| 研究実績の概要 |
In September 2022 I finished a paper with my student: "Primordial Black Hole Formation in Starobinsky's Linear Potential Model", Shi Pi and Jianing Wang, e-Print: 2209.14183, accepted by JCAP. We revisit Starobinsky model with a piecewise linear potential, and find the exact position and height of the maximum of the power spectrum of the curvature perturbation, which is useful for determining the primordial black hole (PBH) formation.
In November 2022 I finished a paper with Prof. Misao Sasaki: "Logarithmic Duality of the Curvature Perturbation", Shi Pi and Misao Sasaki, e-Print: 2211.13932. We studied single-field inflation with a piecewise quadratic potential. By using (classical) δΝ formalism, we found that in general the curvature perturbation can be expressed by a sum of logarithmic functions of the inflaton field perturbation δφ, while each logarithmic expression has a dual expression due to the second-order nature of the equation of motion. We clarified the condition under which a single logarithm dominates, which yields either the renowned "exponential tail" of the PDF of R or a Gumbel-distribution-like tail. Our formula unifies all previous works on the fully nonlinear PDFs of the curvature perturbation, including USR inflation, slow-roll inflation, constant-roll inflation, curvaton scenario, etc., and reveals new analytically solvable models. It sheds light on accurate calculation of the PBH formation and the induced gravitational wave spectrum.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
Probing the primordial black holes (PBHs) by induced gravitational waves (GWs) depends crucially on the accurate calculating the PBH mass function, as well as the GW spectrum, both of which relies on the statistics of the primordial curvature perturbation. Our research in 2022 found the fully nonlinear probability distribution function (PDF) of the curvature perturbation in a quite broad class of inflation models which can enhance the power spectrum. Our conclusion is that, for single field inflation, enhancement of the power spectrum is usually accompanied by a large non-Gaussianity, which should be taken into account carefully in the calculation of PBH abundance and induced GW spectrum. Taking into account such a fully nonlinear PDF, the relation between PBH mass function and the induced GW spectrum can made more accurate, which sheds light on indirect detection of PBHs by the induced GWs.
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| 今後の研究の推進方策 |
As now we know the fully nonlinear PDF of the curvature perturbation, we can proceed to realize our goal of probing the PBHs by the induced GWs. Here are some concrete projects we are going to do.
(1) Check whether such a PDF is consistent with the stochastic approach of inflation.
(2) Calculate the PBH mass function from such an fully-nonlinear PDF, by the peak theory of random fields and by considering an enhanced power spectrum of finite width.
(3) Use the result of the induced GWs from the non-Gaussian curvature perturbation, constrain the PBH abundance by the sensitivity curves of the pulsar timing arrays, space-borne interferometers, and LIGO O5.
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