We measure cosmological parameters using the three-dimensional power spectrum P (k) from over 200,000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with WMAP and other data. Our results are consistent with a "vanilla" flat adiabatic ΛCDM model without tilt (ns = 1), running tilt, tensor modes or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening 1σ constraints on the Hubble parameter from h ≈ 0.74−0.03 , on the matter density from Ωm ≈ 0.25 ± 0.10 to Ωm ≈ 0.30 ± 0.04 (1σ) and on neutrino masses from < 11 eV to < 0.6 eV (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the 2dF Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from t0 ≈ 16.3 +2.3 −1.8 Gyr to t0 ≈ 14.1Gyr by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened.

Many aspects of the large-scale structure of the universe can be described successfully using cosmological models in which 27 ± 1% of the critical mass-energy density consists of cold dark matter (CDM). However, few-if any-of the predictions of CDM models have been successful on scales of ∼ 10 kpc or less. This lack of success is usually explained by the difficulty of modeling baryonic physics (star formation, supernova and black-hole feedback, etc.). An intriguing alternative to CDM is that the dark matter is an extremely light (m ∼ 10 −22 eV) boson having a de Broglie wavelength λ ∼ 1 kpc, often called fuzzy dark matter (FDM). We describe the arguments from particle physics that motivate FDM, review previous work on its astrophysical signatures, and analyze several unexplored aspects of its behavior. In particular, (i) FDM halos or sub-halos smaller than about 10 7 (m/10 −22 eV) −3/2 M do not form, and the abundance of halos smaller than a few times 10 10 (m/10 −22 eV) −4/3 M is substantially smaller in FDM than in CDM; (ii) FDM halos are comprised of a central core that is a stationary, minimum-energy solution of the Schrödinger-Poisson equation, sometimes called a "soliton", surrounded by an envelope that resembles a CDM halo. The soliton can produce a distinct signature in the rotation curves of FDM-dominated systems. (iii) The transition between soliton and envelope is determined by a relaxation process analogous to two-body relaxation in gravitating N-body systems, which proceeds as if the halo were composed of particles with mass ∼ ρλ 3 where ρ is the halo density. (iv) Relaxation may have substantial effects on the stellar disk and bulge in the inner parts of disk galaxies, but has negligible effect on disk thickening or globular cluster disruption near the solar radius. (v) Relaxation can produce FDM disks but an FDM disk in the solar neighborhood must have a half-thickness of at least ∼ 300(m/10 −22 eV) −2/3 pc and a mid-plane density less than 0.2(m/10 −22 eV) 2/3 times the baryonic disk density. (vi) Solitonic FDM sub-halos evaporate by tunneling through the tidal radius and this limits the minimum subhalo mass inside ∼ 30 kpc of the Milky Way to a few times 10 8 (m/10 −22 eV) −3/2 M . (vii) If the dark matter in the Fornax dwarf galaxy is composed of CDM, most of the globular clusters observed in that galaxy should have long ago spiraled to its center, and this problem is resolved if the dark matter is FDM. (viii) FDM delays galaxy formation relative to CDM but its galaxy-formation history is consistent with current observations of high-redshift galaxies and the late reionization observed by Planck. If the dark matter is composed of FDM, most observations favor a particle mass 10 −22 eV and the most significant observational consequences occur if the mass is in the range 1-10×10 −22 eV. There is tension with observations of the Lyman-α forest, which favor m 10-20 × 10 −22 eV and we discuss whether more sophisticated models of reionization may resolve this tension. *

We measure the large-scale real-space power spectrum P (k) using a sample of 205,443 galaxies from the Sloan Digital Sky Survey, covering 2417 effective square degrees with mean redshift z ≈ 0.1. We employ a matrix-based method using pseudo-Karhunen-Loève eigenmodes, producing uncorrelated minimumvariance measurements in 22 k-bands of both the clustering power and its anisotropy due to redshift-space distortions, with narrow and well-behaved window functions in the range 0.02 h/Mpc < k < 0.3 h/Mpc. We pay particular attention to modeling, quantifying and correcting for potential systematic errors, nonlinear redshift distortions and the artificial red-tilt caused by luminosity-dependent bias. Our results are robust to omitting angular and radial density fluctuations and are consistent between different parts of the sky. Our final result is a measurement of the real-space matter power spectrum P (k) up to an unknown overall multiplicative bias factor. Our calculations suggest that this bias factor is independent of scale to better than a few percent for k < 0.1 h/Mpc, thereby making our results useful for precision measurements of cosmological parameters in conjunction with data from other experiments such as the WMAP satellite. The power spectrum is not well-characterized by a single power law, but unambiguously shows curvature. As a simple characterization of the data, our measurements are well fit by a flat scaleinvariant adiabatic cosmological model with hΩ m = 0.213 ± 0.023 and σ 8 = 0.89 ± 0.02 for L * galaxies, when fixing the baryon fraction Ω b /Ω m = 0.17 and the Hubble parameter h = 0.72; cosmological interpretation is given in a companion paper.

We develop an efficient method to study the effects of reionization history on the temperature-density relation of the intergalactic medium in the low density limit (overdensity δ < ∼ 5). It is applied to the study of photo-reionization models in which the amplitude, spectrum and onset epoch of the ionizing flux, as well as the cosmology, are systematically varied. We find that the mean temperature-density relation at z = 2 − 4 is well approximated by a powerlaw equation of state for uniform reionization models. We derive analytical expressions for its evolution and exhibit its asymptotic behavior: it is found that for sufficiently early reionization, imprints of reionization history prior to z ∼ 10 on the temperature-density relation are washed out. In this limit the temperature at cosmic mean density is proportional toWhile the amplitude of the radiation flux at the ionizing frequency of H i is found to have a negligible effect on the temperature-density relation as long as the universe reionizes before z ∼ 5, the spectrum can change the overall temperature by about 20%, through variations in the abundances of helium species. However the slope of the mean equation of state is found to lie within a narrow range for all reionization models we study, where reionization takes place before z ∼ 5. We discuss the implications of these findings for the observational properties of the Lyα forest. In particular, uncertainties in the temperature of the intergalactic medium, due to the uncertain reionization history of our universe, introduces a 30% scaling in the amplitude of the column density distribution while the the slope of the distribution is only affected by about 5%. Finally, we discuss how a fluctuating ionizing field affects the above results. We argue that under certain conditions, the loss of memory c 0000 RAS 2 Hui and Gnedin of reionization history implies that at late times, the temperature-density relation of a gas in a fluctuating ionizing background can be approximated by one that results from a uniform radiation field, provided the universe reionizes sufficiently early.

We study galaxy clustering in the framework of halo models, where gravitational clustering is described in terms of dark matter halos. At small scales, dark matter clustering statistics are dominated by halo density profiles, whereas at large scales, correlations are the result of combining non-linear perturbation theory with halo biasing. Galaxies are assumed to follow the dark matter profiles of the halo they inhabit, and galaxy formation efficiency is characterized by the number of galaxies that populate a halo of given mass. This approach leads to generic predictions: the galaxy power spectrum shows a power-law behavior even though the dark matter does not, and the galaxy higher-order correlations show smaller amplitudes at small scales than their dark matter counterparts. Both are in qualitatively agreement with measurements in galaxy catalogs. We find that requiring the model to fit both the second and third order moments of the APM galaxies provides a strong constraint on galaxy formation models. The data at large scales require that galaxy formation be relatively efficient at small masses, m ≈ 10 10 M ⊙ /h, whereas data at smaller scales require that the number of galaxies in a halo scale approximately as the mass to the 0.8th power in the high-mass limit. These constraints are independent of those derived from the luminosity function or Tully-Fisher relation. We also predict the power spectrum, bispectrum, and higher-order moments of the mass density field in this framework. Although halo models agree well with measurements of the mass power spectrum and the higher order S p parameters in N-body simulations, the model assumption that halos are spherical leads to disagreement in the configuration dependence of the bispectrum at small scales. We stress the importance of finite volume effects in higher-order statistics and show how they can be estimated in this approach.

We introduce an efficient and accurate alternative to full hydrodynamic simulations, hydro‐PM (HPM), for the study of the low column density Lyα forest (NH I1014 cm−2). It consists of a particle mesh (PM) solver, modified to compute, in addition to the gravitational potential, an effective potential due to the gas pressure. Such an effective potential can be computed from the density field because of a tight correlation between density and pressure in the low‐density limit (δ≲10), which can be calculated for any photo‐re‐ionization history by a method outlined by Hui & Gnedin. Such a correlation exists, in part, because of minimal shock heating in the low‐density limit. We compare carefully the density and velocity fields as well as absorption spectra, computed using HPM versus hydrodynamic simulations, and find good agreement. We show that HPM is capable of reproducing measurable quantities, such as the column density distribution, computed from full hydrodynamic simulations, to a precision comparable to that of observations. We discuss how, by virtue of its speed and accuracy, HPM can enable us to use the Lyα forest as a cosmological probe.  We also discuss in detail the smoothing of the gas (or baryon) fluctuation relative to that of the dark matter on small scales due to finite gas pressure. First, it is shown that the conventional wisdom that the linear gas fluctuation is smoothed on the Jeans scale is incorrect for general re‐ionization (or reheating) history; the correct linear filtering scale is in general smaller than the Jeans scale after reheating, but larger prior to it. Secondly, it is demonstrated that in the mildly non‐linear regime, a PM solver, combined with suitable pre‐filtering of the initial conditions, can be used to model the low‐density IGM. However, such an approximation is shown to be less accurate than HPM, unless a non‐uniform pre‐filtering scheme is implemented.

We study the clustering of luminous red galaxies in the latest spectroscopic Sloan Digital Sky Survey data releases (DR), DR6 and DR7, which sample over 1 Gpc3 h−3 to z= 0.47. The two‐point correlation function ξ(σ, π) is estimated as a function of perpendicular σ and line‐of‐sight π (radial) directions. We find significant detection of a peak at r≃ 110 Mpc h−1, which shows as a circular ring in the σ–π plane. There is also significant evidence of a peak along the radial direction whose shape is consistent with its origination from the recombination‐epoch baryon acoustic oscillations (BAO). A ξ(σ, π) model with no radial BAO peak is disfavoured at 3.2σ, whereas a model with no magnification bias is disfavoured at 2σ. The radial data enable, for the first time, a direct measurement of the Hubble parameter H(z) as a function of redshift. This is independent of earlier BAO measurements which used the spherically averaged (monopole) correlation to constrain an integral of H(z). Using the BAO peak position as a standard ruler in the radial direction, we find H(z= 0.24) = 79.69 ± 2.32 (±1.29) km s−1 Mpc−1 for z= 0.15–0.30 and H(z= 0.43) = 86.45 ± 3.27 (±1.69) km s−1 Mpc−1 for z= 0.40–0.47. The first error is a model‐independent statistical estimation and the second accounts for systematics both in the measurements and in the model. For the full sample, z= 0.15–0.47, we find H(z= 0.34) = 83.80 ± 2.96 (±1.59) km s−1 Mpc−1.

We consider the low-energy effective field theory describing the infrared dynamics of nondissipative fluids. We extend previous work to accommodate conserved charges, and we clarify the matching between field theory variables and thermodynamical ones. We discuss the systematics of the derivative expansion, for which field theory offers a conceptually clear and technically neat scheme. As an example, we compute the correction to the sound-wave dispersion relation coming from a sample second-order term. This formalism forms the basis for a study of anomalies in hydrodynamics via effective field theory, which is initiated in a companion paper.