  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)
