We present a detailed study of the methodology for correlating 'dark sirens' (compact binaries coalescences without electromagnetic counterpart) with galaxy catalogs. We propose several improvements on the current state of the art, and we apply them to the GWTC-2 catalog of LIGO/Virgo gravitational wave (GW) detections, and the GLADE galaxy catalog, performing a detailed study of several sources of systematic errors that, with the expected increase in statistics, will eventually become the dominant limitation. We provide a measurement of H 0 from dark sirens alone, finding as the best result H 0 = 67.3 +27.6 −17.9 km s −1 Mpc −1 (68% c.l.) which is, currently, the most stringent constraint obtained using only dark sirens. Combining dark sirens with the counterpart for GW170817 we find H 0 = 72.2 +13.9 −7.5 km s −1 Mpc −1 . We also study modified GW propagation, which is a smoking gun of dark energy and modifications of gravity at cosmological scales, and we show that current observations of dark sirens already start to provide interesting limits. From dark sirens alone, our best result for the parameter Ξ 0 that measures deviations from GR (with−1.2 . We finally discuss limits on modified GW propagation under the tentative identification of the flare ZTF19abanrhr as the electromagnetic counterpart of the binary black hole coalescence GW190521, in which case our most stringent result is Ξ 0 = 1.8 +0.9 −0.6 . We release the publicly available code DarkSirensStat, which is available under open source license at https://github.com/CosmoStatGW/DarkSirensStat.

We study the impact of the limit on |Ġ|/G from Lunar Laser Ranging on "nonlocal gravity", i.e. on models of the quantum effective action of gravity that include nonlocal terms relevant in the infrared, such as the "RR" and "RT" models proposed by our group, and the Deser-Woodard (DW) model. We elaborate on the analysis of Barreira et al.[1] and we confirm their findings that (under plausible assumptions such as the absence of strong backreaction from non-linear structures), the RR model is ruled out. We also show that the mechanism of "perfect screening for free" suggested for the DW model actually does not work and the DW model is also ruled out. In contrast, the RT model passes all phenomenological consistency tests and is still a viable candidate.

We provide a systematic and updated discussion of a research line carried out by our group over the last few years, in which gravity is modified at cosmological distances by the introduction of nonlocal terms, assumed to emerge at an effective level from the infrared behavior of the quantum theory. The requirement of producing a viable cosmology turns out to be very stringent and basically selects a unique model, in which the nonlocal term describes an effective mass for the conformal mode. We discuss how such a specific structure could emerge from a fundamental local theory of gravity, and we perform a detailed comparison of this model with the most recent cosmological datasets, confirming that it fits current data at the same level as ΛCDM.Most notably, the model has striking predictions in the sector of tensor perturbations, leading to a very large effect in the propagation of gravitational wave (GWs) over cosmological distances. At the redshifts relevant for the next generation of GW detectors such as Einstein Telescope, Cosmic Explorer and LISA, this leads to deviations from GR that could be as large as 80%, and could be verified with the detection of just a single coalescing binary with electromagnetic counterpart. This would also have potentially important consequences for the search of the counterpart since, for a given luminosity distance to the source, as inferred through the GW signal, the actual source redshift could be significantly different from that predicted by ΛCDM. At the redshifts relevant for advanced LIGO/Virgo/Kagra the effect is smaller, but still potentially observable over a few years of runs at target sensitivity. arXiv:2001.07619v1 [astro-ph.CO] 21 Jan 2020 4 Conclusions 66 A Difficulties of alternative nonlocal models 68 -1 -2 The Lichnerowicz operator is defined by E µν,ρσ ≡ 1 2, where 2 = η µν ∂µ∂ν is the flat-space d'Alembertian. We use the signature ηµν = (−, +, +, +) and MTW [14] sign conventions. 3 We assume here 3 + 1 spacetime dimensions. See [13] for the corresponding equations in d + 1 spacetime dimensions, with d generic.

We discuss a modified gravity model which fits cosmological observations at a level statistically indistinguishable from ΛCDM and at the same time predicts very large deviations from General Relativity (GR) in the propagation of gravitational waves (GWs) across cosmological distances. The model is a variant of the RT nonlocal model proposed and developed by our group, with initial conditions set during inflation, and predicts a GW luminosity distance that, at the redshifts accessible to LISA or to a third-generation GW detector such as the Einstein Telescope (ET), can differ from that in GR by as much as 60%. An effect of this size could be detected with just a single standard siren with counterpart by LISA or ET. At the redshifts accessible to a LIGO/Virgo/Kagra network at target sensitivity the effect is smaller but still potentially detectable. Indeed, for the recently announced LIGO/Virgo NS-BH candidate S190814bv, the RT model predicts that, given the measured GW luminosity distance, the actual luminosity distance, and the redshift of an electromagnetic counterpart, would be smaller by as much as 7% with respect to the value inferred from ΛCDM.

In the recent experimental and theoretical literature well-established nonclassicality criteria from the field of quantum optics have been directly applied to the case of excitations in matter-waves. Among these are violations of Cauchy-Schwarz inequalities, Glauber-Sudarshan P-nonclassicality, sub-Poissonian number-difference squeezing (also known as the two-mode variance) and the criterion of nonseparability. We review the strong connection of these criteria and their meaning in quantum optics, and point out differences in the interpretation between light and matter waves. We then calculate observables for a homogeneous Bose-Einstein condensate undergoing an arbitrary modulation in the interaction parameter at finite initial temperature, within both the quantum theory as well as a classical reference. We conclude that to date in experiments relevant for this scenario nonclassical effects have not conclusively been observed and conjecture that additional, noncommuting, observables have to be measured to this end. Moreover this has important implications for proposed analog gravity models where the observation of nonclassical effects is a major goal.Bose-Einstein condensation (BEC) is a macroscopic quantum phenomenon where a large fraction of the bosons occupy the same lowest energy quantum state, and thus form a coherent matter wave. Many properties of the condensate can be captured by a Schrödinger-type equation for a complex field with a nonlinear potential referred to as the Gross-Pitaevskii equation (GPE) [1-3]. To cite one example, the GPE correctly predicts discrete values for the circulation of the velocity field in a BEC [4]. Nevertheless, within this description the evolution of the condensate can be considered a classical process [5]. On the other hand it is possible to excite small fluctuations of the condensate, for example by means of rapid changes in the condensate parameters [6][7][8][9][10][11], which may activate their nonclassical behavior. An ongoing line of research is to investigate experimentally the manipulation and detection of fluctuations in BECs, e.g. exploring their quantum nature [12][13][14] and correlations [11,15]. This is partially motivated by various analogue gravity studies [16][17][18][19], where BECs are utilized as quantum simulators [5] of quantum field theories in curved spacetime (QFTCS). In QFTCS one is interested in how quantum fields propagate on a classical curved spacetime geometry acting as a non-trivial background configuration. Within analogue gravity studies the ultimate goal is to mimic and capture genuine quantum effects predicted from QFTCS. The field of experimental analogue gravity in BECs started only a few years ago, and with recent advances, e.g.mimicking black hole evaporation [9,10,[20][21][22] and cosmological particle production in our Universe [13,[23][24][25][26], and the debate on the nonclassicality of the observed effects is as timely as ever. Hence, it is essential to find suitable observables that can distinguish between classical and nonclas...