  We discuss the quench dynamics near a quantum critical point focusing on the
sine-Gordon model as a primary example. We suggest a unified approach to sudden
and slow quenches, where the tuning parameter $\lambda(t)$ changes in time as
$\lambda(t)\sim \upsilon t^r$, based on the adiabatic expansion of the
excitation probability in powers of $\upsilon$. We show that the universal
scaling of the excitation probability can be understood through the singularity
of the generalized adiabatic susceptibility $\chi_{2r+2}(\lambda)$, which for
sudden quenches ($r=0$) reduces to the fidelity susceptibility. In turn this
class of susceptibilities is expressed through the moments of the connected
correlation function of the quench operator. We analyze the excitations created
after a sudden quench of the cosine potential using a combined approach of
form-factors expansion and conformal perturbation theory for the low-energy and
high-energy sector respectively. We find the general scaling laws for the
probability of exciting the system, the density of excited quasiparticles, the
entropy and the heat generated after the quench. In the two limits where the
sine-Gordon model maps to hard core bosons and free massive fermions we provide
the exact solutions for the quench dynamics and discuss the finite temperature
generalizations.
