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A<sc>bstract</sc> It is difficult to construct a post-inflation QCD axion model that solves the axion quality problem (and hence the Strong CP problem) without introducing a cosmological disaster. In a post-inflation axion model, the axion field value is randomized during the Peccei-Quinn phase transition, and axion domain walls form at the QCD phase transition. We emphasize that the gauge equivalence of all minima of the axion potential (i.e., domain wall number equals one) is insufficient to solve the cosmological domain wall problem. The axion string on which a domain wall ends must exist as an individual object (as opposed to a multi-string state), and it must be produced in the early universe. These conditions are often not satisfied in concrete models. Post-inflation axion models also face a potential problem from fractionally charged relics; solving this problem often leads to low-energy Landau poles for Standard Model gauge couplings, reintroducing the quality problem. We study several examples, finding that models that solve the quality problem face cosmological problems, and vice versa. This is not a no-go theorem; nonetheless, we argue that it is much more difficult than generally appreciated to find a viable post-inflation QCD axion model. Successful examples may have a nonstandard cosmological history (e.g., multiple types of cosmic axion strings of different tensions), undermining the widespread expectation that the post-inflation QCD axion scenario predicts a unique mass for axion dark matter. 

A<sc>bstract</sc> Curvatons are light (compared to the Hubble scale during inflation) spectator fields during inflation that potentially contribute to adiabatic curvature perturbations post-inflation. They can alter CMB observables such as the spectral indexn_s, the tensor-to-scalar ratior, and the local non-Gaussianity$$ {f}_{\textrm{NL}}^{\left(\textrm{loc}\right)} $$ $f_{\mathrm{NL}}^{\left(\mathrm{loc}\right)}$. We systematically explore the observable space of a curvaton with a quadratic potential. We find that when the underlying inflation model does not satisfy then_sandrobservational constraints but can be made viable with a significant contribution from what we call a savior curvaton, a large$$ \left|{f}_{\textrm{NL}}^{\left(\textrm{loc}\right)}\right| $$ $\left(f_{\mathrm{NL}}^{\left(\mathrm{loc}\right)}\right)$>0.05, such that the model is distinguishable from single-field inflation, is inevitable. On the other hand, when the underlying inflation model already satisfies then_sandrobservational constraints, so significant curvaton contribution is forbidden, a large$$ \left|{f}_{\textrm{NL}}^{\left(\textrm{loc}\right)}\right| $$ $\left(f_{\mathrm{NL}}^{\left(\mathrm{loc}\right)}\right)$>0.05 is possible in the exceptional case when the isocurvature fluctuation in the curvaton fluid is much greater than the global curvature fluctuation. 

Abstract We lay out a comprehensive physics case for a future high-energy muon collider, exploring a range of collision energies (from 1 to 100 TeV) and luminosities. We highlight the advantages of such a collider over proposed alternatives. We show how one can leverage both the point-like nature of the muons themselves as well as the cloud of electroweak radiation that surrounds the beam to blur the dichotomy between energy and precision in the search for new physics. The physics case is buttressed by a range of studies with applications to electroweak symmetry breaking, dark matter, and the naturalness of the weak scale. Furthermore, we make sharp connections with complementary experiments that are probing new physics effects using electric dipole moments, flavor violation, and gravitational waves. An extensive appendix provides cross section predictions as a function of the center-of-mass energy for many canonical simplified models. 

Abstract A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.