Brane Gravity and Fundamental Problems in Cosmology

弦理论中的“膜”给出了关于万有引力的新概念，由于它可能导致宇宙学的新范式，近年来得到了广泛的研究。在本研究项目中，我们从膜世界的角度系统地分析了宇宙学的基本问题，以研究膜引力的基本和重要问题，以及膜宇宙学的新范式。特别是在研究新的膜引力理论时，我们讨论了宇宙学中最重要的课题，如“暗能量”、“宇宙常数问题”、“宇宙的创造”和“宇宙奇点”。我们主要分析了以下三个主题：(1)基于膜碰撞的非常规早期宇宙模型的研究考虑到自引力，我们分析了一个膜碰撞，证明了由于引力不稳定性而形成的时空奇点。我们还研究了通过膜碰撞在宇宙中创造物质（物质的起源）的可能性。(2)基于弦理论的暴胀模型研究我们提出了基于弦理论的新的暴胀模型。我们研究了超弦理论中通过量子修正出现的高曲率项。虽然我们发现了宇宙的充分膨胀，但我们需要对初始条件进行微调。这表明我们必须找到合适的里奇曲率张量和黎曼曲率张量的校正项。(3)基于弦理论的黑洞解的构造我们提出了在弦理论中寻找黑洞解的新方法。利用BPS方程对传统方法进行了推广。我们得到了一个新的黑洞（笼状黑洞）解。

New idea of gravitation is given from a "brane" in string theory, and it has recently been intensively studied because it may lead to new paradigm of cosmology. In the present research project, we have analyzed systematically fundamental problems in cosmology from the view point of a brane world in order to study new subjects such as what is the fundamental and important in brane gravity or what will be new paradigm of brane cosmology. Especially, studying new gravitational theory with a brane, we have discussed most important subjects in cosmology such as "dark energy", "cosmological constant problem", "creation of the universe" and "cosmological singularity". We have analyzed mainly the following three subjects:(1) The study of the unconventional early universe models based on brane collisionTaking into account self-gravity, we have analyzed a brane collision and shown that a spacetime singularity is formed because of gravitational instability. We have also studied the possibility of creation of matter (the origin of matter) in the universe via a brane collision.(2) The study of the inflation models based on string theoryWe have proposed new inflationary model based on string theory. We have studied the higher curvature terms which appear via quatum corrections in superstring theory. Although we find sufficient expansion of the universe, we need a fine tuning of initial conditions. It suggests that we have to find the proper correction terms with the Ricci curvature tensor as well as the Riemann one.(3) The construction of black hole solutions based on string theoryWe have presented new method to find black hole solutions in string theory. It is generalization of the conventional method using the BPS equations. We have obtained a new black hole (a caged black hole) solution.