@article {2012,
title = {Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime},
journal = {Phys. Rev. D 86 (2012) 124035},
number = {arXiv:1206.5315;},
year = {2012},
note = {12 pages, 5 figures},
publisher = {American Physical Society},
abstract = {The interest of part of the quantum-gravity community in the possibility of\r\nPlanck-scale-deformed Lorentz symmetry is also fueled by the opportunities for testing the relevant scenarios with analyses, from a signal-propagation perspective, of observations of bursts of particles from cosmological distances. In this respect the fact that so far the implications of deformed Lorentz symmetry have been investigated only for flat (Minkowskian) spacetimes represents a very significant limitation, since for propagation over cosmological distances the curvature/expansion of spacetime is evidently tangible. We here provide a significant step toward filling this gap by exhibiting an explicit example of Planck-scale-deformed relativistic symmetries of a spacetime with constant rate of expansion (deSitterian). Technically we obtain the first ever example of a relativistic theory of worldlines of particles with 3 nontrivial relativistic invariants: a large speed scale (\"speed-of-light scale\"), a large distance scale (inverse of the \"expansion-rate scale\"), and a large momentum scale (\"Planck scale\"). We address some of the challenges that had obstructed success for previous attempts by exploiting the recent understanding of the connection between deformed Lorentz symmetry and relativity of spacetime locality. We also offer a preliminary analysis of the differences between the scenario we here propose and the most studied scenario for broken (rather than deformed) Lorentz symmetry in expanding spacetimes.},
keywords = {Doubly special relativity},
doi = {10.1103/PhysRevD.86.124035},
author = {Giovanni Amelino-Camelia and Antonino Marciano and Marco Matassa and Giacomo Rosati}
}
@article {2006,
title = {A cyclic integral on k-Minkowski noncommutative space-time},
journal = {Int. J. Mod. Phys. A 21 (2006) 3133-3150},
number = {arXiv.org;hep-th/0407227v1},
year = {2006},
abstract = {We examine some alternative possibilities for an action functional for $\\\\kappa$-Minkowski noncommutative spacetime, with an approach which should be applicable to other spacetimes with coordinate-dependent commutators of the spacetime coordinates ($[x_\\\\mu,x_\\\\nu]=f_{\\\\mu,\\\\nu}(x)$). Early works on $\\\\kappa$-Minkowski focused on $\\\\kappa$-Poincar\\\\\\\'e covariance and the dependence of the action functional on the choice of Weyl map, renouncing to invariance under cyclic permutations of the factors composing the argument of the action functional. A recent paper (hep-th/0307149), by Dimitrijevic, Jonke, Moller, Tsouchnika, Wess and Wohlgenannt, focused on a specific choice of Weyl map and, setting aside the issue of $\\\\kappa$-Poincar\\\\\\\'e covariance of the action functional, introduced in implicit form a cyclicity-inducing measure. We provide an explicit formula for (and derivation of) a choice of measure which indeed ensures cyclicity of the action functional, and we show that the same choice of measure is applicable to all the most used choices of Weyl map. We find that this {\textquoteleft}{\textquoteleft}cyclicity-inducing measure\\\'\\\' is not covariant under $\\\\kappa$-Poincar\\\\\\\'e transformations. We also notice that the cyclicity-inducing measure can be straightforwardly derived using a map which connects the $\\\\kappa$-Minkowski spacetime coordinates and the spacetime coordinates of a {\textquoteleft}{\textquoteleft}canonical\\\'\\\' noncommutative spacetime, with coordinate-independent commutators.},
doi = {10.1142/S0217751X06031077},
url = {http://hdl.handle.net/1963/2158},
author = {Alessandra Agostini and Giovanni Amelino-Camelia and Michele Arzano and Francesco D{\textquoteright}Andrea}
}