Press Releases

DATE2022.03.15 #Press Releases

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


Overview of the press release

We theoretically showed that the density fluctuations created during the inflationary expansion in the early Universe, namely the dense and the sparse region, must be distributed very symmetrical. We found that the amplitude of the fluctuations will deviate significantly from the observation unless the dense and the sparse region is very symmetric. Our result provides a clue to identify the origin of inflation.
Our Universe is filled with celestial objects of various sizes, as we can see many stars when we look at the night sky with the naked eye, and many galaxies and galaxy clusters when we look through a telescope. On the other hand, when we look at the Universe, we see a large expanse of homogeneous space extending over tens of billions of light years. This characteristic of the Universe is explained by the fact that the Universe underwent a very rapid expansion called inflation before the Big Bang. While inflation greatly expands the Universe to create a homogeneous space, since this occurred when the Universe was much smaller than a hydrogen atom, quantum effects working in the microscopic world play an important role.

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.

The traces of these small fluctuations created during inflation can be observed by measuring the temperature of the cosmic microwave background. Full-sky observations by the Planck satellite have shown that fluctuations on larger scales created earlier during inflation have slightly larger amplitudes than those on smaller scales. They also found that the frequency distribution of fluctuations of various amplitudes is perfectly consistent with a normal distribution (Gaussian distribution) to the best of current observational accuracy. In other words, the interactions of the fluctuations that represent the difference between dense and sparse regions have only small observational upper bound. Jason Kristiano, a doctoral student at Graduate School of Science, The University of Tokyo, and Professor Jun'ichi Yokoyama have analyzed how these interactions affect the distribution of the fluctuations by applying quantum field theory, which is usually used to study particle physics theory, to cosmology.
“ In previous studies, it was thought that the effects of such interactions were completely negligible, since the difference between dense and sparse region caused by the interaction of fluctuations would only add a correction of 1/100,000 to the quantity of 1/100,000 at the single point where it occurred. In fact, it was thought that the effect of such interactions could be completely ignored. Moreover, theoretical calculations made without taking these corrections into account reproduced the observed data very well.” said Professor Jun'ichi Yokoyama.
On the other hand, previous studies that attempted to calculate such corrections assumed that the amplitude of any scale of fluctuations were equally created, and thus only infinite quantities that are physically meaningless, as is often the case in calculations of quantum field theory, were obtained.

” 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.
” This result means that for theoretical calculations of inflation to be consistent with observations, the interactions must be a further factor of 10 below the current observational limit, and deviations from the normal distribution will not be detectable in the future (Fig. 2). This result gives us a clue to the high energy physics theory that describes inflation.” Professor Jun'ichi Yokoyama continued.

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

Physical Review Letters
Why Must Primordial Non-Gaussianity Be Very Small?
Jason Kristiano and Jun’ichi Yokoyama