  We study the evolution of the cosmic-mass-density contrast beyond the
Robertson-Walker geometry including the small contribution of acceleration. We
derive a second-order evolution equation for the density contrast within the
spherical model for CDM collisionless fluid including the cosmological
constant, the expansion and the non-vanishing vector of acceleration. While the
mass-density is not seriously affected by acceleration, the mass-density
contrast changes its shape at smaller redshifts even for a small amount of the
acceleration parameter. This could help to resolve current controversial
results in cosmology from measurements of WMAP, gravitational lensing, XMM
X-ray cluster or type Ia supernovae data, etc.
