# Research Statement

My research interests lie in revealing the history and the fundamental laws of the Universe through the interplay among cosmology, particle physics, and gravitation. In particular, I am interested in topics such as cosmology based on supergravity and superstring, the properties of primordial perturbations, the mystery of dark matter, dark energy, and baryon asymmetry, the dynamics of phase transitions and topological defects, and so on. Below, I describe the representative accomplishments of my research, and current and future research projects more concretely. The postdocs and students in my group work on the particle physics side and/or gravity side, depending on their interests.

The list and cite summary of my publications can be found below.## Research accomplishments

### Inflation

#### Chaotic inflation and shift symmetry

Supergravity is the most fundamental theory with a scalar field that can lead to inflation. Though chaotic inflation is the most natural inflationary model, free from any initial-condition problems, for almost twenty years it was thought to be impossible to cause it naturally within supergravity due to the exponential growth of the potential. Contrary to this conventional wisdom, I, in collaboration with M. Kawasaki and T. Yanagida, have succeeded in realizing chaotic inflation naturally by introducing a shift symmetry. This symmetry is now regarded as an essential one to realize inflation. Though it is now known that chaotic inflation cannot be responsible for the generation of large scale structures in the universe at the late stages of the inflationary period, it is still an attractive mechanism to explain how naturally inflation happens.

#### The most general inflation models and ghost free conditions

The best method to discriminate inflation models proposed so far, and to deal with them comprehensively, is to consider the most general model. From the mathematical interest, more than 40 years ago, Horndeski proposed the most general single-field scalar-tensor theory with second-order equations of motion (to avoid ghost instabilities). On the other hand, the Generalized Galileon theory was proposed from a modern viewpoint. With T. Kobayashi and J. Yokoyama, I proved the equivalence of both theories and gave the generic formulae of primordial perturbations, which apply to almost all single-field inflation models proposed thus far. Recently, with D. Langlois, H. Motohashi, K. Noui, and T. Suyama, I gave conditions for the absence of ghosts associated with arbitrary higher time derivatives for a point particle system.

### Dark energy (current acceleration of the Universe)

#### k-essence

Recent observations have revealed that the Universe is now accelerating. With T. Chiba and T. Okabe, I proposed a completely new candidate for dark energy, in which a scalar field, with only a non-canonical kinetic term (no potential) as suggested from string theory, plays the role of dark energy. This new candidate was named k-essence and is still under intensive study.

#### Direct relation between inflation and dark energy

Prior to this work, no other had given a direct link between inflation and dark energy. With C. Ringeval, T. Suyama, T. Takahashi, and S. Yokoyama, I have shown that if a light scalar field is responsible for the current acceleration of the universe, such field would have acquired quantum fluctuations during inflation, which automatically determines its value at the end of the inflationary period, giving a definite relation between the energy scales of inflation and the current acceleration. More concretely, the inflation energy scale must be around TeV in this scenario. This work was the first to give a direct link between the energy scales of inflation and dark energy.

### Non-Gaussianity of primordial perturbations (Suyama-Yamaguchi inequality)

With T. Suyama, I have derived the generic (model-independent) relation between correlation functions of primordial density perturbations . In particular, if only one field is responsible for the primordial curvature perturbations, this inequality is saturated and effectively becomes an equality, whereas if the perturbations are due to multiple fields, this relation remains as an inequality. Thus, by inspecting it, one can identify the number of fields responsible for the primordial curvature perturbations. If by any chance this inequality is observationally seen to be violated, the paradigm of quantum fluctuations generated during inflation as the origin of the primordial curvature perturbations does not hold anymore. Therefore, this relation can serve as a smoking-gun of the (non)inflationary paradigm. Due to its significant importance, it is now called Suyama-Yamaguchi inequality, and, together with the Maldacenaâ€™s consistency relation, it has lead to a technique and a whole new research field, the so-called soft limit of the primordial perturbations correlation functions.

### Dark matter and baryon asymmetry

#### Dynamics of global strings and axion abundances

With M. Kawasaki and J. Yokoyama, I, for the first time, realized a field-theoretical simulation of global strings based on the global U(1) symmetry. We have confirmed the almost scaling properties of the global string system, in which a characteristic scale grows with the horizon scale. Recently, we have also found that there is a slight (logarithmic) deviation from the scaling regime and that the number of long strings per horizon volume for the global string system is still less than that for local strings system. The axion, which is one of the strong candidates for cold dark matter, is emitted from global strings which are formed as a result of the Peccei-Quinn symmetry breaking. The spectrum of axions emitted from such global strings had been under severe dispute for a long time. We gave the first realistic estimate for this spectrum, which is sharply peaked around the horizon scale, and yielding a more accurate estimate for the abundance of emitted axions. Thus, we derived an upper bound on the breaking scale of the Peccei-Quinn symmetry as 10^{12}GeV.

#### Baryogenesis from flat direction with neither baryon nor lepton number

In general, the flat directions of the scalar field in supersymmetric extensions of the standard model of particle physics carry baryon and/or lepton numbers, and hence it has been used in several baryogenesis and leptogenesis scenarios have been proposed so far. However, a flat direction with neither baryon nor lepton charge is usually considered to have nothing to do with baryo/leptogenesis. Contrary to this conventional wisdom, I showed with T. Chiba and F. Takahashi that, in case a flat direction has neither baryon nor lepton charge but has another global one, like a Peccei-Quinn charge, baryogenesis is still possible by virtue of an interaction violating another global symmetry in addition to baryon (lepton) symmetry. This scenario opens a new window for baryogenesis.

## Current and future research projects

The LHC experiments and the Planck satellite succeeded in discovering the Higgs particle and confirming the standard inflationary Universe, respectively. However, neither has yet found new signal beyond the standard models of particle physics and cosmology, unfortunately. Because of that, it is often said that there might be no hope in the future. But, I believe that the current epoch is just before the dawn of a new golden era. In order to open this era, we want to study topics beyond the framework of the standard models, and come up with new tools to probe them. Concrete themes are given below. More details will be given upon request if you are interested in joining our group.

- Cosmology as a collider
- The most general theories for inflation and dark energy
- Mystery of vacuum energy
- Beyond inflation and birth of the Universe
- Axion as a powerful dark matter candidate
- Small scale cosmological perturbations as a frontier
- Invention and establishment of new observational methods
- Non-local field theory