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If I am understanding big bang correctly... During big bang

Approximately $10^{−37}$ seconds into the expansion, a phase transition caused a cosmic inflation,

Which was 'free lunch' of energy and it continued for some time but then suddenly 'free lunch' was over and energy conservation started...

The universe continued to decrease in density and fall in temperature, hence the typical energy of each particle was decreasing.

and quarks and other particles formed....

Did inflation stop because of energy density drop or some other reason?

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There is no single answer, since there are many models for inflation and no one knows if any of them are correct.

Broadly speaking, what all the models contain is a scalar field at early times with a non-zero value, which is often termed a false-vacuum. The energy density of this field completely dominates the dynamics of the universe, like a super version of dark energy today. In such circumstances, the universe expands exponentially with time.

Whilst the field is present, the universe inflates, but at some point in time and for some reason (e.g. symmetry breaking), the scalar field decays to a true vacuum, converting it's energy into mass.

As I said, nobody knows why inflation stopped, just that the process of field decay must take long enough for the universe to inflate sufficiently to solve the various problems of the original big bang model.

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The standard Big Bang model meets at the singularity proposed by the original Big Bang model, a classical General Relativity model, which was proposed when it was observed that all clusters of galaxies are retreating from each other as if coming from a cosmic explosion.

enter image description here

Diagram of evolution of the (observable part) of the universe from the Big Bang (left) - to the present.

The inflationary model assumes an effective quantization of gravity during the period of rapid inflation. This was deemed necessary because the homogeneity of the cosmic microwave background radiation (the blue plane in the diagram) could not be explained . At the time of separation of the electromagnetic radiation there were regions in the observable universe that could not come into thermodynamic equilibrium .

The inflaton field was proposed so that it would create the homogeneity from the quantum mechanical indeterminacy, generating an enormous expansion. At some point the expansion stopped because the energy density dropped and the elementary particles in the table were created out of the available energy.

The inflaton field is a hypothetical scalar field that is theorized to drive cosmic inflation in the very early universe.The field provides a mechanism by which a period of rapid expansion from 10^−35 to 10^−34 seconds after the initial expansion can be generated, forming a universe consistent with observed spatial isotropy and homogeneity.

If there is another reason than energy density, it is dependent on the specific quantum mechanical modeling. The gross reason is the drop in the energy density, the same for determining all periods of the Big Bang expansion.

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