DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) is the future Japanese space gravitational wave antenna. DECIGO is expected to open a new window of observation for gravitational wave astronomy especially between 0.1 Hz and 10 Hz, revealing various mysteries of the universe such as dark energy, formation mechanism of supermassive black holes, and inflation of the universe. The pre-conceptual design of DECIGO consists of three drag-free spacecraft, whose relative displacements are measured by a differential Fabry-Perot Michelson interferometer. We plan to launch two missions, DECIGO pathfinder and pre-DECIGO first and finally DECIGO in 2024.

DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) is the future Japanese space gravitational wave antenna. It aims at detecting various kinds of gravitational waves between 1 mHz and 100 Hz frequently enough to open a new window of observation for gravitational wave astronomy. The pre-conceptual design of DECIGO consists of three drag-free satellites, 1000 km apart from each other, whose relative displacements are measured by a Fabry–Perot Michelson interferometer. We plan to launch DECIGO in 2024 after a long and intense development phase, including two pathfinder missions for verification of required technologies.

Based on a physical argument, we derive a new analytic formula for the amplitude of density perturbation at the threshold of primordial black hole formation in the Universe dominated by a perfect fluid with the equation of state p = wρc 2 for w ≥ 0. The formula gives δ UH Hc = sin, where δ UH Hc andδ c are the amplitude of the density perturbation at the horizon crossing time in the uniform Hubble slice and the amplitude measure used in numerical simulations, respectively, while the conventional one gives δ UH Hc = w and δ c = 3w(1 + w)/(5 + 3w). Our formula shows a much better agreement with the result of recent numerical simulations both qualitatively and quantitatively than the conventional formula. For a radiation fluid, our formula gives δ UH Hc = sin 2 ( √ 3π/6) ≃ 0.6203 andδ c = (2/3) sin 2 ( √ 3π/6) ≃ 0.4135. We also discuss the maximum amplitude and the cosmological implications of the present result.

We construct cosmological long-wavelength solutions without symmetry in general gauge conditions which are compatible with the long-wavelength scheme. We then specify the relationship among the solutions in different time slicings. Nonspherical long-wavelength solutions are particularly important for primordial structure formation in the epoch of very soft equations of state. Applying this general framework to spherical symmetry, we show the equivalence between longwavelength solutions in the constant mean curvature slicing with conformally flat spatial coordinates and asymptotic quasihomogeneous solutions in the comoving slicing with the comoving threading. We derive the correspondence relation between these two solutions and compare the results of numerical simulations of primordial black hole (PBH) formation in these two different approaches. To discuss the PBH formation, it is convenient and conventional to useδc, the value which the averaged density perturbation at threshold in the comoving slicing would take at horizon entry in the lowestorder long-wavelength expansion. We numerically find that within (approximately) compensated models, the sharper the transition from the overdense region to the Friedmann-Robertson-Walker universe is, the larger theδc becomes. We suggest that, for the equation of state p = (Γ − 1)ρ, we can apply the analytic formulas for the minimumδc,min ≃ [3Γ/(3Γ+2)] sin 2 π √ Γ − 1/(3Γ − 2) and the maximumδc,max ≃ 3Γ/(3Γ + 2). As for the threshold peak value of the curvature variable ψ0,c, we find that the sharper the transition is, the smaller the ψ0,c becomes. We analytically explain this intriguing feature qualitatively with a compensated top-hat density model. Using simplified models, we also analytically deduce an environmental effect that ψ0,c can be significantly larger (smaller) if the underlying density perturbation of much longer wavelength is positive (negative).

The production rate of primordial black holes is often calculated by considering a nearly Gaussian distribution of cosmological perturbations, and assuming that black holes will form in regions where the amplitude of such perturbations exceeds a certain threshold. A threshold ζ th for the curvature perturbation is somewhat inappropriate for this purpose, because it depends significantly on environmental effects, not essential to the local dynamics. By contrast, a threshold δ th for the density perturbation at horizon crossing seems to provide a more robust criterion. On the other hand, the density perturbation is known to be bounded above by a maximum limit δ max at the horizon entry, and given that δ th is comparable to δ max , the density perturbation will be far from Gaussian near or above the threshold. In this paper, we provide a new plausible estimate for the primordial black hole abundance based on peak theory. In our approach, we assume that the curvature perturbation is given as a random Gaussian field with the power spectrum characterized by a single scale, while an optimized criterion for PBH formation is imposed, based on the locally averaged density perturbation around the nearly spherically symmetric high peaks. Both variables are related by the full nonlinear expression derived in the long-wavelength approximation of general relativity. We do not introduce a window function which is usually introduced to obtain the scale dependence of the spectrum. The scale of the inhomogeneity is introduced as a random variable in the peak theory, and the scale dependent PBH fraction is automatically induced. We find that the mass spectrum is shifted to larger mass scales by one order of magnitude or so, compared to a conventional calculation. The abundance of PBHs becomes significantly larger than the conventional one, by many orders of magnitude, mainly due to the optimized criterion for PBH formation and the removal of the suppression associated with a window function.