## Quantum nature makes spacetime fluctuations in the early Universe to be very symmetrical

**Overview of the press release**

It is believed that the inflation of the universe is caused by field called "inflaton" that fills the space uniformly. The ultimate goal of research in inflationary cosmology is to clarify the nature of this field in particle physics. The universe must have been practically in a vacuum state, since all other matter would have been completely diluted by the rapid expansion of the universe during inflation. Within the framework of quantum field theory in such a rapidly expanding universe, we can see that as the universe expands, fluctuations are created one after another. As a property of fluctuations around a vacuum, dense and sparse regions with various heights (amplitudes) always appear with the same frequency, and their distribution follows a normal distribution (Gaussian distribution). The normal distribution is a standard distribution that is used in statistical tests, where areas higher and lower than the average value appear with the same frequency. However, the fluctuations can dynamically interact each other, resulting in a difference between the numbers of the dense and sparse regions. Since the difference is determined by the strength of the interactions, if we can observe the difference in the number and height (amplitude) between the dense and sparse regions, we can gain an insight into high energy physics that cannot be obtained by accelerator experiments. (Figure 1)

**Figure1: **Conceptual diagram of density fluctuation generation that was the seed of galaxies and clusters of galaxies in the inflationary universe. Quantum fluctuations produce an equal number of dense and sparse regions, but strong interactions cause a misalignment between the two. However, it has now been discovered that these interactions also significantly change the amplitude of fluctuations, imposing a limit on the strength of the interactions that is 10 times stricter than before.

These fluctuations will be stretched out by continued inflation, so that the Universe will eventually be filled with fluctuations of various sizes. Such fluctuations are only about 1/100,000 of the average energy value, so the fluctuations are as slight as a one-millimeter-high ripple in a 100-meter-deep ocean. Even with such small inhomogeneities, a dense region has stronger gravity than a sparse region, and this effect attracts more and more matter from the surrounding area, eventually leading to the development of cosmic structures such as stars and galaxies.

” We were able to get this value right by performing a calculation that correctly incorporated the scale dependence of fluctuations’ amplitude. As a result, we found that even if these corrections are negligible at a single point, they must be added up over the entire exponentially large inflationary universe, resulting in corrections well in excess of one part in 100,000 unless the interactions are sufficiently weak, and that the theoretical calculations that ignored these corrections, which had been used in the past, broke down.” explained Jason Kristiano.

**Figure2: **The distribution of the magnitude of quantum fluctuations in the vacuum follows a symmetric normal distribution (Gaussian distribution) around the mean, as shown by the blue line, but when the effect of the interaction is taken into account, the distribution becomes asymmetric as shown by the red line. The present study shows that the strength of the interaction must be less than 1/200 of that of the red line in the figure. Such a distribution is indistinguishable from the blue line.

**Research Team**

Jason Kristiano (Doctoral Student, Department of Physics, Graduate School of Science, The University of Tokyo).

Jun’ichi Yokoyama (Professor, Research Center for the Early Universe, Graduate School of Science, The University of Tokyo).

**Publication details**

Journal *Physical Review Letters*Title Why Must Primordial Non-Gaussianity Be Very Small?Authors Jason Kristiano and Jun’ichi YokoyamaDOI https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.061301

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