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Mass-Energy of the Universe:

5% ordinary matter, 27% dark matter, 68% dark energy

What about other energies such as thermal energy, potential energy, kinetic energy, chemical energy, and radiant energy?

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Various missions such as WMAP and the Planck Satellite have measured the mass-energy content of the universe. You tend to see images like the one below produced by these scientific ventures.

WMAP results Credit: NASA/WMAP Science Team

This breaks the entire mass-energy content of the universe into three buckets: Dark Energy, Dark Matter, and (the mass of) atoms. But what about the rest of the universe. Surely there's other mass-energy out there such as the energy in the curved space-time metric, or kinetic energy of atoms, or radiation energy in photons, or the mass-energy of neutrinos! Have the astronomers and physicists forgotten about those things? Well the answer is no, they're just not telling you about it because it doesn't matter.

Equation for the universe

The universe's content and evolution is defined by something known as the Friedmann equation (technically there's a set of equations, but that's not relevant here). One important and useful form of this equation is given below.

$$\frac{H(a)^2}{H_0^2} = \Omega_{0,R}a^{-4} + (\Omega_{0,b} + \Omega_{0,c})a^{-3} + \Omega_{0,k}a^{-2} + \Omega_{0,\Lambda} +\ ...$$

This equation may seem complicated, but let me explain the parts. The left hand side more or less is the expansion rate of the universe in the past (or future) compared to the present day expansion rate. The right hand side is the sum of all the various contributions to the mass-energy of the universe. The important parameters here are the various "energy density parameters", denoted by $\Omega$. I've included the parameters for radiation ($\Omega_{0,R}$), baryonic matter ($\Omega_{0,b}$), cold dark matter ($\Omega_{0,c}$), space-time curvature ($\Omega_{0,k}$), and dark energy ($\Omega_{0,\Lambda}$), but you could add more energy density parameters as well. The ultimate point I'm going to show is that there are only a few energy density parameters that are actually important or significant and the rest can be ignored completely.

Thermal/Kinetic Energy

You mention things like thermal and kinetic energies (which are effectively the same thing since thermal energy just comes from the total kinetic energy of a collection of particles). We can't and don't count these because there's no way to absolutely define the thermal or kinetic energy of something. To define kinetic energy of a given mass requirements specifying it's velocity, but that velocity must be defined with respect to a particular reference frame. Special relativity tells us that there is no absolute reference frame though, which means I could define your velocity with respect to me, or the Sun, or the center of the Galaxy and get a different kinetic energy for you with each definition.

Radiation Energy

Radiation energy is just the energy in light. The universe is flooded with photons (a very large portion of which are CMB photons) and these photons have non-zero energy. But that energy is almost completely negligible in the current universe. From WMAP results, it is estimated that $\Omega_{0,R} = 5\times10^{-5}$ which equates to contributing about $0.005\%$ of the Universe's mass-energy budget. It would be a tiny, tiny sliver in the above graph. Interestingly, this wasn't always the case. If you run the universe backwards, you find that very early on, $\Omega_{R}$ was the dominant source of mass-energy in the Universe.

Neutrino Energy

Similar to radiation energy, neutrino energy is negligibly small. In part, this is because the neutrino mass is so tiny. I don't have an estimate for $\Omega_{0,\nu}$ but I can say it's probably as small or smaller than $\Omega_{0,R}$ and equally insignificant.

Gravitational and Chemical Energy

These types of energies are what's known as potential energies. They're a weird sort of energy because they're not actually real. They're potential. It's the energy you would get if you performed some action (e.g., moving a body through a field). If you hold a ball up high, you might say that ball has gravitational potential energy, but the ball doesn't actually have that energy, it just has the potential to gain energy when you drop it. We simply say it does have that energy to make balancing energy more tidy and simple. When you do drop the ball, it gains energy by falling through the gravitational field and taking energy from it. So really, your question boils down to talking about the energy inherent in background gravitational fields. The same is true for chemical energy. Chemical processes such as extreme oxidation, aka fire, release energy, but that energy comes from breaking atomic bonds and that breaking of bonds involves converting electric potential energy to something else.

Ultimately you just want to add in energy from the quantum fields that permeate the universe, $\Omega_{QF}$. I can't estimate this number, nor have I ever even seen someone try, but I can almost assure you that this number would be extremely tiny, even more so that the previous considered energies. Again, we find it's negligible and would by the tiniest mote of a sliver on the above pie chart.

Space-Time Curvature Energy

There's energy in space-time itself. This is known from General Relativity. This space-time energy of the Universe is denoted by $\Omega_{k}$. The interesting thing about this is that it appears the universe is flat! This implies, to decent precision, that $\Omega_{0,k} = 0$. This energy is more than negligible, it is non-existent (to within observational precision).

Conclusion

I'm sure you could think up a lot of different types of other energies you might want to include in this, but hopefully you see the point I'm driving at. They're all completely negligible. The arguably largest contribution comes from radiation and that's been shown to be $0.005\%$ of the Universe's mass-energy budget. What we see is that the Universe is dominated by Dark Energy, has a bit of Dark Matter, a small amount of atoms, and negligible amounts of the rest of everything else. And overtime, the Dark Energy portion of that pie chart will get bigger and bigger until we'll be able to throw out atoms and dark matter from the plot as well since they'll be just as insignificant as neutrinos and radiation are now.

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  • $\begingroup$ Thanks for the very generous explanation. Regarding your explanation for the kinetic energy - wouldn't there be some of that energy, if we just stick to some frame of reference(it could be any frame of reference) for all the atoms of universe? $\endgroup$ – amsquareb Jun 27 '17 at 17:50
  • $\begingroup$ @amsquareb Sure, but that misses the point. There's no "correct" value for any kinetic energy. I could arbitrary pick any reference frame to make your kinetic energy zero or $10^{10^{10^{...}}}$. $\endgroup$ – zephyr Jun 27 '17 at 17:52
  • $\begingroup$ Why is that so? Wouldn't the velocities of all the atoms just average out when all the universe is considered? I think it will eventually come as same for every different frame of reference. Even if you are right, isn't that absurd? I mean, is there no way to measure the kinetic energy of a system? $\endgroup$ – amsquareb Jun 27 '17 at 18:20
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    $\begingroup$ It's perfectly sensible to talk about, say, the thermal kinetic energy in the reference system at rest with respect to the cosmic background radiation; this is what most calculations for the early universe assume. It's just negligible now compared with the rest-mass energy of (even just) the baryons. $\endgroup$ – Peter Erwin Jun 28 '17 at 14:58
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    $\begingroup$ @zephyr -- are you really trying to suggest that all the early-universe calculations, for which temperature is a key parameter (along with whether particles particles are relativistic -- with kinetic energy dominating over rest-mass energy -- or not) are just completely confused? (And why do you think photons are immune to reference-frame effects?) $\endgroup$ – Peter Erwin Jun 28 '17 at 15:27
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I'm gonna give this a shot, without going into QFT vocabulary.

Those energies you've mentioned are not fundamental forces of the universe. Instead, they are all expressions of the four fundamentals gravitation, electromagnetism, weak and strong force.

The weak force is the weirdest one, it's effect is not to move things, but to change particle species. For this particles must meet, thus it doesn't act on distance. It is also as the name says weak, because in any particle encounter a change of species is very improbable.

The strong force is not active on large distances, only very small ones, of about a femtometer ($10^{-15}$m, the typical size of an atomic nucleus). Thus this one drops out as well.

The electromagnetic force is also fairly strong compared to gravity, but due to having equal amounts of positive and negative charges in the universe, this is shielded on large length scales.

Then gravity remains, which cannot be shielded. Thus on cosmic length-scales gravity dominates.

thermal energy, potential energy, kinetic energy, chemical energy, and radiant energy

Thermal energy is just the kinetic energy of microscopically moving particles, that hit each other often enough so that their momenta are redistributed all the time and thus on average they stay in the same place.
Potential energy is the exact energy of whatever fundamental force field you're in.
Chemical energy is electromagnetism + quantum mechanics.

Radiation energy requires a bit more explanation: However thanks to general relativity we understand better how gravity rules over the universe: It is actually the energy-momentum-density of the universe that governs cosmic expansion. This is I guess what you refer to as mass-energy. And 'radiant energy' is the energy-momentum of photons, which do contribute to the energy-momentum of the universe. Physical cosmology takes this into account, and is even able to derive that there was a phase in the life of our universe where photons were dominating the energy-momentum.

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  • $\begingroup$ I fail to see how this answers the question. You just defined a bunch of (unrelated) forces and energies. $\endgroup$ – zephyr Jun 27 '17 at 13:20
  • $\begingroup$ @Zephyr I fail to see what you fail to see. I define what forces exist, say which ones do not contribute significantly to the dynamics of the universe. The dynamics of the universe is controlled by what OP calls the 'mass-energy'. Maybe this is what you're missing. Also I explain what OP's energies are in terms of the fundamental ones. $\endgroup$ – AtmosphericPrisonEscape Jun 27 '17 at 13:42

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