Theoretical modeling on the Early Universe

String theory has a much richer set of fundamental degree of freedom, consisting of D-branes. Inspired by such speculation, recently a new paradigm on the early universe has been proposed, the so-called brane-world. Moreover, a cosmological scenario based on by such string theory including branes, is called string cosmology. In string cosmology, brane inflation such as the DBI inflation, is so attractive, because one may understand the origin of inflaton as the position of moving brane. In brane inflationary scenario, two branes approach each other, that is related to inflation in our 4-dimensional universe, and then collide. Collision is related to some mechanism to connect the universe with a hot big bang (reheating of the universe). The fluctuations generated during inflation, evolve through such dynamical events of background spacetime given by dynamics of branes. Namely, it is important to study dynamics of branes in string cosmology to research full story of primordial fluctuations. 。

Nonlinear cosmological perturbation theory

In order to estimate the primordial non-Gaussianity, nonlinear cosmological perturbation theory is so important. Cosmological perturbations on superhorizon scales have been studied extensively in the so-called separate universe approach or delta N- formalism. These approaches are powerful tool to estimate non-Gaussianity since the evolution of curvature perturbation can be described only by background quantities and it is easy to calculate. However, their formalism are essentially the leading-order approximation to the spatial gradient expansion and many of the previous studies were confined to it. Higher order corrections to the leading-order results can be important to get more detailed information about non-Gaussianity with the future precision observations. Especially, in order to calculate non-Gaussianity due to a temporary non-slow roll stage on superhorizon scales, the decaying mode of the curvature perturbation plays an important role, which can be ignored in the leading-order approximation, i.e. $\delta N$-formalism. We have developed a theory of nonlinear superhorizon perturbations and obtained a general solution valid up to the next-leading order in the gradient expansion for a single scalar field with non-canonical kinetic terms and a general potential and found the solution satisfies a nonlinear second-order differential equation as a natural extension of the equation for the linear curvature perturbation on the comoving hypersurface. Then we formulate a general method to match a perturbation solution accurate to standard n-th-order perturbation inside the horizon to our nonlinear solution accurate to second-order in the gradient expansion. We call this formalism \underline Beyond delta N-formalism, which is powerful tool to be applied to a temporary violation of slow-roll conditions for a general single scalar field.

CMB bispectrum estimator

It is important to derive direct information about primordial perturbations generated by inflaton from the observational data of the CMB temperature anisotropy. As for the direct probe of primordial non-Gaussiantiy, the current constraints are studied when some shape of bispectrum is determined as an assumption: local, equilateral and orthogonal type, but it is more suitable to investigate any shapes of bispectrum. P. Shellard and his collaborators can provide the best constraints on the non-Gaussian parameters in future observations such as PLANCK for any non-separable primordial and CMB bispectrum from an observational map. They develop a mode expansion estimator methodology by using a basis function constructed from polynomial products which can be self-orthogonal with respect to the inner product in the three-dimensional domain of allowed multipoles. We focus on the feature model which has some feature in the power spectrum, for example that is generated by a sudden change of inflaton's potential slope. Actually, Ichiki, Yokoyama and Nagata 09 shows that there exists some local feature located at the multipole l=120, which gives a violation of scale-invariant and may be related to a violation of slow-roll condition which we focus on in the first study described above. These local features in the CMB power spectrum are also found as several sharp glitches in the WMAP data corresponding to l=20-40, that are famous and most intensively studied. Shellard et.al. have investigated the non-scaling feature models for a particular feature scale l>150, however, we wish to improve it around l=120. The localized feature model is also a hot topic on the theoretical side and we have constructed varying sound speed model as a new scenario.