2021 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, 理論センター, シニアフェロー (10195258)
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| Project Period (FY) |
2016-04-01 – 2023-03-31
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| Keywords | slow roll inflation / de Sitter entropy / conformal zeromode / Fokker-Planck equation / UV complete spacetime / inflationary spacetime / de Sitter duality |
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| Outline of Annual Research Achievements |
The scale invariance of the universe is slightly broken by slow roll parameters. It is likely the slow roll is dual to the random walk. We investigate the distribution function of the conformal zeromode. We identify de Sitter entropy SdS with the distribution entropy of the conformal zeromode ρ(ω). We have collected convincing support on our postulate. The semiclassical evidence is that the both are given by the gravitational coupling 1/g=logN/2 where g=GNH2/π and N is the e-folding number. We show the renormalized distribution function obeys gravitational Fokker-Planck equation (GFP) and Langevin equations . Under the Gaussian approximation, they boil down to a simple first order partial differential equation. The identical equation is derived by the thermodynamic arguments in the inflationary space-time. GFP determines the evolution of de Sitter entropy of the universe. It coincides with β function of g. We find two types of the solutions of GFP:(1) UV complete spacetime and (2) inflationary spacetime with power potentials. The maximum entropy principle favors the scenario: (a) born small epsilon; and (b) grow large by inflation. We like to convey the emerging notion of de Sitter duality. The inflationary universe: (bulk/geometrical) is dual to the stochastic space-time on the boundary (cosmological horizon ) as the both are the solutions of GFP.
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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 gravity has always been investigated from geometric point of view. Inflation theory is no exception. On the other hand, that approach leaves too many freedom. There is an alternative stochastic point of view. This approach relays on more microscopic point of view. Inflaton coud be understood as quantum effects. More systematically, stochastic equations on the boundary play the major role like the Einstein’s field equation. We derive Fokker Planck equation as the major apparatus to explore the universe. This dual approach has instant rewards. In fact FP equation becomes as important as the Einstein’s equation. We derive FP equation from the renormalization group. It can determine the evolution of the entropy of the universe. So each solution is a history of the universe.
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| Strategy for Future Research Activity |
From holographic perspective, we have formulated the FP equation for the conformal mode at the boundary, i.e., the horizon. The GFP is derived under the Gaussian approximation, which may be justifiable for small g = GNH2/π. The von Neumann entropy of conformal zero mode gives the quantum correction to the dS entropy S = 1/g. g(t) undergoes time evolution: i.e., a quantum-induced inflation picture.The FP equation has two types of solutions. One of them is the pre-inflation solution (3.28) which is UV complete . The other is the subsequent inflation solution (4.32) which is not UV complete but the inflation stops when epsilon grows up to 1. This transition scenario is supported by the expectation that the solution with dominant entropy is chosen.
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| Causes of Carryover |
コロナの影響により次年度使用額が生じた。主に国内旅費および国外旅費に使用する予定。リモート参加も活用した、国内外の研究者と議論及び情報交換を行うための、研究会参加費、及び論文による研究成果発表に関する費用にも充てる事を想定している。
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Research Products
(2 results)
