Impact of small scale inhomogeneities on observations of standard candles

We investigate the effect of small scale inhomogeneities on standard candle observations, such as type Ia supernovae (SNe) observations. Existence of the small scale inhomogeneities may cause a tension between SNe observations and other observations with larger diameter sources, such as the cosmic microwave background (CMB) observation. To clarify the impact of the small scale inhomogeneities, we use the Dyer-Roeder approach. We determined the smoothness parameter $\alpha(z)$ as a function of the redshift $z$ so as to compensate the deviation of cosmological parameters for SNe from those for CMB. The range of the deviation which can be compensated by the smoothness parameter $\alpha(z)$ satisfying $0\leq\alpha(z)\leq1$ is reported. Our result suggests that the tension may give us the information of the small scale inhomogeneities through the smoothness parameter.Comment: 10 pages, 4 figure

The basics of primordial black hole formation and abundance estimation

This paper is a biased review of the primordial black hole (PBH) formation and abundance estimation. We first review the three-zone model for PBH formation to help an intuitive understanding of the PBH formation process. Then, for more accurate analyses, we introduce necessary tools such as cosmological long-wavelength solutions, the definition of the mass and compaction function in a spherically symmetric spacetime and peak theory. Combining all these tools, we calculate the PBH mass spectrum for the case of the monochromatic curvature power spectrum as a demonstration.Comment: Review paper, 37 pages, 6 figure