Past exam of the relativistic Astrophysics and Cosmology course of the University of Cambridge / 2012 / Paper 1 / 2 / b / Solution

Vacuum density is constant for a true cosmological constant. Hence $0.3(1+z{)}^3=0.7$ givesmatter-vacuum density equality is not the same event as the start of accelerating expansion: neglecting radiation, acceleration begins when ${\rho }_m=2{\rho }_{\Lambda }$.