The existence of the dark matter and perhaps even dark energy
The need to understand the evolution of perturbations around the zero order, smooth universe
inflation, the generator of these perturbations
When the universe was much hotter and denser, when the temperature of order an MeV/kB, there were no neutral atoms or even bound nuclei. The vast amounts of radation in such a hot environment ensured that any atom or nucleus produced would be immediately destroyed by a high energy photon. As the universe cooled well below the blinding energies of typical nuclei, light elements began to form.
The very early universe was hot and dense. As a result, interactions among particles occurred much more frequently than they do today. As an example, a photon today can travel across the observable universe without deflection or capture, so it has a mean free path greater than 10^28 cm. When the age of the universe was equal to 1 sec, though, the mean free path of a photon was about the size of an atom. Thus in the time it took the universe to expand by a factor of 2, a given photon interacted many, many times. These multiple interactions kept the constituents in the universe in equilibrium in most cases. Nonetheless, there were times when reactions could not proceed rapidly enough to maintain equilibrium conditions. These times are perhaps not coincidentally of the utmost interest to cosmologists today.