We present a novel theory of gravity by considering an extension of symmetric teleparallel gravity. This is done by introducing, in the framework of the metric-affine formalism, a new class of theories where the nonmetricity $Q$ is nonminimally coupled to the matter Lagrangian. More specifically, we consider a Lagrangian of the form $L\sim f_1(Q)+f_2(Q)L_M$, where $f_1$ and $f_2$ are generic functions of $Q$, and $L_M$ is the matter Lagrangian. This nonminimal coupling entails the nonconservation of the energy-momentum tensor, and consequently the appearance of an extra force. The formulation of the gravity sector in terms of the $Q$ instead of the curvature may result in subtle improvements of the theory. In the context of nonminimal matter couplings, we are therefore motivated to explore whether the new geometrical formulation in terms of the $Q$, when implemented also in the matter sector, would allow more universally consistent and viable realizations of the nonminimal coupling. Furthermore, we consider several cosmological applications by presenting the evolution equations and imposing specific functional forms of the functions $f_1(Q)$ and $f_2(Q)$, such as power-law and exponential dependencies of the nonminimal couplings. Cosmological solutions are considered in two general classes of models, and found to feature accelerating expansion at late times.

Einstein Telescope (ET) is the European project for a gravitational-wave (GW) observatory of third-generation. In this paper we present a comprehensive discussion of its science objectives, providing state-of-the-art predictions for the capabilities of ET in both geometries currently under consideration, a single-site triangular configuration or two L-shaped detectors. We discuss the impact that ET will have on domains as broad and diverse as fundamental physics, cosmology, early Universe, astrophysics of compact objects, physics of matter in extreme conditions, and dynamics of stellar collapse. We discuss how the study of extreme astrophysical events will be enhanced by multi-messenger observations. We highlight the ET synergies with ground-based and space-borne GW observatories, including multi-band investigations of the same sources, improved parameter estimation, and complementary information on astrophysical or cosmological mechanisms obtained combining observations from different frequency bands. We present advancements in waveform modeling dedicated to third-generation observatories, along with open tools developed within the ET Collaboration for assessing the scientific potentials of different detector configurations. We finally discuss the data analysis challenges posed by third-generation observatories, which will enable access to large populations of sources and provide unprecedented precision.

In this work, we obtain the shadow images of spherically symmetric scalar boson and Proca stars using analytical fittings of numerical solutions, when illuminated by a geometrically thin accretion disk. We chose a sample of four boson and four Proca stars with radii ranging from more compact configurations with $R\sim 9M$ to more dilute configurations with $R\sim 20M$, where $M$ is the total mass of the bosonic star. In these configurations, the absence of the light sphere (the locus of unstable bound geodesics) makes the optical appearance of these stars to be dominated by a single luminous ring enclosing a central brightness depression, and no further photon rings are available. We show that if one considers face-on observations and a disk model whose emission is truncated at some finite radius at which the luminosity attains its maximum value, both the size of the shadow, as well as the luminosity and depth of the bright region, are heavily influenced by the emission profile, with the choice of the type and parameters of the bosonic stars in our samples having a sub-dominant influence. These differences are nonetheless significantly magnified when one allows the accretion disk to extend close enough to the center of the star. Our results point out that even though bosonic stars are horizonless and do not have a photon sphere, some of them may be able to produce conventional black hole shadowlike images provided that their compactness is large enough, thus being potentially consistent with current and future observations.