Investigations of the possibility that some novel "quantum" properties of spacetime might induce a Planck-scale modification of the energy/momentum dispersion relation focused at first on scenarios with Planck-scale violations of Lorentz symmetry, with an associated reduced n-parameter (n < 6) rotation-boost symmetry group. More recently several studies have considered the possibility of a "doubly special relativity", in which the modification of the dispersion relation emerges from a framework with both the Planck scale and the speed-of-light scale as characteristic scales of a 6-parameter group of rotation-boost symmetry transformations (a deformation of the Lorentz transformations). For the schemes with broken Lorentz symmetry at the Planck scale there is a large literature on the derivation of experimental limits. We provide here a corresponding analysis for the doubly-special-relativity framework. We find that the analyses of photon stability, synchrotron radiation, and threshold conditions for particle production in collision processes, the three contexts which are considered as most promising for constraining the broken-Lorentz-symmetry scenario, cannot provide significant constraints on doubly-special-relativity parameter space. However, certain types of analyses of gamma-ray bursts are sensitive to the symmetry deformation. A key element of our study is an observation that removes a possible sign ambiguity for the doubly-special-relativity framework. This result also allows us to characterize more sharply the differences between the doubly-special-relativity framework and the framework of κ-Poincaré Hopf algebras, two frameworks which are often confused with each other in the literature. a While sometimes, especially when commenting on the logical structure of the DSR framework, it is convenient for us to indicate explicitly the speed-of-light scale c, in most equations we adopt conventions such that c = = 1.

In several approaches to the quantum-gravity problem evidence has emerged of the validity of a "GUP" (a Generalized position-momentum Uncertainty Principle) and/or a "MDR" (a modification of the energy-momentum dispersion relation), but very little is known about the implications of GUPs and MDRs for black-hole thermodynamics, another key topic for quantum-gravity research. We investigate an apparent link, already suggested in an earlier exploratory study involving two of us, between the possibility of a GUP and/or a MDR and the possibility of a log term in the area-entropy black-hole formula. We then obtain, from that same perspective, a modified relation between the mass of a black hole and its temperature, and we examine the validity of the "Generalized Second Law of black-hole thermodynamics" in theories with a GUP and/or a MDR. After an analysis of GUP-and MDR-modifications of the black-body radiation spectrum, we conclude the study with a description of the black-hole evaporation process.

We compute the Zero Point Energy in a spherically symmetric background distorted at high energy as predicted by Gravity's Rainbow. In this context we setup a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The eigenvalue equation is a reformulation of the Wheeler-DeWitt equation. With the help of a canonical decomposition, we find that the relevant contribution to one loop is given by the graviton quantum fluctuations around the given background. By means of a variational approach based on gaussian trial functionals, we find that the ordinary divergences can here be handled by an appropriate choice of the rainbow's functions, in contrast to what happens in other conventional approaches. A final discussion on the connection of our result with the observed cosmological constant is also reported.

The realization that forthcoming experimental studies, such as the ones planned for the GLAST space telescope, will be sensitive to Planck-scale deviations from Lorentz symmetry has increased interest in noncommutative spacetimes in which this type of effects is expected. We focus here on κ-Minkowski spacetime, a muchstudied example of Lie-algebra noncommutative spacetime, but our analysis appears to be applicable to a more general class of noncommutative spacetimes. A technical controversy which has significant implications for experimental testability is the one concerning the κ-Minkowski relation between group velocity and momentum. A large majority of studies adopted the relation v = dE(p)/dp, where E(p) is the κ-Minkowski dispersion relation, but recently some authors advocated alternative formulas. While in these previous studies the relation between group velocity and momentum was introduced through ad hoc formulas, we rely on a direct analysis of wave propagation in κ-Minkowski. Our results lead conclusively to the relation v = dE(p)/dp. We also show that the previous proposals of alternative velocity/momentum relations implicitly relied on an inconsistent implementation of functional calculus on κ-Minkowski and/or on an inconsistent description of spacetime translations.

Several recent studies have considered the implications for astrophysics and cosmology of some possible nonclassical properties of spacetime at the Planck scale. The new effects, such as a Planck-scale-modified energy-momentum (dispersion) relation, are often inferred from the analysis of some quantum versions of Minkowski spacetime, and therefore the relevant estimates depend heavily on the assumption that there could not be significant interplay between Planck-scale and curvature effects. We here scrutinize this assumption, using as guidance a quantum version of de Sitter spacetime with known Inönü-Wigner contraction to a quantum Minkowski spacetime. And we show that, contrary to common (but unsupported) beliefs, the interplay between Planckscale and curvature effects can be significant. Within our illustrative example, in the Minkowski limit the quantum-geometry deformation parameter is indeed given by the Planck scale, while in the de Sitter picture the parameter of quantization of geometry depends both on the Planck scale and the curvature scalar. For the much-studied case of Planck-scale effects that intervene in the observation of gamma-ray bursts we can estimate the implications of "quantum spacetime curvature" within robust simplifying assumptions. For cosmology at the present stage of the development of the relevant mathematics one cannot go beyond semiheuristic reasoning, and we here propose a candidate approximate description of a quantum FRW geometry, obtained by patching together pieces (with different spacetime curvature) of our quantum de Sitter. This semiheuristic picture, in spite of its limitations, provides rather robust evidence that in the early Universe the interplay between Planck-scale and curvature effects could have been particularly significant. * Electronic address: antonino.marciano@cpt.univ-mrs.fr † Electronic address: r.bruno@bnrenergia.it ‡ Electronic address: gianluca.mandanici@istruzione.it

Basing on the results obtained in a our previous study on Gravity's Rainbow, we determine the quantum corrections to the space-time metric for the Schwarzschild and the de Sitter background, respectively. We analyze how quantum fluctuations alter these metrics inducing modifications on the propagation of test particles. Significantly enough we find that quantum corrections can become relevant not only for particles approaching the Planck energy but, due to the one loop contribution, even for low-energy particles as far as Planckian length scales are considered. We briefly compare our results with others obtained in similar studies and with the recent experimental OPERA announcement of superluminal neutrino propagation.

We investigate some issues that are relevant for the derivation of experimental limits on the parameters of canonical noncommutative spacetimes. By analyzing a simple Wess-Zumino-type model in canonical noncommutative spacetime with soft supersymmetry breaking we explore the implications of ultraviolet supersymmetry on low-energy phenomenology. The fact that new physics in the ultraviolet can modify low-energy predictions affects significantly the derivation of limits on the noncommutativity parameters based on low-energy data. These are, in an appropriate sense here discussed, "conditional limits". We also find that some standard techniques for an effective low-energy description of theories with non-locality at short distance scales are only applicable in a regime where theories in canonical noncommutative spacetime lack any predictivity, because of the strong sensitivity to unknown UV physics. It appears useful to combine high-energy data, from astrophysics, with the more readily available low-energy data.

Communicated by D. V. AhluwaliaThe literature on quantum-gravity-inspired scenarios for the quantization of space-time has so far focused on particle-physics-like studies. This is partly justified by the present limitations of our understanding of quantum gravity theories, but we here argue that valuable insight can be gained through semi-heuristic analyses of the implications for gravitational phenomena of some results obtained in the quantum space-time literature. In particular, we show that the types of description of particle propagation that emerged in certain quantum space-time frameworks have striking implications for gravitational collapse and for the behavior of gravity at large distances. * This essay received honorable mention in the Gravity Research Foundation 2010 Awards for Essays on Gravitation. 2385 Int. J. Mod. Phys. D 2010.19:2385-2392. Downloaded from www.worldscientific.com by PENNSYLVANIA STATE UNIVERSITY on 03/15/15. For personal use only.