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Under the inflation theory, what was the initial conditions when inflation began? I know they talk about a scalar field, can someone help describe it verbose (or generally well explained) what happens after initial state in the inflation theory?

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A key idea is that of phase transitions. A phase transition corresponds to a dramatic change in the properties of a physical system as it is heated or cooled. Familiar examples are the freezing of water into ice, the lining up of domains in a cooled ferromagnet, or the onset of superconductivity or superfluidity at low temperatures. It is believed that the Universe itself will have undergone a series of phase transitions as it cooled, an example being when quarks first condensed to form hadrons. A phase transition is a particularly dramatic event in the history of the Universe, a time when its properties change substantially. Phase transitions are controlled by an unusual form of matter known as a scalar field. Depending on the precise nature of the transition, scalar fields can behave with a negative pressure, and can satisfy the inflationary condition $pc^2$ +$3$p < $0$. That is, they behave like an effective cosmological constant. Once the phase transition comes to an end, the scalar field decays away and the inflationary expansion terminates, hopefully having achieved the necessary expansion by a factor of $10^{27}$ or more.

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