We show that relaxion, that addresses the hierarchy problem, can account for the observed dark matter (DM) relic density. The setup is similar to the case of axion DM models topped with a dynamical misalignment mechanism. After the reheating, when the temperature is well above the electroweak scale, the backreaction potential disappears and the relaxion is displaced from its vacuum. When the "wiggles" reappear the relxion coherently oscillates around its minimum as in the case of vanilla axion DM models. We identify the parameter space such that the relaxion is retrapped leading to the standard cosmology. When the relaxion is lighter than 10 −4 eV, Hubble friction during radiation-domination is sufficiently strong for retrapping, and even minimal models are found to be viable. It also leads to a new constraint on relaxion models, as a sizable region of their parameter space could lead to overabundant relaxion DM. Alternatively, even a larger parameter space exists when additional friction is obtained by particle production from additional coupling to an additional dark photon field. The phenomenology of this class of models is quite unique, as it implies that, on the one hand, we are surrounded by a time-dependent axion-like field, while, on the other hand, its background behaves as a time-dependent oscillating dilaton/scalar field due to the relaxion-Higgs mixing.

The cosmological relaxion can address the hierarchy problem, while its coherent oscillations can constitute dark matter in the present universe. We consider the possibility that the relaxion forms gravitationally bound objects that we denote as relaxion stars. The density of these stars would be higher than that of the local dark matter density, resulting in enhanced signals in table-top detectors, among others. Furthermore, we raise the possibility that these objects may be trapped by an external gravitational potential, such as that of the Earth or the Sun. This leads to formation of relaxion halos of even greater density. We discuss several interesting implications of relaxion halos, as well as detection strategies to probe them. I. INTRODUCTIONResolving the nature of the dark matter (DM) is one of the most fundamental questions in modern physics [1]. Although particle DM at the electroweak scale is a highly motivated solution [2], no discovery of such DM was made to date, either directly [3-5], indirectly [6] or at the LHC [7]. Another intriguing possibility is that of a cold, ultra-light, DM field, coherently oscillating to account for the observed DM density. We consider a class of models where a light scalar particle composes the DM. A well-motivated example is the relaxion, where even a minimal model that addresses the hierarchy problem [8] may lead to the right relic abundance in a manner similar to axion models, however geared with a dynamical misalignment mechanism [9] for relaxion masses roughly above 10 −11 eV. Due to spontaneous CP violation, the relaxion mixes with the Higgs, and, as a result, acquires both pseudoscalar and scalar couplings to the Standard Model (SM) fields [10,11] (this effect could be suppressed in particle-production-based models [12]). The latter distinguishes the relaxion from axion dark matter, which has only pseudoscalar couplings, and where the same property of generation of CP violation was shown to lead to a solution of the strong CP problem [13] as well as potentially generating the cosmological baryon asymmetry [14].A striking consequence of the relaxion-Higgs mixing is that, as the relaxion forms a classical oscillating DM background, all basic constants of nature effectively vary with time since they all depend on the Higgs vacuum expectation value [9]. (For earlier discussion in the context of dilaton DM see [15][16][17].) There are active experimental efforts searching for this form of scalar DM (e.g. [18][19][20][21][22][23][24]). Despite the unprecedented accuracy achieved by the various searches, none of the current experiments reach the sensitivity required to probe physically motivated models. Furthermore, the resulting sensitivity in the region of our main interest, characterised by oscillation frequencies above the Hz level, is weaker than that of the probes related to fifth-force searches and equivalence-principle tests (see e.g. [10, 15-17, 20, 21, 24-27]).In this paper, we demonstrate that if the scalar DM forms a self-gravitating compact object, usually ...

Cosmological relaxation of the electroweak scale is an attractive scenario addressing the gauge hierarchy problem. Its main actor, the relaxion, is a light spin-zero field which dynamically relaxes the Higgs mass with respect to its natural large value. We show that the relaxion is generically stabilized at a special position in the field space, which leads to suppression of its mass and potentially unnatural values for the model's effective low-energy couplings. In particular, we find that the relaxion mixing with the Higgs can be several orders of magnitude above its naive naturalness bound. Low energy observers may thus find the relaxion theory being fine-tuned although the relaxion scenario itself is constructed in a technically natural way. More generally, we identify the lower and upper bounds on the mixing angle. We examine the experimental implications of the above observations at the luminosity and precision frontiers. A particular attention is given to the impressive ability of future nuclear clocks to search for rapidly oscillating scalar ultra-light dark matter, where the future projected sensitivity is presented.

We discuss the sensitivity of the present and near-future axion dark matter experiments to a halo of axions or axion-like particles gravitationally bound to the Earth or the Sun. Such halos, assuming they are formed, can be searched for in a wide variety of experiments even when the axion couplings to matter are small, while satisfying all the present experimental bounds on the local properties of dark matter. The structure and coherence properties of these halos also imply novel signals, which can depend on the latitude or orientation of the detector. We demonstrate this by analyzing the sensitivity of several distinct types of axion dark matter experiments.

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