Total energy of the universe is not conserved
"The Question is: What is The Question?" John Archibald Wheeler
The total energy of the universe is obviously not conserved in the standard model that fits observations to ~ 1% precision.
The total w = -1 dark energy repulsive cosmic antigravity field accelerating the 3D space expansion of the universe is obviously not conserved. The total w = -1 dark energy content of our universe from Rocky Kolb's first slide above scales as a(t)^3.
The total w = 0 on-mass shell finite rest mass matter-energy is conserved scaling as a(t)^0 = 1.
The total zero rest mass w = +1/3 on light cone radiation energy is not conserved, it scales as a(t)^-1 -> zero from the cosmic redshift. Note that the chemical potential of radiation is zero, therefore there is no general global conservation law for radiation.
The general point here is that global space-time conservation laws are not fundamental unlike the local versions, which are satisfied e.g.
Tuv(matter)^;v = 0
locally in 1915 GR with the (LC) connection covariant partial derivative ;v.
Global conservation laws require
[Tuv(Matter) + tuv(Matter-Gravity)]^,v = 0
where ,v is the ordinary partial derivative.
This cannot be done in general in curved space-time with tuv(Matter-Gravity) as a kosher localized T4 tensor. tuv(Matter-Gravity) is a pseudo-tensor because in LNIF's the energy-momentum of the non-geodesic detectors powered by non-gravity forces makes a contribution to the vacuum gravity field that, by the equivalence principle, cannot be locally distinguished from the "real gravity field." Garbage in -> garbage out. Ask a stupid question, get a stupid answer. Trying to globally conserve total energy, trying to conserve total linear and angular momentum in a generally curved and torsioned spacetime is a stupid thing to try to do. We already know this from Noether's theorem. This is simply because the global Poincare group is locally gauged and all we can hope for is to locally conserve the total stress-energy current densities, which in fact is the case.
((-detguv)^1/2Tuv(matter))^,v + (-detguv)^1/2(LC(observer))u^v^wTvw(matter) = 0
Actual observations given above show that the total energy of the universe is not conserved. It's time to slay that Sacred Cow.
What the pure mathematicians, who lack physical understanding do not get, is that any representation of curved space-time guv is observer dependent i.e. relative to any conceivable network of ideal local observers on arbitrary worldlines inside the local light cone field. For example, in the non-rotating black hole outside the event horizon rs/r < 1
g00 = -1/g11 = 1 - rs/r
is only for that special class of static LNIF "shell" (J.A. Wheeler's term) observers at fixed r without orbital angular momentum. They need to fire rockets to stay in place. Note that warp drive "UFO" observers see a different metric field representation. What "Diff(4)" (local T4) frame shifts do is to connect different networks of local observers. That's the physical meaning of the abstract math missed by many of the formalists in the field. The local relation between objective reality and the observer's experience is
ds^2(objective observer invariant) = guv(observer dependent)dx^udx^v
Space-time physics is local only because curved space-time is emergent from a local vacuum ODLRO world hologram Higgsian field with several coherent Goldstone phases that encode the 10^122 bits of our universe retrocausally from far future Omega to past Alpha at The Creation in our deSitter Universe.
"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein