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 ...