Inflationary quantum fluctuations

According to quantum field theory, empty space is not entirely empty. It is filled with quantum fluctuations of all types of physical fields. The wavelengths of all quantum fluctuations of the scalar field 0 grow exponentially during inflation. When the wavelength of any particular fluctuation becomes greater than H-1, the fluctuation stops oscillating and its amplitude freezes at some non-zero value S0(x) because of the large friction term 3H0 in the equation of motion of the field. The amplitude of this fluctuation then remains almost unchanged for a very long time, whereas its wavelength grows exponentially. Therefore, the appearance of such a frozen fluctuation is equivalent to the appearance of a classical field S0(x) produced from quantum fluctuations.

Because the vacuum contains fluctuations of all wavelengths, inflation leads to the continuous creation of new perturbations of the classical field with wavelengths greater than H-1. The average amplitude of perturbations generated during a time interval H-1 (in which the Universe expands by a factor e) is given by \50(x)\ &H/(2n) [15,16]. These quantum fluctuations are responsible for galaxy formation [17-21]. But if the Hubble constant during inflation is sufficiently large, quantum fluctuations of the scalar fields may lead not only to the formation of galaxies, but also to the division of the Universe into exponentially large domains with different properties.

As an example, consider again the simplest supersymmetric theory unifying weak, strong and electromagnetic interactions. Different minima of the effective potential in this model are separated from each other by a distance ~10-3Mp. The amplitude of quantum fluctuations in the fields 0, $ and p at the beginning of chaotic inflation can be as large as 10-1Mp. This means that, at the early stages of inflation, the fields $ and p could easily jump from one minimum of the potential to another. Therefore, even if these fields initially occupied the same minimum everywhere, after the stage of chaotic inflation the Universe becomes divided into many exponentially large domains, corresponding to all possible minima of the effective potential [6,14].

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