High-spatial-frequency periodic structures on the surfaces of InP, GaP, and GaAs have been observed after multiple-pulse femtosecond laser irradiation at wavelengths in the transparency regions of the respective solids. The periods of the structures are substantially shorter than the wavelengths of the incident laser fields in the bulk materials. In contrast, high-frequency structures were not observed for laser photon energies above the band gaps of the target materials.

Alternative gravitational theories described by Lagrangians depending on general functions of the Ricci scalar have been proven to give coherent theoretical models to describe the experimental evidence of the acceleration of universe at present time. In this paper we proceed further in this analysis of cosmological applications of alternative gravitational theories depending on (other) curvature invariants. We introduce Ricci squared Lagrangians in minimal interaction with matter (perfect fluid); we find modified Einstein equations and consequently modified Friedmann equations in the Palatini formalism. It is striking that both Ricci scalar and Ricci squared theories are described in the same mathematical framework and both the generalized Einstein equations and generalized Friedmann equations have the same structure. In the framework of the cosmological principle, without the introduction of exotic forms of dark energy, we thus obtain modified equations providing values of w ef f < −1 in accordance with the experimental data. The spacetime bi-metric structure plays a fundamental role in the physical interpretation of results and gives them a clear and very rich geometrical interpretation.

The current accelerated universe could be produced by modified gravitational dynamics as it can be seen in particular in its Palatini formulation. We analyze here a specific non-linear gravity-scalar system in the first order Palatini formalism which leads to a FRW cosmology different from the purely metric one. It is shown that the emerging FRW cosmology may lead either to an effective quintessence phase (cosmic speed-up) or to an effective phantom phase. Moreover, the already known gravity assisted dark energy dominance occurs also in the first order formalism. Finally, it is shown that a dynamical theory able to resolve the cosmological constant problem exists also in this formalism, in close parallel with the standard metric formulation. * Electronic address: allemandi@dm.unito.it † Electronic address: borow@ift.uni.wroc.pl ‡ Electronic address: francaviglia@dm.unito.it § Electronic address: odintsov@ieec.uab.es also at TSPU, Tomsk

Two one-parameter families of twists providing κ−Minkowski * -product deformed spacetime are considered:Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two perspectives. The first one is the Hopf module algebra point of view, which is strictly related with Drinfeld's twisting tensor technique. The other one relies on an appropriate extension of "deformed realizations" of nondeformed Lorentz algebra by the quantum Minkowski algebra. This extension turns out to be de Sitter Lie algebra. We show the way both approaches are related. The second path allows us to calculate deformed dispersion relations for toy models ensuing from different twist parameters. In the Abelian case one recovers κ−Poincaré dispersion relations having numerous applications in doubly special relativity. Jordanian twists provide a new type of dispersion relations which in the minimal case (related to Weyl-Poincaré algebra) takes an energy-dependent linear mass deformation form.

It has been recently shown that, in the rst order (Palatini) formalism, there is universality of Einstein equations and Komar energy{ momentum complex, in the sense that for a generic nonlinear Lagrangian depending only on the scalar curvature of a metric and a torsionless connection one always gets Einstein equations and Komar's expression for the energy{momentum complex. In this paper a similar analysis (also in the framework of the rst order formalism) is performed for all nonlinear Lagrangians depending on the (symmetrized) Ricci square invariant. The main result is that the universality of Einstein equations and Komar energy{momentum complex also extends to this case (modulo a conformal transformation of the metric).

We investigate the phenomenological consequences of κ-Minkowski extension of the Standard Model, working in the linear order in inverse κ. At this order the *-deformed Lagrangian can be expanded in the series of dimension five operators that have non-trivial transformation properties under the ordinary Lorentz invariance. Such operators cause the Lorentz-violating signatures at low energies, and in particular lead to the anomalous spin precession linked to the external direction. The experimental bounds on this phenomenon then restrict parameter κ to be above 10 23 GeV, making it difficult to impose a direct connection between this theory and quantum gravity.

Several issues concerning quantum κ−Poincaré algebra are discussed and reconsidered here. We propose two different formulations of κ−Poincaré quantum algebra. Firstly we present a complete Hopf algebra formulae of κ−Poincaré in classical Poincaré basis. Further by adding one extra generator, which modifies the classical structure of Poincaré algebra, we eliminate non polynomial functions in the κ− parameter. Hilbert space representations of such algebras make Doubly Special Relativity (DSR) similar to the Stueckelberg's version of (proper-time) relativistic Quantum Mechanics.

Abstract. Some classes of Deformed Special Relativity (DSR) theories are reconsidered within the Hopf algebraic formulation. For this purpose we shall explore a minimal framework of deformed Weyl-Heisenberg algebras provided by a smash product construction of DSR algebra. It is proved that this DSR algebra, which uniquely unifies κ-Minkowski spacetime coordinates with Poincaré generators, can be obtained by nonlinear change of generators from undeformed one. Its various realizations in terms of the standard (undeformed) Weyl-Heisenberg algebra opens the way for quantum mechanical interpretation of DSR theories in terms of relativistic (Stückelberg version) Quantum Mechanics. On this basis we review some recent results concerning twist realization of κ-Minkowski spacetime described as a quantum covariant algebra determining a deformation quantization of the corresponding linear Poisson structure. Formal and conceptual issues concerning quantum κ-Poincaré and κ-Minkowski algebras as well as DSR theories are discussed. Particularly, the so-called "q-analog" version of DSR algebra is introduced. Is deformed special relativity quantization of doubly special relativity remains an open question. Finally, possible physical applications of DSR algebra to description of some aspects of Planck scale physics are shortly recalled.