Some indications for tension have long been identified between cosmological constraints obtained from galaxy clusters and primary CMB measurements. Typically, assuming the matter density and fluctuations, as parameterized with Omega_m and sigma_8, estimated from CMB measurements, many more clusters are expected than those actually observed. One possible explanation could be that certain types of galaxy groups or clusters were missed in samples constructed in previous surveys, resulting in a higher incompleteness than estimated. We aim to determine if a hypothetical class of very extended, low surface brightness, galaxy groups or clusters have been missed in previous X-ray cluster surveys based on the ROSAT All-Sky Survey (RASS). We applied a dedicated source detection algorithm sensitive also to more unusual group or cluster surface brightness distributions. We found many known but also a number of new group candidates, which are not included in any previous X-ray / SZ cluster catalogs. In this paper, we present a pilot sample of 13 very extended groups discovered in the RASS at positions where no X-ray source has been detected previously and with clear optical counterparts. The X-ray fluxes of at least 5 of these are above the nominal flux-limits of previous RASS cluster catalogs. They have low mass ($10^{13} - 10^{14} M_{odot}$; i.e., galaxy groups), are at low redshift (z<0.08), and exhibit flatter surface brightness distributions than usual. We demonstrate that galaxy groups were missed in previous RASS surveys, possibly due to the flat surface brightness distributions of this potential new population. Analysis of the full sample will show if this might have a significant effect on previous cosmological parameter constraints based on RASS cluster surveys. (This is a shortened version of the abstract - full text in the article)
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