Recent progress on inflation and dark energy from string theory

We review recent progress in string model building in both early and late time cosmology. We describe the main theoretical and phenomenological features of an entire class of inflationary models where inflation is driven by a type IIB Kähler modulus which enjoys an effective and approximate shift symmetry. We illustrate how reheating can occur via the perturbative decay of the modulus into visible and hidden sector degrees of freedom, paying particular attention to the associated production of axionic dark radiation. We quickly discuss the status of de Sitter vacua versus quintessence model building in string theory, analysing the level of control of these constructions and the main challenges faced by models of dynamical dark energy. We finally present a working model of axion hilltop quintessence in string theory, stressing the importance of initial conditions.