If empty space has energy, and space is expanding, is this energy equally distributed as space expands? The cosmological constant (dark energy) is often described in terms of empty space having a non 0 energy value and this energy being the source of the accelerated expansion of the universe. If space is expanding, what does this imply for energy conservation? Is this energy conserved by being more thinly distributed as space expands? Does this question make any sense or am I just crazy?
 A: The cosmological constant is a constant energy density per unit volume of space, so as the universe expands this does indeed create energy as it creates new space. In this sense conservation of energy is violated.
Actually this is less surprising than you might think. Conservation of energy is linked to a symmery called time shift symmetry by Noether's theorem. However this symmetry is violated by the expanding universe so there's no reason why energy should be conserved (though you should note that the symmetry is strongly broken only on vast scales and conservation of energy is an excellent approximation locally).
But, but, but ...
There is a long and sometimes heated debate about whether energy really is or isn't conserved in an expanding universe. See for example this article by a member of this site. Basically the argument comes down to how you define the total energy - in General Relativity this is not a trivial question.
A: Actually, energy is often not Conserved in general Relativity. For are more in deep explanation see:
http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html
But just notice that Dark Energy might not necessarily end up being the cosmological constant, but a new force field, so its behavior might differ from that of an actual cosmological constant (which would increase total energy as you suggest in your question)
A: Dark energy due to a cosmological constant does not get diluted by metric expansion of space. However, this does not violate energy conservation as the increase in energy will be cancelled by gravitational potential energy. The problem with general relativity is (some would say arguably) not energy conservation, but energy localization:
In a rotating frame of reference, energy conservation only holds if you include the contribution of the centrifugal potential. Analogously, in general relativity, energy conservation only holds if you include the contribution of the gravitational potential. In both cases, you cannot associate a meaningful energy density with these contributions. General relativity just comes with the additional complication that you cannot transform away gravitational energy by going to a globally inertial frame of reference.
Note that there are ways to separate gravity from inertia if you go beyond general relativity (eg the teleparallel approach or bimetric theories) and get a gravitational energy density this way, but energy conservation will only hold if you include inertial effects.
