Rainbows without unicorns: Metric structures in theories with Modified Dispersion Relations

Rainbow metrics are a widely used approach to metric formalism for theories with Modified Dispersion Relations. They have had a huge success in the Quantum Gravity Phenomenology literature, since they allow to introduce momentum-dependent spacetime metrics into the description of systems with Modified Dispersion Relation. In this paper, we introduce the reader to some realizations of this general idea: the original Rainbow metrics proposal, the momentum-space-inspired metric, the standard Finsler geometry approach and our alternative definition of a four-velocity-dependent metric with a massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations.Comment: 10 pages. Discussion on the role of connections was added. Matches published versio

Generalized energy conditions in Extended Theories of Gravity

Theories of physics can be considered viable if the initial value problem and the energy conditions are formulated self-consistently. The former allow a uniquely determined dynamical evolution of the system, and the latter guarantee that causality is preserved and that "plausible" physical sources have been considered. In this work, we consider the further degrees of freedom related to curvature invariants and scalar fields in Extended Theories of Gravity (ETG). These new degrees of freedom can be recast as effective perfect fluids that carry different meanings with respect to the standard matter fluids generally adopted as sources of the field equations. It is thus somewhat misleading to apply the standard general relativistic energy conditions to this effective energy-momentum, as the latter contains the matter content and a geometrical quantity, which arises from the ETG considered. Here, we explore this subtlety, extending on previous work, in particular, to cases with the contracted Bianchi identities with diffeomorphism invariance and to cases with generalized explicit curvature-matter couplings, which imply the non-conservation of the energy-momentum tensor. Furthermore, we apply the analysis to specific ETGs, such as scalar-tensor gravity, $f(R)$ gravity and modified Gauss-Bonnet gravity. Interesting results appear such as matter that may exhibit unusual thermodynamical features, for instance, and gravity that retains its attractive character in the presence of negative pressures; or alternatively, we verify that repulsive gravity may occur for standard matter.Comment: 12 pages, version accepted for publication in Phys.Rev.

Energy conditions in modified gravity

We consider generalized energy conditions in modified theories of gravity by taking into account the further degrees of freedom related to scalar fields and curvature invariants. The latter are usually recast as generalized {\it geometrical fluids} that have different meanings with respect to the standard matter fluids generally adopted as sources of the field equations. More specifically, in modified gravity the curvature terms are grouped in a tensor $H^{ab}$ and a coupling $g(\Psi^i)$ that can be reorganized in effective Einstein field equations, as corrections to the energy-momentum tensor of matter. The formal validity of such inequalities does not assure some basic requirements such as the attractive nature of gravity, so that the energy conditions have to be considered in a wider sense.Comment: 4 pages. V2: 5 pages; version to appear in Physics Letters B. V3: typo in Eq. (4) correcte

Gravitational induced particle production through a nonminimal curvature-matter coupling

We consider the possibility of a gravitationally induced particle production through the mechanism of a nonminimal curvature-matter coupling. An interesting feature of this gravitational theory is that the divergence of the energy-momentum tensor is nonzero. As a first step in our study we reformulate the model in terms of an equivalent scalar-tensor theory, with two arbitrary potentials. By using the formalism of open thermodynamic systems, we interpret the energy balance equations in this gravitational theory from a thermodynamic point of view, as describing irreversible matter creation processes. The particle number creation rates, the creation pressure, and the entropy production rates are explicitly obtained as functions of the scalar field and its potentials, as well as of the matter Lagrangian. The temperature evolution laws of the newly created particles are also obtained. The cosmological implications of the model are briefly investigated, and it is shown that the late-time cosmic acceleration may be due to particle creation processes. Furthermore, it is also shown that due to the curvature--matter coupling, during the cosmological evolution a large amount of comoving entropy is also produced.Comment: 15 pages; accepted for publication in the European Physical Journal

Cosmological solutions in generalized hybrid metric-Palatini gravity

We construct exact solutions representing a Friedmann-Lema\^itre-Robsertson-Walker (FLRW) universe in a generalized hybrid metric-Palatini theory. By writing the gravitational action in a scalar-tensor representation, the new solutions are obtained by either making an ansatz on the scale factor or on the effective potential. Among other relevant results, we show that it is possible to obtain exponentially expanding solutions for flat universes even when the cosmology is not purely vacuum. We then derive the classes of actions for the original theory which generate these solutions.Comment: 14 pages, 17 figure

An anti-Schwarzshild solution: wormholes and scalar-tensor solutions

We investigate a static solution with an hyperbolic nature, characterised by a pseudo-spherical foliation of space. This space-time metric can be perceived as an anti-Schwarzschild solution, and exhibits repulsive features. It belongs to the class of static vacuum solutions termed "a degenerate static solution of class A". In the present work we review its fundamental features, discuss the existence of generalised wormholes, and derive its extension to scalar-tensor gravity theories in general.Comment: 3 pages, contribution to the proceedings of the Spanish Relativity Meeting-ERE200

Large scale clustering of protein sequences with FORCE -A layout based heuristic for weighted cluster editing

Wittkop T, Baumbach J, Lobo FP, Rahmann S. Large scale clustering of protein sequences with FORCE - a layout based heuristic for weighted cluster editing. BMC Bioinformatics. 2007;8(1): 396.Background: Detecting groups of functionally related proteins from their amino acid sequence alone has been a long-standing challenge in computational genome research. Several clustering approaches, following different strategies, have been published to attack this problem. Today, new sequencing technologies provide huge amounts of sequence data that has to be efficiently clustered with constant or increased accuracy, at increased speed. Results: We advocate that the model of weighted cluster editing, also known as transitive graph projection is well-suited to protein clustering. We present the FORCE heuristic that is based on transitive graph projection and clusters arbitrary sets of objects, given pairwise similarity measures. In particular, we apply FORCE to the problem of protein clustering and show that it outperforms the most popular existing clustering tools ( Spectral clustering, TribeMCL, GeneRAGE, Hierarchical clustering, and Affinity Propagation). Furthermore, we show that FORCE is able to handle huge datasets by calculating clusters for all 192 187 prokaryotic protein sequences ( 66 organisms) obtained from the COG database. Finally, FORCE is integrated into the corynebacterial reference database CoryneRegNet. Conclusion: FORCE is an applicable alternative to existing clustering algorithms. Its theoretical foundation, weighted cluster editing, can outperform other clustering paradigms on protein homology clustering. FORCE is open source and implemented in Java. The software, including the source code, the clustering results for COG and CoryneRegNet, and all evaluation datasets are available at http://gi.cebitec.uni-bielefeld.de/comet/force/