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Notice that we define atoms as  nuclei having bound electrons. The particles that make up atoms were formed in the lepton epoch (electrons) and in the nuclear epoch, but atoms were not formed until the universe further cooled to temperatures where electrons could stay bound to atoms.

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When the electrons became bound to nuclei, only photons with certain energies interacted with matter. Photons with energies that corresponded to differences between excited electron states could interact with electrons. Other photons were free to flow. When atoms were formed, the universe became transparent to most wavelengths of light. This phenomenon is called recombination, or the decoupling of light from matter.

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When the universe became transparent to photons, light was free to move. We can calculate the distance that the light has traveled since its release, at somewhat under 14 billion light years, by comparing the peak wavelength that the light would have at the temperature where atoms could form to the redshifted light that we see in the cosmic microwave background radiation.

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The cosmic microwave background radiation is very uniform across the sky. In every direction, we measure the same temperature, with very tiny fluctuations. The problem is that when the light was released, the universe was already so large that light would not have enough time to traverse the distance to carry the signal from one horizon to the other. In other words, light could not have a causal effect across distant regions of the universe. The regions marked "A" and "B" in the diagram above look practically identical to us, yet they were separated by millions of parsecs when they emitted the light that is reaching us now. It is possible, but unlikely, that the  reason these regions look the same now is that they started out with the same characteristics.

One way of solving the horizon problem is to consider the possibility that they universe went through a short burst of very rapid expansion at the end of the quark era, called "inflation." We believe that the universe underwent something like a phase change when the fundamental forces reorganized as they were being frozen out. It entered a false vacuum state with very high energy, acquiring enormous pressure, resulting in an ultrafast readjustment.

A very rapid expansion of the universe could be seen as analogous to a rapid phase change in normal matter, like what is seen when supercooled water freezes.

Very pure water can be cooled to a temperature somewhat below the freezing point without actually freezing until it is perturbed, then it freezes very rapidly. Cosmologists believe that the same thing could have happened in the early universe. It may have been undergoing transitions like phase changes, and delayed the change, staying in a metastable phase for a bit too long, then rapidly dropping into the lower energy state. Some cosmologists think this could have happened several times.

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Another cosmological issue that inflation addresses is the flatness problem. When we add up all of the normal matter, dark matter and dark energy of the universe, the density of the universe turns out to be extremely close to the critical density of the universe. We appear to have a flat universe. Simply stated, the flatness problem asks, of all possible densities for the universe, why we should happen to have this special value?

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Inflation solves this problem by looking at the whole picture. At early times before inflation, there could have been strong curvature to the universe. After the universe was blown up by inflation, the curvature looks locally flat because we are only seeing a very small part it.

Image source: discovermagazine.com/2014/april/12-first-light

After recombination, the universe entered what we call the "Dark Ages." There would be nor more light produced until fusion took place in the first stars. The galactic epoch was marked by the formation of the large scale structure of the universe.

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It is believed that cold dark matter played a very important role in the formation of the large scale structure of the universe. Quantum mechanical fluctuations are very similar in character to large scale fluctuations we see today. Matter densities, however, vary much more than the CMBR temperatures. Hot dark matter does not have a tendency to clump, since the particles are moving so fast. Cold dark matter is attracted gravitationally but not repelled electromagnetically, and moves at slow enough speed that it could form clumps early in the history of the universe. It could provide the scaffold for normal matter to gravitationally contract into structures like early galaxies.

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Computer simulations show good agreement between structure seen in quantum mechanical fluctuations and large scale structure seen in the universe today.

Image credit NASA/ESA/Massey

Three dimensional mapping of dark matter using gravitational lensing slices indicates that there is good agreement between dark matter haloes and large scale structure involving galaxy clusters.

Animation source

Analysis of data from NASA's Fermi gamma ray telescope was used to understand the fossil radiation field of light from stars even after they cease to shine. This animation tracks several gamma ray photons along their journey through the universe, encountering optical and UV photons from starlight, ultimately arriving at the Fermi telescope.

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This diagram illustrates the timeline for the radiation, matter and dark energy dominance in the universe. At the present time, we are in the dark energy epoch. The radiation density and matter density both continued to fall as the universe expanded, but dark energy density remained constant. Eventually, dark energy became the dominant material in the universe. This raises some interesting questions.

How can the density of dark energy remain constant?

The size of the universe keeps getting bigger and bigger. Doesn't this mean that there is more and more dark energy? Doesn't that break some kind of conservation law?

It could be that there exists a kind of potential dark energy. It would be similar in concept to gravitational potential energy. When you lift a massive object, say a bowling ball, you do work against gravity to lift it. The higher you lift it, the more work you do. That work energy is stored as potential energy. When you drop the ball, it falls to Earth, moving faster and faster. The gravitational potential energy is converted to kinetic energy of motion. The total energy is conserved; it just changes form from potential to kinetic energy.

Similarly, the dark energy we see could be arising from a potential dark energy. It is not being created from nothing. It is just changing form.

Now, what about the curvature of the universe? We think we have a flat universe, but now we see that the expansion rate of the universe is increasing. Isn't that a contradiction?

How can we say that we have a flat, accelerating universe?

In the purest sense, we originally defined curvature to be measured by the path that light takes through the universe.

Specifically, the CMBR has rippling, or fluctuations in temperature. We see hot spots and cooler spots. We can calculate what the relative sizes of the hot spots should be, based on quantum mechanical fluctuations in the kind of matter and energy field that we think existed early in the universe. If they appear magnified, compared to our theory, it indicates positive curvature (like a magnifying glass). If they appear smaller than our theory predicts, it indicates that the curvature of the universe is negative.

It turns out that the size of the ripples in the CMBR are what we would expect them to be, compared to our simulations of the early universe. This indicates a flat universe.

We can independently calculate the density of normal matter, dark matter and electromagnetic radiation. The density of the combined normal matter, dark matter and electromagnetic radiation gives a value below critical density for the universe. This would indicate a closed universe.

What we see is that the evidence indicates we have an accelerating universe. This evidence comes from the intersection of three observational methods: (1) the rippling of the CMBR, (2) the redshifts of distant galaxies using Hubble’s law and supernovae, and (3) the large scale structure seen in galaxy clusters.

Now we need to add in the density of dark energy. Our evidence indicates that something is pushing galaxies apart on a very large scale, we call it dark energy. We can calculate how much energy that would take. We can find the density by dividing the energy by volume. When we add the density of the dark energy to the density of the other three sources, we end up with a value for density that is extremely close to critical density.

But critical density no longer equates to a critically unbound universe. That is because dark energy does not act like normal matter or dark matter. It adds density without adding gravitational attraction. It appears to add density while also adding something that acts like repulsive gravity, or negative pressure.