ABSTRACT
This chapter uses the dynamical equations derived within the Friedmann-lemaitre-Robertson-Walker (FLRW) framework to explore the range of expansion scenarios permitted by several historically important equations-of-state. In deriving Equation, it places no constraint on the lapse function in connection with our choice of stress-energy tensor. Two of the solutions we have examined here—the Milne universe and de Sitter space—also happen to be members of a very special category of FLRW cosmologies. These are models with a constant spacetime curvature, sometimes also referred to as the ‘static’ solutions since their metric coefficients are independent of time. Gravitational effects are present even when the FLRW metric is time-independent, as is well known from the analogous Schwarzschild and Kerr spacetimes. The sixth, and final, FLRW metric with constant spacetime curvature is known as anti-de Sitter space—a universe with negative mass density and spatial curvature constant.
