  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 a ground state in the disordered phase. In the limit of infinite
$N$, the exponents and scaling forms of the relevant two-time correlation
functions can be calculated exactly. Our analytical predictions are confirmed
by the numerical solution of the corresponding equations. Moreover, we find
that the same scaling functions, yet with different exponents, also describe
the coarsening dynamics for quenches below the dynamical critical point.
