Simultaneously probing the sound speed and equation of state of the early Universe with pulsar timing arrays

Recently, several major pulsar timing array (PTA) collaborations have assembled strong evidence for the existence of a gravitational-wave background at frequencies around the nanohertz regime. Assuming that the PTA signal is attributed to scalar-induced gravitational waves, we jointly employ the PTA data from the NANOGrav 15-year data set, PPTA DR3, and EPTA DR2 to probe the conditions of the early Universe. Specifically, we explore the equation of state parameter ($w$), the sound speed ($c_s$), and the reheating temperature ($T_\mathrm{rh}$), finding $w=0.60^{+0.32}_{-0.39}$, $c_s\gtrsim 0.09$, and $T_\mathrm{rh}\lesssim 0.2\,\mathrm{GeV}$ for a lognormal power spectrum of the curvature perturbation. Furthermore, we compute Bayes factors to compare different models against the radiation domination model ($c_s^2 = w = 1/3$), effectively excluding the pressure-less fluid domination model. Our study underscores the significance of scalar-induced gravitational waves as a powerful tool to explore the nature of the early Universe.Comment: 22 pages, 3 figures, 2 table

Constraining the Merger History of Primordial-Black-Hole Binaries from GWTC-3

Primordial black holes (PBHs) can be not only cold dark matter candidates but also progenitors of binary black holes observed by LIGO-Virgo-KAGRA (LVK) Collaboration. The PBH mass can be shifted to the heavy distribution if multi-merger processes occur. In this work, we constrain the merger history of PBH binaries using the gravitational wave events from the third Gravitational-Wave Transient Catalog (GWTC-3). Considering four commonly used PBH mass functions, namely the log-normal, power-law, broken power-law, and critical collapse forms, we find that the multi-merger processes make a subdominant contribution to the total merger rate. Therefore, the effect of merger history can be safely ignored when estimating the merger rate of PBH binaries. We also find that GWTC-3 is best fitted by the log-normal form among the four PBH mass functions and confirm that the stellar-mass PBHs cannot dominate cold dark matter.Comment: 11 pages, 8 figures, 2 tables; accepted for publication in PR

Constraints on peculiar velocity distribution of binary black holes using gravitational waves with GWTC-3

The peculiar velocity encodes rich information about the formation, dynamics, evolution, and merging history of binary black holes. In this work, we employ a hierarchical Bayesian model to infer the peculiar velocity distribution of binary black holes for the first time using GWTC-3 by assuming a Maxwell-Boltzmann distribution for the peculiar velocities. The constraint on the peculiar velocity distribution parameter is rather weak and uninformative with the current GWTC-3 data release. However, the measurement of the peculiar velocity distribution can be significantly improved with the next-generation ground-based gravitational wave detectors. For instance, the uncertainty on the peculiar velocity distribution parameter will be measured within $\sim$ 10\% with $10^3$ golden binary black hole events for the Einstein Telescope. We, therefore, conclude that our statistical approach provides a robust inference for the peculiar velocity distribution.Comment: 15 pages, 2 figures

Establishment of OPG Transgenic Mice and the Effect of OPG on Bone Microarchitecture

Osteoprotegerin (OPG) plays a determinant role in regulating bone metabolism, but the effect of OPG on bone microarchitecture needs to be further elucidated. We attempted to construct pCI-hOPGp-mOPG vector containing human OPG promoter and FLAG tag and to microinject vector into fertilized zygotes from C57BL/6J × CBA mice to prepare transgenic mice. The OPG transgenic positive mice were identified by PCR and western blotting. Twelve-week-old OPG transgenic mice (OPG-Tg mice) and wild-type mice (WT mice) were utilized in the study of bone microarchitecture. Microcomputed tomography (micro-CT) data showed that compared with WT mice, the tibia of OPG-Tg mice showed an increased volumetric BMD (vBMD), tissue BMD (tBMD), trabecular thickness (Tb.Th), and trabecular number (Tb.N), and a decreased trabecular separation (Th.Sp) (P<0.05) . The cortical bone microarchitecture parameters, such as cortical area (Ct.Ar), cortical thickness (Ct.Th), cortical BMD (Ct.BMD), cortical BMC (Ct.BMC), BMD, and BMC of femur, were increased, and the inner perimeter (In.Pm) was decreased, in OPG-Tg mice, compared to those in WT mice (P<0.05). The established OPG transgenic mouse model could be valuable for further studying the biological significance and gene regulation of OPG in vivo

Dirac-Electrons-Mediated Magnetic Proximity Effect in Topological Insulator / Magnetic Insulator Heterostructures

The possible realization of dissipationless chiral edge current in a topological insulator / magnetic insulator heterostructure is based on the condition that the magnetic proximity exchange coupling at the interface is dominated by the Dirac surface states of the topological insulator. Here we report a polarized neutron reflectometry observation of Dirac electrons mediated magnetic proximity effect in a bulk-insulating topological insulator (Bi$_{0.2}$Sb$_{0.8}$)$_{2}$Te$_{3}$ / magnetic insulator EuS heterostructure. We are able to maximize the proximity induced magnetism by applying an electrical back gate to tune the Fermi level of topological insulator to be close to the charge neutral point. A phenomenological model based on diamagnetic screening is developed to explain the suppressed proximity induced magnetism at high carrier density. Our work paves the way to utilize the magnetic proximity effect at the topological insulator/magnetic insulator hetero-interface for low-power spintronic applications.Comment: 5 pages main text with 4 figures; 2 pages supplemental materials; suggestions and discussions are welcome