Static Universe - Einstein's Universe

Einstein's Universe

Einstein's static universe is closed (i.e. has hyperspherical topology and positive spatial curvature), and contains uniform dust and a positive cosmological constant with value precisely, where is Newtonian gravitational constant, is the energy density of the matter in the universe and is the speed of light. The radius of curvature of space of the Einstein universe is equal to

The Einstein universe is one of Friedmann's solutions to Einstein's field equation for dust with density, cosmological constant, and radius of curvature . It is the only non-trivial static solution to Friedmann's equations.

Because the universe is now known to be expanding the Einstein universe is no longer regarded as a viable model for our universe. Moreover, it is unstable in the sense that any change in either the value of the cosmological constant, the matter density, or the spatial curvature will result in a universe that either expands and accelerates forever or re-collapses to a big crunch.

After observations indicated that the universe was expanding, most physicists of the twentieth century assumed the cosmological constant is zero. If so (absent some other form of dark energy), the expansion of the universe would be decelerating. However, with the discovery of the accelerating universe, a positive cosmological constant has been revived as a simple explanation for dark energy.