# When they say that the universe cooled after the big bang, where did the heat go?

Layman here,

Stumbling through some physics stack posts and started reading the Wikipedia for the chronology of the big bang. In it, it states

The very earliest universe was so hot, or energetic, that initially no matter particles existed or could exist except perhaps fleetingly, and the forces we see around us today were believed to be merged into one unified force. Space-time itself expanded during an inflationary epoch due to the immensity of the energies involved. Gradually the immense energies cooled – still to a temperature inconceivably hot compared to any we see around us now, but sufficiently to allow forces to gradually undergo symmetry breaking, a kind of repeated condensation from one status quo to another, leading finally to the separation of the strong force from the electroweak force and the first particles.

Where is the "immense energy" going to when it is "cooled"? Is there now no "immense energy"?

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@GlenTheUdderboat I believe that to be the case (same energy spread thin over a larger universe). When a gas expands, if the pressure or amount of mass go up together with the volume, it will become colder. –  Renan Jul 14 '14 at 18:58
My only guess it that the energy transferred from the particles movement to them forming particles. That prior they moved so fast they had too much energy to coagulate, and once they slowed down enough they could then coagulate. Though, how did they slow down? –  user1596244 Jul 14 '14 at 19:00
possible duplicate of Is the total energy of the universe constant? –  David Hammen Jul 14 '14 at 19:09
Related: Is the total energy of the universe constant? and Total energy of the Universe. Energy is not conserved in general relativity. –  David Hammen Jul 14 '14 at 19:14

Temperature means energy. The heat energy is still here. It's just that the "object" (the Universe) grown bigger so this energy had to spread through it. The more energy in a single point, the hotter it is. That's why they say it got cooler. It's like the expanding gas from your spray deodorant is cold when it leaves the can, but it was at room temperature inside the can. The energy is still the same.

Please note that this is just a simple analogy and it should be aknowledged that there are much more complex processes involved. It was asked for an Layman's answer.

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Isn't it true that your deodorant argument doesn't work if the propellent is an ideal gas? Free expansion doesn't change the kinetic energy of the gas molecules nor the temperature of the gas. The cooling relates to inter-molecular potential energy. Does the same argument work for the expansion of the universe? If the universe were an ideal gas, would it have cooled? If not, then the "spreading" argument needs to be developed in a little more detail. –  garyp Jul 14 '14 at 20:00
This answer isn't exactly right. In GR energy is not conserved, and there actually is a loss in energy associated with expansion (at least in the early universe, depending on the nature of dark energy this may be the opposite today). Whether this energy difference is compensated by the so called negative energy of gravity is another far more controversial question, but it is completely uncontroversial that the heat energy of the universe decreased as it cooled. –  ticster Jul 14 '14 at 22:36
@garyp: not that it's relevant but see Why does deodorant always feel cold?. –  John Rennie Jul 15 '14 at 10:52
I edited my answer to consider that it was asked for a Layman's answer and note that this is just a simple analogy. –  Bruno Finger Jul 15 '14 at 14:02
"The energy is still the same" This is still false though, regardless of whether it's written for a layman or not. It's quite essential to point, even without describing it in detail, that energy is not conserved in General Relativity. It's not just a question of "it's too dumbed down". What you're saying is just wrong, and only applies if all the energy of the universe is mass energy, which is very far from the truth for the time period he is asking about. –  ticster Jul 15 '14 at 14:05

When the universe expands, it is important to understand that how its energy content evolves depends on the form of energy involved. If all that energy is locked up in the form of mass energy, then the density of that matter will decrease proportionally to the relative increase of any arbitrary volume of the universe (i.e. if expansion doubles the size of things, all volumes will be multiplied by 8, and correspondingly all densities will be divided by 8). In other words, if $a$ is the scale factor of the universe, and $\rho_m$ its matter density, we have :

$$\rho_m \propto a^{-3}$$

Hence, the total amount of mass energy (which is $\rho_m \times a^3$) is conserved. What happens if the energy content of the universe is dominated by radiation ? In that situation, on top of the decrease in density, radiation is also redshifted proportionally to the scale factor. Hence, if $\rho_R$ is the radiation energy density, we have :

$$\rho_R \propto a^{-4}$$

Here, the total energy ($\rho_R \times a^3$) is not conserved, which, remember, is not a problem in General Relativity. The period your textbook is referring to is likely the radiation era (roughly the first $50,000$ years of the universe's history). Indeed, during this time, the universe cooled in a way that decreased the total energy of the universe. It didn't go anywhere, it is indeed "lost" in a sense.

Conversely, we can have a situation where energy is gained. This is the case for any dark energy model, but let's keep it simple and consider the case of a cosmological constant $\Lambda$. This corresponds to a constant energy density. That is to say $\rho_\Lambda$ is independent of $a$. The total energy will then be $\rho_\Lambda \times a^3$, and will therefore increase with expansion.

Here I loosely used the word "total" given that it doesn't mean much in an infinite universe. A more rigorous expression for "total" would be any arbitrarily chosen sphere in comoving coordinates, so long as its radius is above the inhomogeneity scale.

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If matter energy stays constant, and radiation energy decreases, why do articles like this one say the energy in the universe is increasing as it expands? blogs.discovermagazine.com/cosmicvariance/2010/02/22/… –  B T Aug 11 '14 at 20:43
@BT See my edit. –  ticster Aug 12 '14 at 7:12
Every answer leads me to more questions. I'm getting the feeling that there other classifications than "matter energy" and "radiation energy". If matter energy stays constant, radiation energy decreases, are you saying that dark energy is neither radiation nor matter? What is it? Is it in its own class? Are there other types of energy in this regard? –  B T Aug 13 '14 at 1:18
@BT While the most obvious cases for the energy content of the universe are matter and radiation, explaining the observed acceleration (by relying only on additional energy content) requires another form of energy, one whose exact nature is still up for debate. You can see my answer here for a cursory review of possible explanations. –  ticster Aug 14 '14 at 10:27