There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

The combination of seven-year data from WMAP and improved astrophysical data rigorously tests the standard cosmological model and places new constraints on its basic parameters and extensions. By combining the WMAP data with the latest distance measurements from the baryon acoustic oscillations (BAO) in the distribution of galaxies and the Hubble constant (H0) measurement, we determine the parameters of the simplest six-parameter ΛCDM model. The power-law index of the primordial power spectrum is ns = 0.968 ± 0.012 (68% CL) for this data combination, a measurement that excludes the Harrison–Zel’dovich–Peebles spectrum by 99.5% CL. The other parameters, including those beyond the minimal set, are also consistent with, and improved from, the five-year results. We find no convincing deviations from the minimal model. The seven-year temperature power spectrum gives a better determination of the third acoustic peak, which results in a better determination of the redshift of the matter-radiation equality epoch. Notable examples of improved parameters are the total mass of neutrinos, � mν < 0.58 eV (95% CL), and the effective number of neutrino species, Neff = 4.34 +0.86 −0.88 (68% CL), which benefit from better determinations of the third peak and H0. The limit on a constant dark energy equation of state parameter from WMAP+BAO+H0, without high-redshift Type Ia supernovae, is w =− 1.10 ± 0.14 (68% CL). We detect the effect of primordial helium on the temperature power spectrum and provide a new test of big bang nucleosynthesis by measuring Yp = 0.326 ± 0.075 (68% CL). We detect, and show on the map for the first time, the tangential and radial polarization patterns around hot and cold spots of temperature fluctuations, an important test of physical processes at z = 1090 and the dominance of adiabatic scalar fluctuations. The seven-year polarization data have significantly improved: we now detect the temperature–E-mode polarization cross power spectrum at 21σ , compared with 13σ from the five-year data. With the seven-year temperature–B-mode cross power spectrum, the limit on a rotation of the polarization plane due to potential parity-violating effects has improved by 38% to Δα =− 1. 1 ± 1. 4(statistical) ± 1. 5(systematic) (68% CL). We report significant detections of the Sunyaev–Zel’dovich (SZ) effect at the locations of known clusters of galaxies. The measured SZ signal agrees well with the expected signal from the X-ray data on a cluster-by-cluster basis. However, it is a factor of 0.5–0.7 times the predictions from “universal profile” of Arnaud et al., analytical models, and hydrodynamical simulations. We find, for the first time in the SZ effect, a significant difference between the cooling-flow and non-cooling-flow clusters (or relaxed and non-relaxed clusters), which can explain some of the discrepancy. This lower amplitude is consistent with the lower-than-theoretically expected SZ power spectrum recently measured by the South Pole Telescope Collaboration.

/pdf/seven-year-wilkinson-microwave-anisotropy-probe-wmap-19dgu0rhy7.pdf

Seven-year wilkinson microwave anisotropy probe (wmap *) observations: cosmological interpretation

This paper presents the first cosmological results based on Planck measurements of the cosmic microwave background (CMB) temperature and lensing-potential power spectra. We find that the Planck spectra at high multipoles (l ≳ 40) are extremely well described by the standard spatially-flat six-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations. Within the context of this cosmology, the Planck data determine the cosmological parameters to high precision: the angular size of the sound horizon at recombination, the physical densities of baryons and cold dark matter, and the scalar spectral index are estimated to be θ∗ = (1.04147 ± 0.00062) × 10-2, Ωbh2 = 0.02205 ± 0.00028, Ωch2 = 0.1199 ± 0.0027, and ns = 0.9603 ± 0.0073, respectively(note that in this abstract we quote 68% errors on measured parameters and 95% upper limits on other parameters). For this cosmology, we find a low value of the Hubble constant, H0 = (67.3 ± 1.2) km s-1 Mpc-1, and a high value of the matter density parameter, Ωm = 0.315 ± 0.017. These values are in tension with recent direct measurements of H0 and the magnitude-redshift relation for Type Ia supernovae, but are in excellent agreement with geometrical constraints from baryon acoustic oscillation (BAO) surveys. Including curvature, we find that the Universe is consistent with spatial flatness to percent level precision using Planck CMB data alone. We use high-resolution CMB data together with Planck to provide greater control on extragalactic foreground components in an investigation of extensions to the six-parameter ΛCDM model. We present selected results from a large grid of cosmological models, using a range of additional astrophysical data sets in addition to Planck and high-resolution CMB data. None of these models are favoured over the standard six-parameter ΛCDM cosmology. The deviation of the scalar spectral index from unity isinsensitive to the addition of tensor modes and to changes in the matter content of the Universe. We find an upper limit of r0.002< 0.11 on the tensor-to-scalar ratio. There is no evidence for additional neutrino-like relativistic particles beyond the three families of neutrinos in the standard model. Using BAO and CMB data, we find Neff = 3.30 ± 0.27 for the effective number of relativistic degrees of freedom, and an upper limit of 0.23 eV for the sum of neutrino masses. Our results are in excellent agreement with big bang nucleosynthesis and the standard value of Neff = 3.046. We find no evidence for dynamical dark energy; using BAO and CMB data, the dark energy equation of state parameter is constrained to be w = -1.13-0.10+0.13. We also use the Planck data to set limits on a possible variation of the fine-structure constant, dark matter annihilation and primordial magnetic fields. Despite the success of the six-parameter ΛCDM model in describing the Planck data at high multipoles, we note that this cosmology does not provide a good fit to the temperature power spectrum at low multipoles. The unusual shape of the spectrum in the multipole range 20 ≲ l ≲ 40 was seen previously in the WMAP data and is a real feature of the primordial CMB anisotropies. The poor fit to the spectrum at low multipoles is not of decisive significance, but is an “anomaly” in an otherwise self-consistent analysis of the Planck temperature data.

/pdf/planck-2013-results-xvi-cosmological-parameters-12gx9fa74h.pdf

Planck 2013 results. XVI. Cosmological parameters

We study the big-bang nucleosynthesis (BBN) with the long-lived exotic particle, called X. If the lifetime of X is longer than \sim 0.1 sec, its decay may cause non-thermal nuclear reactions during or after the BBN, altering the predictions of the standard BBN scenario. We pay particular attention to its hadronic decay modes and calculate the primordial abundances of the light elements. Using the result, we derive constraints on the primordial abundance of X. Compared to the previous studies, we have improved the following points in our analysis: The JETSET 7.4 Monte Carlo event generator is used to calculate the spectrum of hadrons produced by the decay of X; The evolution of the hadronic shower is studied taking account of the details of the energy-loss processes of the nuclei in the thermal bath; We have used the most recent observational constraints on the primordial abundances of the light elements; In order to estimate the uncertainties, we have performed the Monte Carlo simulation which includes the experimental errors of the cross sections and transfered energies. We will see that the non-thermal productions of D, He3, He4 and Li6 provide stringent upper bounds on the primordial abundance of late-decaying particle, in particular when the hadronic branching ratio of X is sizable. We apply our results to the gravitino problem, and obtain upper bound on the reheating temperature after inflation.

Big-Bang nucleosynthesis and hadronic decay of long-lived massive particles

Can modified gravity explain accelerated cosmic expansion

We propose a chaotic inflation model in supergravity. In the model the K\"ahler potential has a Nambu-Goldstone--type shift symmetry of the inflaton chiral multiplet which ensures the flatness of the inflaton potential beyond the Planck scale. We show that chaotic inflation naturally takes place by introducing a small breaking term of the shift symmetry in the superpotential. This may open a new branch of model building for inflationary cosmology in the framework of supergravity.

Natural chaotic inflation in supergravity

We derive big-bang nucleosynthesis (BBN) constraints on both unstable and stable gravitino taking account of recent progress in theoretical study of the BBN processes as well as observations of primordial light-element abundances In the case of unstable gravitino, we set the upper limit on the reheating temperature assuming that the primordial gravitinos are mainly produced by the scattering processes of thermal particles For stable gravitino, we consider B-ino, stau, and sneutrino as the next-to-the-lightest supersymmetric particle and obtain constraints on their properties Compared with the previous works, we improved the following points: (i) we use the most recent observational data, (ii) for gravitino production, we include contribution of the longitudinal component, and (iii) for the case with unstable long-lived stau, we estimate the bound-state effect of stau accurately by solving the Boltzmann equation

Big-bang nucleosynthesis and gravitinos

The late-time entropy production by massive particle decay induces various cosmological effects in the early epoch and modifies the standard scenario. We investigate the thermalization process of the neutrinos after entropy production by solving the Boltzmann equations numerically. We find that if the large entropy is produced at $t\ensuremath{\sim}1 \mathrm{sec},$ the neutrinos are not thermalized very well and do not have the perfect Fermi-Dirac distribution. Then the freeze-out value of the neutron to proton ratio is altered considerably and the produced light elements, especially ${}^{4}\mathrm{He},$ are drastically changed. Comparing with the observational light element abundances, we find that ${T}_{R}\ensuremath{\lesssim}0.7 \mathrm{MeV}$ is excluded at 95 % C.L. We also study the case in which the massive particle has a decay mode into hadrons. Then we find that ${T}_{R}$ should be a little higher, i.e., ${T}_{R}\ensuremath{\gtrsim}2.5$--4 MeV, for the hadronic branching ratio ${B}_{h}{=10}^{\ensuremath{-}2}\ensuremath{-}1.$ The possible influence of late-time entropy production on the large scale structure formation and temperature anisotropies of cosmic microwave background is studied. It is expected that the future satellite experiments (MAP and PLANCK) to measure anisotropies of cosmic microwave background radiation temperature will be able to detect the vestige of the late-time entropy production as a modification of the effective number of the neutrino species ${N}_{\ensuremath{\nu}}^{\mathrm{eff}}.$

Masahiro Kawasaki

Papers

Big-Bang nucleosynthesis and hadronic decay of long-lived massive particles

Can modified gravity explain accelerated cosmic expansion

Natural chaotic inflation in supergravity

Big-bang nucleosynthesis and gravitinos

MeV-scale reheating temperature and thermalization of the neutrino background