Spin connection formulations of real Lorentzian General Relativity

We derive the pure spin connection and constraint-free BF formulations of real four-dimensional Lorentzian vacuum General Relativity. In contrast to the existing complex formulations, an important advantage is that they do not require the reality constraints that complicate quantization. We also consider the corresponding modified gravity theories and point out that, contrary to their self-dual analogues, they are not viable because they necessarily contain ghosts. In particular, this constrains the set of potentially viable unified theories one can build by extending the gauge group to the ones with the action structure of General Relativity. We find, however, that the resulting theories do not admit classical solutions. This issue can be solved by introducing extra dynamical fields which, incidentally, could also provide a way to include a matter sector.Comment: 20 page

Distributed Detection in Sensor Networks with Limited Range Sensors

We consider a multi-object detection problem over a sensor network (SNET) with limited range sensors. This problem complements the widely considered decentralized detection problem where all sensors observe the same object. While the necessity for global collaboration is clear in the decentralized detection problem, the benefits of collaboration with limited range sensors is unclear and has not been widely explored. In this paper we develop a distributed detection approach based on recent development of the false discovery rate (FDR). We first extend the FDR procedure and develop a transformation that exploits complete or partial knowledge of either the observed distributions at each sensor or the ensemble (mixture) distribution across all sensors. We then show that this transformation applies to multi-dimensional observations, thus extending FDR to multi-dimensional settings. We also extend FDR theory to cases where distributions under both null and positive hypotheses are uncertain. We then propose a robust distributed algorithm to perform detection. We further demonstrate scalability to large SNETs by showing that the upper bound on the communication complexity scales linearly with the number of sensors that are in the vicinity of objects and is independent of the total number of sensors. Finally, we deal with situations where the sensing model may be uncertain and establish robustness of our techniques to such uncertainties.Comment: Submitted to IEEE Transactions on Signal Processin

Observed Angles and Geodesic Light-Cone Coordinates

We discuss the interpretation of the angles in the Geodesic Light-Cone (GLC) coordinates. In particular, we clarify the way in which these angles can be identified with the observed ones. We show that, although this identification is always possible in principle, one cannot implement it in the usual gauge-fixing way, i.e. through a set of conditions on the GLC metric. Rather, one needs to invoke a tetrad at the observer and a Cartesian-like coordinate system in order to obtain the desired map globally on the observed sky.Comment: 6 pages, final version accepted for publication in Classical and Quantum Gravit

Cosmological dynamics and dark energy from non-local infrared modifications of gravity

We perform a detailed study of the cosmological dynamics of a recently proposed infrared modification of the Einstein equations, based on the introduction of a non-local term constructed with $m^2g_{\mu\nu}\Box^{-1} R$, where $m$ is a mass parameter. The theory generates automatically a dynamical dark energy component, that can reproduce the observed value of the dark energy density without introducing a cosmological constant. Fixing $m$ so to reproduce the observed value $\Omega_{\rm DE}\simeq 0.68$, and writing $w(a)=w_0+(1-a) w_a$, the model provides a neat prediction for the equation of state parameters of dark energy, $w_0\simeq -1.042$ and $w_a\simeq -0.020$. We show that, because of some freedom in the definition of $\Box^{-1}$, one can extend the construction so to define a more general family of non-local models. However, in a first approximation this turns out to be equivalent to adding an explicit cosmological constant term on top of the dynamical dark energy component. This leads to an extended model with two parameters, $\Omega_{\Lambda}$ and $m$. Even in this extension the EOS parameter $w_0$ is always on the phantom side, in the range $-1.33 < w_0\leq -1$, and there is a prediction for the relation between $w_0$ and $w_a$.Comment: 30 pages, 15 figures; v2: cross-reference to 1311.3421 adde