Abstract: In this review, we discuss recent developments in both the theory and the experimental searches of magnetic monopoles in past, current and future colliders and in the Cosmos. The theoretical models include, apart from the standard Grand Unified Theories, extensions of the Standard Model that admit magnetic monopole solutions with finite energy and masses that can be as light as a few TeV. Specifically, we discuss, among other scenarios, modified Cho-Maison monopoles and magnetic monopoles in (string-inspired, higher derivative) Born-Infeld extensions of the hypercharge sector of the Standard Model. We also outline the conditions for which effective field theories describing the interaction of monopoles with photons are valid and can be used for result interpretation in monopole production at colliders. The experimental part of the review focuses on, past and present, cosmic and collider searches, including the latest bounds on monopole masses and magnetic charges by the ATLAS and MoEDAL experiments at the LHC, as well as prospects for future searches.

Abstract: We study for the first time the case in which Dark Matter (DM) is made of Feebly Interacting Massive Particles (FIMP) interacting just gravitationally with the standard model particles in an extra-dimensional Randall-Sundrum scenario. We assume that both the dark matter and the standard model are localized in the IR-brane and only interact via gravitational mediators, namely the graviton, the Kaluza-Klein gravitons and the radion. We found that in the early Universe DM could be generated via two main processes: the direct freeze-in and the sequential freeze-in. The regions where the observed DM relic abundance is produced are largely compatible with cosmological and collider bounds.

Abstract: We attempt to clarify several aspects concerning the recently presented four-dimensional Einstein-Gauss-Bonnet gravity. We argue that the limiting procedure outlined in [Phys. Rev. Lett. 124, 081301 (2020)] generally involves ill-defined terms in the four dimensional field equations. Potential ways to circumvent this issue are discussed, alongside remarks regarding specific solutions of the theory. We prove that, although linear perturbations are well behaved around maximally symmetric backgrounds, the equations for second-order perturbations are ill-defined even around a Minkowskian background. Additionally, we perform a detailed analysis of the spherically symmetric solutions and find that the central curvature singularity can be reached within a finite proper time.

Abstract: Scalar hair of black holes in theories with a shift symmetry are constrained by the no-hair theorem of Hui and Nicolis, assuming spherical symmetry, time-independence of the scalar field and asymptotic flatness. The most studied counterexample is a linear coupling of the scalar with the Gauss-Bonnet invariant. However, in this case the norm of the shift-symmetry current J(2) diverges at the horizon casting doubts on whether the solution is physically sound. We show that this is not an issue since J(2) is not a scalar quantity, since J(mu) is not a diffinvariant current in the presence of Gauss-Bonnet. The same theory can be written in Horndeski form with a non-analytic function G(5)similar to log X . In this case the shift-symmetry current is diff-invariant, but contains powers of X in the denominator, so that its divergence at the horizon is again immaterial. We confirm that other hairy solutions in the presence of non-analytic Horndeski functions are pathological, featuring divergences of physical quantities as soon as one departs from time-independence and spherical symmetry. We generalise the no-hair theorem to Beyond Horndeski and DHOST theories, showing that the coupling with Gauss-Bonnet is necessary to have hair.

Abstract: Dark photon dark matter will resonantly convert into visible photons when the dark photon mass is equal to the plasma frequency of the ambient medium. In cosmological contexts, this transition leads to an extremely efficient, albeit short-lived, heating of the surrounding gas. Existing work in this field has been predominantly focused on understanding the implications of these resonant transitions in the limit that the plasma frequency of the Universe can be treated as being perfectly homogeneous, i.e. neglecting inhomogeneities in the electron number density. In this work we focus on the implications of heating from dark photon dark matter in the presence of inhomogeneous structure (which is particularly relevant for dark photons with masses in the range 10(-15) eV less than or similar to m(A ') less than or similar to 10(-12) eV), emphasizing both the importance of inhomogeneous energy injection, as well as the sensitivity of cosmological observations to the inhomogeneities themselves. More specifically, we derive modified constraints on dark photon dark matter from the Ly-alpha forest, and show that the presence of inhomogeneities allows one to extend constraints to masses outside of the range that would be obtainable in the homogeneous limit, while only slightly relaxing their strength. We then project sensitivity for near-future cosmological surveys that are hoping to measure the 21cm transition in neutral hydrogen prior to reionization, and demonstrate that these experiments will be extremely useful in improving sensitivity to masses near similar to 10(-14) eV, potentially by several orders of magnitude. Finally, we discuss implications for reionization, early star formation, and late-time y-type spectral distortions, and show that probes which are inherently sensitive to the inhomogeneous state of the Universe could resolve signatures unique to the light dark photon dark matter scenario, and thus offer a fantastic potential for a positive detection.