  We consider the evolution of a gas of $N$ bosons in the three-dimensional
Gross-Pitaevskii regime (in which particles are initially trapped in a volume
of order one and interact through a repulsive potential with scattering length
of the order $1/N$). We construct a quasi-free approximation of the many-body
dynamics, whose distance to the solution of the Schr\"odinger equation
converges to zero, as $N \to \infty$, in the $L^2 (\mathbb{R}^{3N})$-norm. To
achieve this goal, we let the Bose-Einstein condensate evolve according to a
time-dependent Gross-Pitaevskii equation. After factoring out the microscopic
correlation structure, the evolution of the orthogonal excitations of the
condensate is governed instead by a Bogoliubov dynamics, with a time-dependent
generator quadratic in creation and annihilation operators. As an application,
we show a central limit theorem for fluctuations of bounded observables around
their expectation with respect to the Gross-Pitaevskii dynamics.
