What is the relationship between the energy of the vacuum and the Cosmological Constant?
The vacuum energy is a property of space-time which is so fundamental that its value will be the same as observed by anyone. It is called a relativistic invariant. In general relativity, the only way you can build such an invariant quantity into the relativistic equation for gravitation is to multiply the constant by the so-called ‘metric tensor’ which also represents both the strength of the gravitational field and the geometric properties of space-time. So, with out knowing anything about the vacuum energy other than it is a relativistic invariant, we can add it as a term to Einstein’s equation for gravity. When we do so, we discover that nay such ‘vacuum energy’ terms added to space-time have exactly the same mathematical form as the famous ‘cosmological constant’ term added by Einstein back in 1917 as a form of ‘anti-gravity’ to make the universe static and eternal.
