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I am interested in how the large-scale properties of the Universe change over time. Does anyone know a trusted website which gives the temperature, density and radius (distance to the particle horizon) of the observable Universe at given points in time in its history? I have been unable to locate any website which gives this information.

For example in the Wikipedia article https://en.wikipedia.org/wiki/Chronology_of_the_universe . there is a table labelled ‘Tabular Summary’ . This gives the temperature of the Universe at various times throughout its history, but it doesn't give its radius or density.

I am particularly interested in the epochs in the early Universe labelled in the Wikipedia article as:

  • electroweak epoch,
  • inflationary epoch,
  • quark epoch
  • hadron epoch
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    $\begingroup$ By "radius of the observable universe", do you mean the radius in the past of the region that we can see now, or the radius of the region that was visible in the past? $\endgroup$
    – Sten
    Mar 9, 2023 at 11:05
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    $\begingroup$ Also, I don't have time to carry out the calculations right now, but given the temperature $T$, you can see how to calculate the radiation density $\rho$ and the cosmic expansion factor $a$ in this earlier answer. Note that the calculations assume Standard Model physics, so they could in principle be valid up to the inflation scale, if there are no new physics at intermediate scales. However they lose validity during and before inflation, since inflation is new physics. $\endgroup$
    – Sten
    Mar 9, 2023 at 11:09
  • $\begingroup$ Just to clarify.... by "radius of the observable Universe" I meant the particle horizon at a given point in time, i.e the proper distance at time t of the furthest object from which light could have reached an observer $\endgroup$ Mar 9, 2023 at 20:40
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    $\begingroup$ I wrote an astropy-based Python code to calculate all these properties. You can find it here on GitHub. I used it to make this timeline of the Universe. $\endgroup$
    – pela
    Mar 9, 2023 at 21:06

1 Answer 1

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Here are some plots, calculated as described here. I assume no physics beyond the Standard Model and the concordance cosmological model.

The temperature

The temperature

The horizontal lines are:

  • The temperature of electroweak symmetry breaking, when the electroweak epoch ended.
  • The QCD phase transition, when quark-gluon plasma transitioned into hadrons.
  • The time of neutrino decoupling. This is significant because it's the earliest time that we have probed observationally.
  • Big Bang nucleosynthesis, or more specifically the time when most of the primordial helium was created.
  • Recombination, when plasma transitioned into neutral atoms. This is when the cosmic microwave background last scattered.

When speaking of the early cosmic history, it's often more convenient to frame it as a function of the temperature, since many processes depend on the temperature more than the time. I adopt this convention in the following plots.

The particle horizon, the past size of the present-day observable universe, and the cosmic expansion factor

Particle horizon, observable universe, and cosmic expansion factor. The radius of the observable universe is just the present-day particle horizon multiplied by the expansion factor. The right-hand axis (expansion factor) is only applicable to the orange curve. The left-hand axis (length) is applicable to both curves.

The density of radiation, matter, and dark energy

Density of radiation, matter, and dark energy. For radiation and dark energy, this is the energy density. For matter, this is really the mass density, because the various matter species become relativistic at sufficiently high temperatures, making their energy density scale like that of radiation. But the matter is certainly nonrelativistic (making its mass and energy density equal) within the time period where it dominates the energy density.

No new physics?

Again, these plots assume no new physics. This means:

  • The universe is assumed to be dominated by the relativistic Standard Model plasma back to arbitrarily early times. In practice, we only have observational confirmation of this state back to the time of neutrino decoupling. Earlier times are unprobed.

  • Dark energy is assumed to be a cosmological constant. In practice, we only know the energy density of dark energy at very late times. If I plotted the density of dark energy only within the time range where it is confirmed, it would be a barely visible tick at the right-hand edge of the second plot.

  • The matter exists at arbitrarily early times. In practice, we expect that (the asymmetric component of) the ordinary matter was created by baryogenesis at some point, and the dark matter was also created at an unknown time.

  • No inflation. We do not know when inflation happened, and it completely changes the expansion and thermal history. Still, if the universe was radiation dominated back to the time that inflation ended, the above plots would accurately describe the state of the universe right after inflation ended (and the universe reheated).

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    $\begingroup$ Top quality. Useful plots. $\endgroup$
    – ProfRob
    Mar 10, 2023 at 12:47

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