You are probably speaking of the perpetual inflation theory? Then your picture is not accurate.
According to this theory the universe's default state is with unbroken Higgs field. The value of the field is 0 and the energy is nonzero. In this state, all particles are massless. The universe filled with massless particles gas expands exponentially, as in de-Sitter solution.
Then, in some moment and place, the Higgs field gets broken. The value of the field goes to some nonzero value (hence symmetry breaking) and energy goes to zero. In the theory of the perpetual inflation, this is the Big Bang. With nonzero Higgs field, particles get mass. The energy of Higgs field de-excitation creates our universe particles. Now some region of space is filled with massive particles. That means that it expands
slower than the rest of the universe. No particles from outside can enter our universe, since the outside universe expands too fast for them to reach us even with light speed.
This theory nicely explains inflation and the observed Hubble factor changes.
Now, some mistakes corrected:
Assuming the higgs field expands at the speed of light
It does, but the background spacetime is not static.
the radius of the higgs field (all of spacetime actually) should be the age of the universe multiplied by the speed of light.
No, it shouldn't. The expansion of the spacetime is not measured in the same way as particles positions.
The spherical volume of spacetime is going to be even larger, so my question is where does the energy come from to expand?
Spacetime does not need any energy to expand. In fact, it needs energy to collapse. Gravity is an attractive force, not repulsive.
The higgs field can be excited to make the higgs boson so it must have energy
The two are unrelated. Excitations (waves) of the Higgs field indeed have more energy than a vacuum (no waves) state. However, in the Higgs field case there may be many semistable vacua. The Higgs field may be in a false vacuum state (high energy) and a true vacuum (low energy). Both these states have no particles. The energy of vacuum and energy of a wave are two different things.
but the endless expansion of spacetime, and the higgs field, seems like it violates conservation of energy
The universe as a whole does not obey conservation of energy, since it is not an isolated system as the law requires. However, in this case "our" expanding sphere is an isolated system and it obeys the conservation of energy.
and does so at exponential rates because of volume
Even if your picture was correct, it would be only at cubic rate.
Shouldn't the higgs field decrease in strength over time?
No. The Higgs strength (field value) does not change in time. The only moment when it had changed was the Big Bang, the moment of decay.
This topic should go into "Beyond Standard Model" forum.
