"Galactic Globular Clusters (GCs) are the most populous, old and dense stellar systems in the Galaxy. Their study addresses fundamental astrophysical questions, ranging from the Galaxy formation, to stellar evolution and dynamics. With Cosmic-Lab we intend to use these natural laboratories to perform three original experiments which will have a major impact on several areas of modern Physics and Astrophysics. To this aim we will adopt as test particles three classes of ""exotica"" (namely blue stragglers - BSS, millisecond pulsars -MSPs, and intermediate-mass black holes -IMBHs):Exp 1 - ""Toward the definition of a dynamical clock for stellar systems"". By exploiting our exceptional multi-wavelength database, we propose to use the observed properties of BSS for defining an innovative tool to measure the degree of dynamical evolution of collisional stellar systems.Exp 2 - ""Hunting for the most massive neutron stars (NSs): probing the equation of state of matter at nuclear densities"" - We propose to search for the companion stars to binary MSPs in a selected sample of GCs thus to exploit the unique opportunity offered by these systems to measure the NS masses. This will finally allow us to determine the upper limit to the NS mass and tightly constrain the equation of state of matter at the nuclear equilibrium density.Exp 3 - ""IMBHs: the missing link in the formation of cosmic structures"" - We propose to use a set of non-conventional data-analysis procedures developed by our group in order to unveil IMBHs at the center of GCs. Proving the existence of these objects is crucial for understanding the formation of super-massive BHs, which are observed at the centre of all massive galaxies at any redshift, with a major impact on the comprehension of the formation and evolution of cosmic structures."