields in curved space-time and the Hawking effect”, in Lectures on Quantum Gravity, A. Gomberoff, D. Marolf (eds). Series of the Centro De Estudios Científicos, Springer (2005) doi:10.1007/0-387-24992-3 ¯ \underline{~} 2 [gr-qc/0308048]
2005
Cited alongside, same era.
V. Mukhanov, S. Winitzki, “Introduction to quantum effects in gravity”, Cambridge University Press (2007), ISBN: 9780521868341
2007
Cited alongside, same era.
U. Jacob, T. Piran, “Lorentz-violation-induced arrival delays of cosmological particles”, JCAP 0801, 031 (2008), [arXiv:0712.2170]
Original
2008
Cited alongside, same era.
A. Borowiec, A. Pachoł, “kappa-Minkowski spacetime as the result of Jordanian twist deformation”, Phys. Rev. D 79

Then

S. Hossenfelder, “Minimal Length Scale Scenarios for Quantum Gravity,” Living Rev. Rel. 16
Original
2013
Later among the works it cites.
P. Aschieri, A. Schenkel, “Noncommutative connections on bimodules and Drinfeld twist deformation”, Adv. Theor. Math. Phys. 18 3 (2014) 513-612 [arXiv:1210.0241]
Original
2014
Later among the works it cites.
G. Rosati, G. Amelino-Camelia, A. Marciano, M. Matassa, “Planck-scale-modified dispersion relations in FRW spacetime”, Phys. Rev. D 92, 124042 (2015) [arxiv:1507.02056]
Original
2015
Later among the works it cites.
G. Amelino-Camelia, G. D’Amico, G. Rosati and N. Loret, “In-vacuo-dispersion features for GRB neutrinos and photons,” Nature Astron. 1
Original
2017
Later among the works it cites.
L. Barcaroli, L. K. Brunkhorst, G. Gubitosi, N. Loret and C. Pfeifer, “Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes,” Phys. Rev. D 95

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

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Original

2009

Cited alongside, same era.

P. Aschieri, M. Dimitrijevic, P. Kulish, F. Lizzi, J. Wess , “Noncommutative Spacetimes: Symmetries in Noncommutative Geometry and Field Theory”, Lect. Notes Phys. 774 (Springer, Berlin Heidelberg 2009), DOI 10.1007/978-3-540-89793-4

2009

Cited alongside, same era.

A. Borowiec, Kumar S. Gupta, S. Meljanac, A. Pachol, “Constraints on the quantum gravity scale from kappa-Minkowski spacetime”, EPL 92, 20006 (2010) [arXiv:0912.3299]

Original

2010

Cited alongside, same era.

Jacob U., Mercati F., Amelino-Camelia G., Piran T., “Modifications to Lorentz invariant dispersion in relatively boosted frames”, Phys. Rev. D 82, 084021 (2010) [gr-qc/1004.0575]

2010

Cited alongside, same era.

P. Aschieri and L. Castellani, “Noncommutative Gravity Solutions,” J. Geom. Phys. 60

Original

2010

Cited alongside, same era.

S. Liberati, “Tests of Lorentz invariance: a 2013 update,” Class. Quant. Grav. 30

Original

2013

Cited alongside, same era.

Original

2017