I have investigated the total energy of Friedmann-Robertson-Walker universes.This is an interesting issue, because if the energy of the universe turns out not to be conserved, it will be in conflict with our common understanding of energy. So intuitivelywe expect the energy of the universe to be constant. Furthermore, if this total energy is constant and zero, it means that 'creating' a universe does not require any energy.Such a universe could then, in principle, just 'pop up' from nothing.
Our universe is dominated by a so-called cosmological constant, or vacuum energy. It has the property that the energy density is constant in volume, so when the universe expands, the total amount of vacuum energy increases. Where does this new energy come from? One might immediately think that it could be energy from other components in theuniverse that is converted into vacuum energy. But it turns out not to be that simple, since the vacuum energy increases also for universe models which contain vacuum energy only. For flat (Minkowski) spacetimes, a global energy conservation law can be set up without problems. But for curved spacetimes, it is in general not possible to set up a global law for conservation of energy.
Because of these problems, calulating the total energy of the universe is not trivial, but different attempts have been made in the past. One particular attempt, made by Faraoni and Cooperstock,is reviewed. Their method for calculating the total energy of FRW universes is applied to three different universe models.