Cosmology: Searching for Deviations from the Standard Cosmological Model

Cosmology is experiencing an exciting phase, characterized by the enor- mous amount of data which are already available or will soon become available. This epoch, which has been dubbed the era of precision cosmology, clearly requires an adequate theoretical effort to provide predictions at high level of accuracy. At the same time, the quality of the data available allows one to face with totally new and challenging questions. In this chapter we will focus on three complementary issues: (i) observable predictions of inflation in the early universe; (ii) a short overview of some cosmological effects of modified gravity scenarios; (iii) neutrinos in cosmology and large-scale structures.