
At the onset of the cosmic journey, the inflationary mechanism produced superhorizon curvature perturbations which affected the future formation of the universe. This study analyzed the growth of superhorizon curvature perturbations in the inflationary universe. Using a simple ultraslowroll model, we derived the coherence function between any two points in the curvature perturbation. It showed that the causality limits the growth of the curvature perturbation, thereby constraining the important inflationary slowroll parameters, allowing the universe to produce a large enough primordial black hole. Our research will help estimate how curvature perturbations form primordial black holes in the universe.
The consensus is that if the primeval universe (i.e., the beginning of the universe) had experienced a phase of rapid inflation, it would explain why the current universe is so homogeneous and isotropic. A single, flat, simple scalar field drives the occurrence of slowroll inflation, producing vacuum fluctuations beyond the size of the horizon, and these quantum fluctuations eventually derive almost scaleindependent curvature perturbations, including matter density fluctuations and gravity waves. Employing the concept of slowrolling inflation, cosmological observations have made extremely precise measurements on matter density perturbation in recent years.
Recently, scientists have observed gravity waves emitted by merging black holes (2017 Nobel Prize in Physics), making people more curious about the origin of primordial black holes. Many studies have used different models of inflation to try to generate large enough curvature perturbations during inflation to form primordial black holes to explain the sources of gravity waves detected by the Laser Interferometer Gravity Wave Observatory (LIGO).
Among many models, there is an ultraslowroll inflation model with a delayed inflection point in its gravitational field, which violates the slowroll condition but generates large enough curvature perturbations to arouse our interest. We thus analyze the evolution of the supervisual perturbation in such an ultraslowroll model. The concept of the conservation of the superhorizon perturbation derived from the assumption of the slowroll condition no longer holds when the universe is in the ultraslowroll stage; therefore, the matter disturbance in the superhorizon mode can grow rapidly. Although the rate of inflation is extremely low and the acceleration of the spatial expansion is extremely large, the material disturbance in the superhorizon mode can indeed grow rapidly. However, this growth is not unlimited and is still restricted by the causality law, thus allowing us to estimate an upper limit on the growth rate of curvature perturbations. After lengthy numerical calculations and comparing with the Cosmic Microwave Background (CMB) observations, we found that the presence of the anticurvature point significantly reduces an important slowroll parameter in the inflation model, resulting in a welldefined spike on the power spectrum of curvature perturbations, about halfway through the inflation, forming the primordial black hole of about 108 solar masses!
The results of our analysis can be applied to infer the growth of curvature perturbations in the universe during ultraslowroll inflation, and we can then estimate the mass range and quantity of primordial black holes formed when these curvature perturbations reenter our horizon, which can be compared with current observations to confirm the origin of gravity waves.
Reference:https://journals.aps.org/prd/abstract/10.1103/PhysRevD.99.063524
Wolung Lee Associate Professor  Department of Physics
Dr. Lee graduated from the University of Arizona and his research interests are in the areas of cosmology such as cosmic inflation, primordial black holes, primordial magnetic fields, and dark energy.