2022 Fiscal Year Annual Research Report
Time dependence of dark energy and microscopic theory
| 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, その他部局等, 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 rolling inflation / random walk / Fokker Planck equation / entangled entropy / inflaton potentia |
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| Outline of Annual Research Achievements |
The slow rolling inflation is dual to the random walk of conformal zero-mode. The O(N) enhancement of the two point function of conformal mode < ω2 >: N is the e-folding number, suppresses the slow roll parameters by O(N). The distribution functionof conformal mode ρt(ω) satisfies the Fokker Planck equation. Under the Gaussian approximation, FP equation boils down to a solvable first order partial differential equation (GFP).
The identical equation is obained by the thermodynamic arguments. We study two types of the solutions of GFP:(1) UV complete spacetime and (2) inflationary spacetime with power potentials. The concavity of entangled entropy ensures the potential for inflaton is also concave. The maximum entropy principle favors the scenario: The universe is (a) born with small e; and (b) grows large by inflation in the concave
potentials. We predict 1－ns = 0.02(0.016) and r = 0.08(0.066) for N = 50(60) at the pivot angle 0.002Mpc－1. We propose a scenario to produce the curvature perturbation in the right ball park.
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