 Patients with Common variable immunodeficiency CVID have various forms of autoimmune and auto inflammatory disorders. The study will investigate if intervention with Rifaximin modifies the gut microbiota with a subsequent alteration in markers of systemic immune activation and inflammation in patients with CVID. The investigators hypothesize that the gut microbiota of CVID patients, at least partly through interaction with the innate immune system within the intestine, contribute to a low-grade systemic inflammation in these patients, and that an intervention with the non-absorbable antibiotic Rifaximin attenuates systemic inflammation through modulation of the gut microbiota. The study may lead to increased understanding of the interaction between microbiota and the immune system. The study could give new insight into important disease processes in relation to the interaction between the microbiota, the intestine and the systemic compartment, and potentially be the basis of new therapeutic strategies in these patients to prevent and down-regulate the auto-inflammatory and autoimmune complications seen in CVID. The findings could also be of relevance for other disorders where the interaction between microbiota and intestinal and systemic inflammation is involved such as various cardiovascular and metabolic disorders. 