Through analytic techniques veriÐed by numerical calculations, we establish general relations between the matter and cosmic microwave background (CMB) power spectra and their dependence on parameters on small scales. Fluctuations in the CMB, baryons, cold dark matter (CDM), and neutrinos receive a boost at horizon crossing. Baryon drag on the photons causes alternating acoustic peak heights in the CMB and is uncovered in its bare form under the photon di †usion scale. Decoupling of the photons at last scattering and of the baryons at the end of the Compton drag epoch freezes the di †usion-damped acoustic oscillations into the CMB and matter power spectra at di †erent scales. We determine the dependence of the respective acoustic amplitudes and damping lengths on fundamental cosmological parameters. The baryonic oscillations, enhanced by the velocity overshoot e †ect, compete with CDM Ñuctuations in the present matter power spectrum. We present new exact analytic solutions for the cold dark matter Ñuctuations in the presence of a growth-inhibiting radiation and baryon background. Combined with the acoustic contributions and baryonic infall into CDM potential wells, this provides a highly accurate analytic form of the small-scale transfer function in the general case. Subject headings : cosmic microwave background È cosmology : theory È dark matter È elementary particles È large-scale structure of universe

We use cosmological simulations to study the origin of primordial star-forming clouds in a ÃCDM universe, by following the formation of dark matter halos and the cooling of gas within them. To model the physics of chemically pristine gas, we employ a nonequilibrium treatment of the chemistry of nine species (e À , H, H + , He, He + , He ++ , H 2 , H þ 2 , H À ) and include cooling by molecular hydrogen. By considering cosmological volumes, we are able to study the statistical properties of primordial halos, and the high resolution of our simulations enables us to examine these objects in detail. In particular, we explore the hierarchical growth of bound structures forming at redshifts z % 25 30 with total masses in the range %10 5 10 6 M . We find that when the amount of molecular hydrogen in these objects reaches a critical level, cooling by rotational line emission is efficient, and dense clumps of cold gas form. We identify these '' gas clouds '' as sites for primordial star formation. In our simulations, the threshold for gas cloud formation by molecular cooling corresponds to a critical halo mass of %5 Â 10 5 h À1 M , in agreement with earlier estimates, but with a weak dependence on redshift in the range z > 16. The complex interplay between the gravitational formation of dark halos and the thermodynamic and chemical evolution of the gas clouds compromises analytic estimates of the critical H 2 fraction. Dynamical heating from mass accretion and mergers opposes relatively inefficient cooling by molecular hydrogen, delaying the production of star-forming clouds in rapidly growing halos. We also investigate the effect of photodissociating ultraviolet radiation on the formation of primordial gas clouds. We consider two extreme cases, first by including a uniform radiation field in the optically thin limit and second by accounting for the maximum effect of gas self-shielding in virialized regions. For radiation with Lyman-Werner band flux J > 10 À23 ergs s À1 cm À2 Hz À1 sr À1 , hydrogen molecules are rapidly dissociated, rendering gas cooling inefficient. In both the cases we consider, the overall effect can be described by computing an equilibrium H 2 abundance for the radiation flux and defining an effective shielding factor. Based on our numerical results, we develop a semianalytic model of the formation of the first stars and demonstrate how it can be coupled with large N-body simulations to predict the star formation rate in the early universe.

We i n troduce a simple yet powerful analytic method which obtains the structure of cosmic microwave background anisotropies to better than 5-10% in temperature uctuations on all scales. It is applicable to any model in which the potential uctuations at recombination are both linear and known. Moreover, it recovers and explains the presence of the \Doppler peaks" at degree scales as driven acoustic oscillations of the photon-baryon uid. We treat in detail such subtleties as the time dependence of the gravitational driving force, anisotropic stress from the neutrino quadrupole, and damping during the recombination process, again all from an analytic standpoint. We apply this formalism to the standard cold dark matter model to gain physical insight i n to the anisotropies, including the dependence of the peak locations and heights on cosmological parameters such a s b and h, a s w ell as model parameters such as the ionization history. Damping due to the nite thickness of the last scattering surface and photon diusion are further more shown to be identical. In addition to being a powerful probe into the nature of anisotropies, this treatment can be used in place of the standard Boltzmann code where 5-10% accuracy in temperature uctuations is satisfactory and/or speed is essential. Equally importantly, it can be used as a portable standard by which n umerical codes can be tested and compared.

We measure cosmic weak lensing shear power spectra with the Subaru Hyper Suprime-Cam (HSC) survey first-year shear catalog covering 137 deg2 of the sky. Thanks to the high effective galaxy number density of ∼17 arcmin−2, even after conservative cuts such as a magnitude cut of i < 24.5 and photometric redshift cut of 0.3 ≤ z ≤ 1.5, we obtain a high-significance measurement of the cosmic shear power spectra in four tomographic redshift bins, achieving a total signal-to-noise ratio of 16 in the multipole range 300 ≤ ℓ ≤ 1900. We carefully account for various uncertainties in our analysis including the intrinsic alignment of galaxies, scatters and biases in photometric redshifts, residual uncertainties in the shear measurement, and modeling of the matter power spectrum. The accuracy of our power spectrum measurement method as well as our analytic model of the covariance matrix are tested against realistic mock shear catalogs. For a flat Λ cold dark matter model, we find $S\,_{8}\equiv \sigma _8(\Omega _{\rm m}/0.3)^\alpha =0.800^{+0.029}_{-0.028}$ for α = 0.45 ($S\,_8=0.780^{+0.030}_{-0.033}$ for α = 0.5) from our HSC tomographic cosmic shear analysis alone. In comparison with Planck cosmic microwave background constraints, our results prefer slightly lower values of S8, although metrics such as the Bayesian evidence ratio test do not show significant evidence for discordance between these results. We study the effect of possible additional systematic errors that are unaccounted for in our fiducial cosmic shear analysis, and find that they can shift the best-fit values of S8 by up to ∼0.6 σ in both directions. The full HSC survey data will contain several times more area, and will lead to significantly improved cosmological constraints.