arXiv subjects

Hayami Iizuka

Publications and source records attributed to Hayami Iizuka.

6 recordsLinked to original sources

arXiv2026

Discrete self-similarity imprints on primordial-black-hole mass functions

We study how discrete self-similarity (DSS) in the critical behavior of scalar-field collapse is imprinted on primordial-black-hole (PBH) mass functions. Using the DSS-modulated critical scaling law found in cosmological simulations, we propagate the near-threshold mass map into normalized PBH mass functions during a {kination} era. We compare Gaussian window function, $k$-space top-hat window function, and real-space top-hat window function, together with a real-space top-hat window function multiplied by a kination transfer function. We find that critical behavior in gravitational collapse produces an irreducible minimum width even for an infinitesimally narrow primordial spectrum. DSS then modulates this critical-scaling profile, generating approximately log-periodic features in mass. At fixed horizon mass, successive equal-phase points of the DSS-modulated critical mass map satisfy $Δ\ln M_{\rm PBH}=γP_{\rm ln}$. Consequently, in the narrow-spectrum limit, the corresponding structures in the final mass function are expected to satisfy $Δ\ln m\simeqγP_{\rm ln}$, or $m_{n+1}/m_n\simeq5.6$, for the fiducial Choptuik DSS parameters $γ$ and $P_{\rm ln}$. For broad primordial spectra, the convolution over horizon masses dephases the DSS pattern and progressively washes out the critical substructure. We normalize the mass functions so that we may primarily study the profile shape and the survival of DSS substructure, rather than the absolute PBH abundance. These results provide a bridge between cosmological DSS collapse simulations and PBH phenomenology including population observables.

gr-qc↗

arXiv2026

COSMOS: A numerical relativity code specialized for PBH formation

Primordial black holes (PBHs) are black holes generated in the early universe without having gone through stellar evolution. In the standard formation process, PBHs are formed from super-horizon primordial fluctuations with non-linearly large initial amplitude. In order to simulate the non-linear gravitational dynamics of PBH formation, one has to rely on numerical relativity solvers to approximate the solution of the Einstein equations. COSMOS is a C++ package for solving the Einstein equations in 3+1 dimensions, providing simple tools for the simulation of PBH formation. In order to resolve the collapsing region, non-Cartesian scale-up coordinates and a fixed mesh-refinement procedure are implemented. In COSMOS, a massless scalar field and a perfect fluid with a linear equation of state are implemented as matter fields. To achieve a practically acceptable computational speed, OpenMP is used for the parallelization. COSMOS has no other dependencies, which makes for an easier installation.

gr-qc↗

arXiv2026

Primordial black holes in excursion set theory: Formation probabilities, mass functions, and window functions

We study the mass function of primordial black holes (PBHs) within the excursion-set theory, in which the response of the stochastic density contrast to the variation of the coarse-graining scale is described by colored noises. For several window functions often used in the literature, we investigate how this choice affects the formation probability as well as the resultant mass function of PBHs. It is found that the low-mass tail of the mass function differs from the one predicted from Carr's formula. The difference comes from the prevalence of correlated noises, by which degeneracy of the formation probabilities ceases to exist. Nevertheless, Carr's formula still provides a practical estimation in the vicinity of the characteristic mass scale, as long as a smooth window function in Fourier space is used.

astro-ph.CO↗

arXiv2026

Cosmological long-wavelength solutions in non-adiabatic multi-fluid systems

We develop a formulation of nonlinear cosmological perturbations on superhorizon scales in multi-fluid systems. It is based on the Arnowitt-Deser-Misner formalism combined with a spatial gradient expansion characterized by a small expansion parameter defined as the ratio of the comoving wavenumber to the Hubble scale. The background spacetime is assumed to be a flat Friedmann-Lemaitre-Robertson-Walker universe. Within this framework, we explicitly construct nonlinear long-wavelength solutions for cosmological perturbations. Since multi-fluid systems are inherently non-adiabatic, these solutions admit both adiabatic and entropy modes already at leading nonlinear order. We define adiabatic and entropy perturbations and discuss the non-uniqueness in defining pure entropy perturbations. Using different choices of pure entropy initial conditions, we analyze the time evolution of physical quantities such as the curvature perturbation and density perturbations in the geodesic slicing for two-fluid systems.

gr-qc↗

arXiv2025

Geometrical origin for the compaction function for primordial black hole formation

We propose a geometrical origin for the Shibata-Sasaki compaction function, which is known to be a reliable indicator of primordial black hole formation at least during radiation domination. In the long-wavelength limit, we identify it with a compactness function in the static spacetime obtained by removing the cosmological scale factor from the metric and this explains why it cannot be greater than $1/2$. If its maximum is below $1/2$, the perturbation is of type I. If its maximum equals $1/2$, it corresponds to an extremal surface, which is simultaneously a bifurcating trapping horizon and admits a circular photon orbit in the static spacetime. In the long-wavelength regime of the physical expanding Universe, the Shibata-Sasaki compaction reaches its maximum value of $1/2$ at maximal and minimal surfaces on the constant time spacelike hypersurface, which feature a type II perturbation and both correspond to photon spheres expanding along with the cosmological expansion. Thus, the Shibata-Sasaki compaction measures how close to the type II configuration the perturbed region is.

gr-qc↗

arXiv2024

New series expansion method for the periapsis shift

We propose a new series expansion method for the periapsis shift. The method formulates the periapsis shift in various spacetimes analytically without using special functions and provides simple and highly accurate approximate formulae. We derive new series representations for the periapsis shift in the Kerr and the Chazy-Curzon spacetimes by using the method, where the expansion parameter is defined as the eccentricity divided by the non-dimensional quantity that vanishes in the limit of the innermost stable circular orbit. That is to say, the expansion parameter denotes how eccentric the orbit is and how close it is to the innermost stable circular orbit. The smaller the eccentricity, the higher the accuracy of the formulae that are obtained by truncating the new series representations up to a finite number of terms. If the eccentricity is sufficiently small, the truncated new representations have higher accuracy than the post-Newtonian expansion formulae even in strong gravitational fields where the convergence of the post-Newtonian expansion formula is not guaranteed. On the other hand, even if the orbit is highly eccentric, the truncated new representations have comparable or higher accuracy than the post-Newtonian expansion formulae if the semi-major axis is sufficiently large. An exact formula for the periapsis shift of the quasi-circular orbit in the Chazy-Curzon spacetime is also obtained as a special case of the new series representation.

gr-qc↗