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This Symposium is devoted to the Memory of Lev Kofman,June-17-1957-November-12-2009.  The accelerated expansion of the Universe, which is today observed, showsthat cosmological dynamics is dominated by the so-called Dark Energy fieldwhich provides a large negative pressure. This is the standard picture, inwhich such new ingredient is considered as a source of the right hand side ofthe field equations. It should be some form of non-clustered non-zero vacuumenergy which, together with the clustered Dark Matter, drives the globaldynamics. This is the so-called "concordance model" (ACDM) which gives, inagreement with the Cosmic Microwave Background Radiation (CMBR), dim LymanLimit Systems (LLS) and type la supernovae (SNeIa) data, a good framework tounderstand the today observed Universe. However, it presents severalshortcomings as the well known "coincidence" and "cosmological constant"problems . An alternative approach is to have a better understanding of theenergy concept in General Relativity and also to change the left hand side ofthe field equations, and check if observed cosmic dynamics can be achieved byextending general relativity. In this different context, it is not required tosearch candidates for Dark Energy and Dark Matter, which till now have not beenfound. Rather, one can only stand on the "observed" ingredients: curvature andbaryon matter, to account for the observations. Considering this point of view,one can think of that gravity is not scale-invariant. The goal of thisSymposium is to obtain a tapestry of the present status of theory andobservations concerning Gravitation and Dark Universe.

aip conference proceedings

Presentation of the Second Big Challenge Symposium - The Big Challenge  of Cosmological Understanding: Gravitation, Dark Matter and Dark Energy.  Towards New Scenarios