The energy density of empty space is called the cosmological constant. It accounts for the force that causes the expansion of the universe. Its value is approximately 10^-29 g/cm^3. This is an incredibly tiny positive number. They call this stuff dark energy.
As the universe expands, the density of ordinary matter like stars and rocks decreases because new matter is not magically appearing to fill in the space. The incredible thing about the cosmological constant is that the energy density of vacuum does not decrease as the universe expands with time. If this does not surprise you, then let me explore this a little deeper.
mass = density * volume
If the universe is expanding, then the volume is growing larger with time. If the density remains constant, then this would mean that the mass-energy of the universe is ever increasing.
Reconcile that with the First Law of Thermodynamics.
In any process, the total energy of the universe remains the same.
Are we to believe that the universe itself violates the First Law of Thermodynamics?