  The role of slow out of equilibrium modes (OEM), introduced to extend the
validity of hydrodynamics near the QCD critical point on the power spectrum of
dynamical density fluctuations has been studied. We have used the equation of
motion of slow modes for the situation when the extensive nature of
thermodynamics is not altered due to the introduction of OEM. We find that the
extensivity condition puts an extra constraint on the coupling of OEM with the
four divergence of velocity. The dynamic structure factor (Snn) in presence of
the OEM shows four Lorentzian peaks asymmetrically positioned about $\omega
(\text{frequency})=0$, whereas the dynamic structure factor without the
presence of any OEM shows three well-known Lorentzian peaks. The width of the
peaks are reduced in presence of OEM. We find that the asymmetric peaks
originate due to the coupling of the out-of-equilibrium modes with the
hydrodynamic modes. It is also shown that the OEM has negligible effects on Snn
if first order hydrodynamics (relativistic Navier-Stokes) is used. The
introduction of OEM reduces the width of the Rayleigh peak indicating the
reduction in the decay rate of the fluctuation which leads to slowing down, a
well-known characteristics of the critical end point (CEP).
