Restoring General Relativity in massive bi-gravity theory

We study static spherically symmetric solutions of massive bi-gravity theory, free from the Boulware-Deser ghost. We show the recovery of General Relativity via the Vainshtein mechanism, in the weak limit of the physical metric. We find a single polynomial equation determining the behavior of the solution for distances smaller than the inverse graviton mass. This equation is generically of the seventh order, while for a specific choice of the parameters of the theory it can be reduced to lower orders. The solution is analytic in different regimes: for distances below the Vainshtein radius (where General Relativity is recovered), and in the opposite regime, beyond the Vainshtein radius, where the solution approaches the flat metric.Comment: 18 pages, 10 figures, typos corrected, version published in PR

Higher Derivative Field Theories: Degeneracy Conditions and Classes

We provide a full analysis of ghost free higher derivative field theories with coupled degrees of freedom. Assuming the absence of gauge symmetries, we derive the degeneracy conditions in order to evade the Ostrogradsky ghosts, and analyze which (non)trivial classes of solutions this allows for. It is shown explicitly how Lorentz invariance avoids the propagation of "half" degrees of freedom. Moreover, for a large class of theories, we construct the field redefinitions and/or (extended) contact transformations that put the theory in a manifestly first order form. Finally, we identify which class of theories cannot be brought to first order form by such transformations.Comment: 26 pages, 1 figure. v2: minor changes, references added, matches version published in JHE

Finite Energy of Black Holes in Massive Gravity

In GR the static gravitational potential of a self-gravitating body goes as 1/r at large distances and any slower decrease leads to infinity energy. We show that in a class of four-dimensional massive gravity theories there exists spherically symmetric solutions with finite total energy, featuring an asymptotic behavior slower than 1/r and generically of the form $r^\gamma$. This suggests that configurations with nonstandard asymptotics may well turn out to be physical. The effect is due to an extra field coupled only gravitationally, which allows for modifications of the static potential generated by matter, while counterbalancing the apparently infinite energy budget.Comment: 4 page

Extended scalar-tensor theories of gravity

We study new consistent scalar-tensor theories of gravity recently introduced by Langlois and Noui with potentially interesting cosmological applications. We derive the conditions for the existence of a primary constraint that prevents the propagation of an additional dangerous mode associated with higher order equations of motion. We then classify the most general, consistent scalar-tensor theories that are at most quadratic in the second derivatives of the scalar field. In addition, we investigate the possible connection between these theories and (beyond) Horndeski through conformal and disformal transformations. Finally, we point out that these theories can be associated with new operators in the effective field theory of dark energy, which might open up new possibilities to test dark energy models in future surveys

Vainshtein mechanism after GW170817

The almost simultaneous detection of gravitational waves and a short gamma-ray burst from a neutron star merger has put a tight constraint on the difference between the speed of gravity and light. In the four-dimensional scalar-tensor theory with second order equations of motion, the Horndeski theory, this translates into a significant reduction of the viable parameter space of the theory. Recently, extensions of Horndeski theory, which are free from Ostrogradsky ghosts despite the presence of higher order derivatives in the equations of motion, have been identified and classified exploiting the degeneracy criterium. In these new theories, the fifth force mediated by the scalar field must be suppressed in order to evade the stringent Solar System constraints. We study the Vainshtein mechanism in the most general degenerate higher order scalar-tensor theory in which light and gravity propagate at the same speed. We find that the Vainshtein mechanism generally works outside a matter source but it is broken inside matter, similarly to beyond Horndeski theories. This leaves interesting possibilities to test these theories that are compatible with gravitational wave observations using astrophysical objects.Comment: 5 pages, no figure, added references, corrected typos, accepted for publication in Physical Review

A Multi-Objective Method for Short-Term Load Forecasting in European Countries

In this paper we present a novel method for daily short-term load forecasting, belonging to the class of “similar shape” algorithms. In the proposed method, a number of parameters are optimally tuned via a multi-objective strategy that minimizes the error and the variance of the error, with the objective of providing a final forecast that is at the same time accurate and reliable. We extensively compare our algorithm with other state-of-the-art methods. In particular, we apply our approach upon publicly available data and show that the same algorithm accurately forecasts the load of countries characterized by different size, different weather conditions, and generally different electrical load profiles, in an unsupervised manner

Comparison and clustering analysis of the daily electrical load in eight European countries

This paper illustrates and compares the ability of several clustering algorithms to correctly associate a given aggregate daily electrical load curve with its corresponding day of the week. In particular, popular clustering algorithms like the Fuzzy c-Means, Spectral Clustering and Expectation Maximization are compared, and it is shown that the best results are obtained if the daily data are compressed with respect to a single feature, namely the so-called “Morning Slope”. Such a feature-based clustering appears to outperform the clustering results obtained upon using other classic features, and also with respect to using other conventional compression methods, such as the Principal Component Analysis, in all the examined European countries. This result is particularly interesting, as this feature provides a direct physical interpretation that can be used to obtain insights on the structure of the daily load profiles

Neural Posterior Estimation with guaranteed exact coverage: the ringdown of GW150914

We analyze the ringdown phase of the first detected black-hole merger, GW150914, using a simulation-based inference pipeline based on masked autoregressive flows. We obtain approximate marginal posterior distributions for the ringdown parameters, namely the mass, spin, and the amplitude and phases of the dominant mode and its first overtone. Thanks to the locally amortized nature of our method, we are able to calibrate our posteriors with injected simulations, producing posterior regions with guaranteed (i.e. exact) frequentist coverage of the true values. For GW150914, our calibrated posteriors provide only mild evidence (~ 2 sigma) for the presence of an overtone, even if the ringdown is assumed to start at the peak of the amplitude.Comment: 8 pages, 2 figure

Rotating black holes in higher order gravity

We develop a new technique for finding black hole solutions in modified gravity that have “stealth” hair, i.e., hair of which the only gravitational effect is to tune the cosmological constant. We consider scalar-tensor theories in which gravitational waves propagate at the speed of light and show that, subject to a parametric constraint we specify, Einstein metrics can be painted with stealth hair, provided there exists a family of geodesics always normal to spacelike surfaces. We also present a novel scalar-dressed rotating black hole that has finite scalar field at both the black hole and cosmological event horizons