  The cosmological evolution can be described in terms of directly measurable
cosmological scalar parameters (deceleration $q$, jerk $j$, snap $s$, etc...)
constructed out of high order derivatives of the scale factor. Their behavior
at the critical temperature of the Quantum Chromodynamics (QCD) phase
transition in early universe could be a specific tool to study the transition,
analogously to the fluctuations of conserved charges in QCD. We analyze the
effect of the crossover transition from quarks and gluons to hadrons in early
universe on the cosmological scalars and on the gravitational wave spectrum, by
using the recent lattice QCD equation of state and including the electroweak
degrees of freedom and different models of dark matter. Near the transition the
cosmological parameters follow the behavior of QCD trace anomaly and of the
speed of sound of the entire system. The effects of deconfinement turn out to
be more relevant for the modification of the primordial spectrum of
gravitational waves and our complete analysis, based on lattice QCD simulations
and on the hadron resonance gas below the critical temperature, refines
previous results.
