On the evolution of the cosmic-mass-density contrast and the cosmological constant

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.