First Friedmann Equation. The first friedmann equation as conventionally written today in modern notation where the left side details the hubble expansion rate and the evolution of spacetime and the right side includes. C is the critical density for which the geometry is flat.
The first friedmann equation is often seen in terms of the present values of the density parameters that is here is the radiation density today i e. When is the matter dark plus baryonic density today is the spatial curvature density today and is the cosmological constant or vacuum density today. This term originally was used as a means to determine the geometry of the field where.
Show that the first friedman equation can be presented in the form sum limits i omega i 1 where omega i are relative densities of the components omega i equiv frac rho i rho cr quad rho cr frac 3h 2 8 pi g quad rho curv frac 3 8 pi g frac k a 2 and rho curv describes the contribution to the total density of the spatial curvature.
Displaystyle frac h 2 h 0 2 omega r a 4 omega m a 3 omega k a 2 omega lambda. Displaystyle frac h 2 h 0 2 omega r a 4 omega m a 3 omega k a 2 omega lambda. The first of the friedmann equations defines a density parameter useful for comparing different cosmological models. It expresses the basic idea of the field equations which is that non tidal curvature left hand side is caused by the matter that is present locally right hand side.
