2018 Fiscal Year Research-status Report
| Project/Area Number |
16K05336
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| Research Institution | High Energy Accelerator Research Organization |
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Principal Investigator |
北澤 良久 大学共同利用機関法人高エネルギー加速器研究機構, 素粒子原子核研究所, 教授 (10195258)
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Keywords | Liouville action / 2d de Sitter space / a slow roll inflation / de Sitter entropy / cosmological constant / super horizon modes / von-Neumann entropy |
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| Outline of Annual Research Achievements |
We investigate a solution of the exactly renormalized Liouville action to foresee the fate of the 2-dimensional de Sitter space. We work in the semiclassical region with a large matter central charge $c$. Instead of de Sitter expansion, it performs a slow roll inflation with the parameters $\epsilon=(1/2)\eta =6/c$. An inflaton field is induced in the effective theory to describe quantum effects of the Liouville theory. The geometric entropy increases logarithmically with the Hubble radius. We propose that de Sitter entropy is carried by super horizon modes of the metric. We formulate a gravitational Fokker-Planck equation to elucidate the Brownian process at the horizon: the super horizon modes are constantly jolted by new comers. We show that such a built-in entropy generating process diffuses the cosmological constant. We evaluate von Neumann entropy associated with the distribution function of super horizon modes.It always increases under Fokker-Planck equation in a consistent way with semiclassical estimates.The maximum entropy principle operates in quantum gravity. An analogous entropy production mechanism at the horizon might have increased the Hubble radius much beyond the microscopic physics scale in the universe.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
The de Sitter space is known to possess large entropy. It scales inverse square of the cosmological constant. It is crucial to understand the structure of space-time and geometric entropy or more general information associated with. We investigate this problem in 2-dimensional toy model (Liouville thoery) besause it allows us deep penetration of this problem. We obtained a semiclassical formula for geometric entropy of 2d de Sitter space. In the semiclassical region, it increases logarithmically with the size of the universe. Simultaneously the geometric entropy decreases. We have identified the geometric entropy of 2d-de Sitter space with the von-Neumann entropy of super-horizon modes of the conformal degrees of metric. We have found several evidences of this identification.
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| Strategy for Future Research Activity |
We have investigated Dark Energy in search for the fundamental theory which explains it. We have paid a special attention to the existence of the cosmological horizon and accumulation of super horizon modes. We have pointed out that super horizon modes played an important role in the evolution of the universe. Of course, it has seeded the density fluctuation to form large scale structure. Furthermore we have shown that it offers a mechanism to grow the size of universe much beyond microscopic scale of physics through entropy production at the horizon in a 2d toy model. Remarkably inflaton field appears as a quantum gravity effect raising a possibility of eliminating many theoretical uncertainty. Encouraged by the success of 2d toy model, we plan to investigate 4d de Sitter space.
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Research Products
(3 results)
