We have been living in a phase of expansion, individuation of ways, specialization, differentiation
Will the universe continue forever to expand, or will it contract?
If there is a contraction perhaps we will come closer and closer: civilizations will get in touch, many different pasts and ways of seeing the world will become closer and closer, interacting, fusing, meshing together into evermore complex, far-reaching and explicit mirrors of Existence.
Even if this is true many billions of years will be necessary to reach that stage. Right now we are expanding into diversity.
Other hypothesis: infinite expansion (with or without cooling), equilibrium... (others?)