Adding up Cosmic Energy



A simple Newtonian analysis provides a deep insight to the nature of the Universe. Summing the total energy within the Hubble sphere gives roughly c3 / HG kg. Similarly, summing the total (negative) gravitational binding energy within the Hubble sphere gives roughly -c3 / HG kg. Hence, at least averaged over the Hubble sphere, this simple analysis suggests the total energy content of the Universe might be zero!

Of course, the Friedmann equation for a zero curvature (flat) Universe confirms this, since the sum of the kinetic and potential terms is zero. In other words, the condition of flat geometry is the same as the Newtonian condition of zero total energy.

Figure from Whittle's (upcoming) undergraduate cosmology text.