Cosmological contribution from population III stars in ultracompact minihalos

In this work, we investigate the effect of Population~III~(Pop.~III) stars in ultracompact minihalos~(UCMHs) on the cosmic ionization history using the Planck observation data. Although high-redshift astrophysics is not understood yet, UCMHs could host the Pop.~III stars like the halos formed in the standard structure formation scenario. Such Pop.~III stars would emit ionizing photons during their main sequence and facilitate cosmic reionization in high redshifts. To study their effects on the global ionization, we model the cosmic reionization evolution based on the ``tanh"-type reionization model which is expressed by $z_{\mathrm{reio}}$ with additional two parameters characterizing the initial mass of UCMHs and the number density of UCMHs. We implement the Monte Carlo Markov Chain analysis with the latest Planck observation data for our reionization model. As the result, we found that if the UCMH initial mass is larger than $10^{8.4}\mathrm{M}_{\odot}$, the number density of UCMHs is strictly limited. Then we obtained the constraint on the amplitude of the primordial power spectrum through the constraint on the UCMH number density like $\mathcal{A}_{\zeta}\lesssim 10^{-8}$ in the scales, $k\lesssim 50\mathrm{Mpc}^{-1}$, when we assume that the standard ``tanh"-type reionization occurs by $z=3$, so that we set $z_{\mathrm{reio}}>3$.Comment: 12 pages, 7 figure

Translating nano-Hertz gravitational wave background into primordial perturbations taking account of the cosmological QCD phase transition

The evidence of the nano-Hertz stochastic gravitational wave (GW) background is reported by multiple pulsar timing array collaborations. While a prominent candidate of the origin is astrophysical from supermassive black hole binaries, alternative models involving GWs induced by primordial curvature perturbations can explain the inferred GW spectrum. Serendipitously, the nano-Hertz range coincides with the Hubble scale during the cosmological quantum chromodynamics (QCD) phase transition. The influence of the QCD phase transition can modify the spectrum of induced GWs within the nano-Hertz frequency range, necessitating careful analysis. We estimate GWs induced by power-law power spectra of primordial curvature perturbations taking account of the QCD phase transition. Then we translate the implication of the NANOGrav data into the constraint on the power spectrum of the primordial curvature perturbation, which suggests that one may miss the correct interpretation if neglecting the QCD effect. We also derive fitting formulae for their amplitude and scale dependence, helping to update the constraint in future experiments.Comment: 7 pages, 5 figure

Effective Monopole Action at Finite Temperature in SU(2) Gluodynamics

Effective monopole action at finite temperature in SU(2) gluodynamics is studied on anisotropic lattices. Using an inverse Monte-Carlo method and the blockspin transformation for space directions, we determine 4-dimensional effective monopole action at finite temperature. We get an almost perfect action in the continuum limit under the assumption that the action is composed of two-point interactions alone. It depends on a physical scale $b_s$ and the temperature $T$. The temperature-dependence appears with respect to the spacelike monopole couplings in the deconfinement phase, whereas the timelike monopole couplings do not show any appreciable temperature-dependence. The dimensional reduction of the 4-dimensional SU(2) gluodynamics ((SU(2))$_{4D}$) at high temperature is the 3-dimensional Georgi-Glashow model ($(GG)_{3D}$). The latter is studied at the parameter region obtained from the dimensional red uction. We compare the effective instanton action of $(GG)_{3D}$ with the timelike monopole action obtained from (SU(2))$_{4D}$. We find that both agree very well for $T \ge 2.4T_c$ at large $b$ region. The dimensional reduction works well also for the effective action.Comment: 34 pages, 23 figure

Gauge invariance of color confinement due to the dual Meissner effect caused by Abelian monopoles

The mechanism of non-Abelian color confinement is studied in SU(2) lattice gauge theory in terms of the Abelian fields and monopoles extracted from non-Abelian link variables without adopting gauge fixing. Firstly, the static quark-antiquark potential and force are computed with the Abelian and monopole Polyakov loop correlators, and the resulting string tensions are found to be identical to the non-Abelian string tension. These potentials also show the scaling behavior with respect to the change of lattice spacing. Secondly, the profile of the color-electric field between a quark and an antiquark is investigated with the Abelian and monopole Wilson loops. The color-electric field is squeezed into a flux tube due to monopole supercurrent with the same Abelian color direction. The parameters corresponding to the penetration and coherence lengths show the scaling behavior, and the ratio of these lengths, i.e, the Ginzburg-Landau parameter, indicates that the vacuum type is near the border of the type1 and type2 (dual) superconductor. These results are summarized that the Abelian fundamental charge defined in an arbitrary color direction is confined inside a hadronic state by the dual Meissner effect. As the color-neutral state in any Abelian color direction corresponds to the physical color-singlet state, this effect explains non-Abelian color confinement and supports the existence of a gauge-invariant mechanism of color confinement due to the dual Meissner effect caused by Abelian monopoles.Comment: 11 pages, 14 figure

The Dual Meissner Effect and Magnetic Displacement Currents

The dual Meissner effect is observed without monopoles in quenched $SU (2)$ QCD with Landau gauge-fixing. Magnetic displacement currents which are time-dependent Abelian magnetic fields play a role of solenoidal currents squeezing Abelian electric fields. Monopoles are not always necessary to the dual Meissner effect. The squeezing of the electric flux means the dual London equation and the massiveness of the Abelian electric fields as an asymptotic field. The mass generation of the Abelian electric fields is related to a gluon condensate $\neq 0$ of mass dimension 2.Comment: 4 pages, 5 Postscript figures, title modified, some references added, minor changes made ; Accepted for publication in Phys.Rev.Let

Entropy of monopoles from percolating cluster in quenched SU(2) QCD

The length distribution and the monopole action of the infrared monopole clusters are studied numerically in quenched SU(2) QCD. We determine the effective entropy of the monopole currents which turns out to be a descending function of the blocking scale, indicating that the effective degrees of freedom of the extended monopoles are getting smaller as the blocking scale increases.Comment: 3 pages, 3 figures, uses espcrc2.sty; Lattice2003(topology