Abstract: The non-equilibrium dynamics of an isolated quantum system after a sudden quench to a dynamical critical point is expected to be characterized by scaling and universal exponents due to the absence of time scales. We explore these features for a quench of the parameters of a Hamiltonian with O(N) symmetry, starting from the ground state of the disordered phase. In the limit of large N, the exponents and scaling forms of the relevant two-time correlation functions can be calculated exactly. For generic N, we use a perturbative renormalization-group approach to compute such exponent, to leading order in a dimensional expansion.