Large scale structure surveys will likely become the next leading cosmological probe. In our universe, matter perturbations are large on short distances and small at long scales, i.e. strongly coupled in the UV and weakly coupled in the IR. To make precise analytical predictions on large scales, we develop an effective field theory formulated in terms of an IR effective fluid characterized by several parameters, such as speed of sound and viscosity. These parameters, determined by the UV physics described by the Boltzmann equation, are measured from N-body simulations. We find that the speed of sound of the effective fluid is $ c_s^2 \approx {1}{0^{{ - {6}}}}{c^{2}} $
 and that the viscosity contributions are of the same order. The fluid describes all the relevant physics at long scales k and permits a manifestly convergent perturbative expansion in the size of the matter perturbations δ(k) for all the observables. As an example, we calculate the correction to the power spectrum at order δ(k)4. The predictions of the effective field theory are found to be in much better agreement with observation than standard cosmological perturbation theory, already reaching percent precision at this order up to a relatively short scale k ⋍ 0.24h Mpc−1.

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The Effective Field Theory of Cosmological Large Scale Structures

We measure cosmic weak lensing shear power spectra with the Subaru Hyper Suprime-Cam (HSC) survey first-year shear catalog covering 137 deg^2 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 S_8, 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 S_8 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.

Cosmology from cosmic shear power spectra with Subaru Hyper Suprime-Cam first-year data

We develop a new approach to study the nonlinear evolution in the large-scale structure of the Universe both in real space and in redshift space, extending the standard perturbation theory of gravitational instability. Infinite series of terms in standard Eulerian perturbation theory are resummed as a result of our starting from a Lagrangian description of perturbations. Delicate nonlinear effects on scales of the baryon acoustic oscillations are more accurately described by our method than the standard one. Our approach differs from other resummation techniques recently proposed, such as the renormalized perturbation theory, etc., in that we use simple techniques and thus resulting equations are undemanding to evaluate, and in that our approach is capable of quantifying the nonlinear effects in redshift space. The power spectrum and correlation function of our approach are in good agreement with numerical simulations in literature on scales of baryon acoustic oscillations. Especially, nonlinear effects on the baryon acoustic peak of the correlation function are accurately described both in real space and in redshift space. Our approach provides a unique opportunity to analytically investigate the nonlinear effects on baryon acoustic scales in observable redshift space, which is requisite in constraining the nature of dark energy, the curvature of the Universe, etc., by redshift surveys.

Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space

We present precise measurements of the growth rate of cosmic structure for the redshift range 0.1 < z < 0.9, using redshift-space distortions in the galaxy power spectrum of the WiggleZ Dark Energy Survey. Our results, which have a precision of around 10 per cent in four
independent redshift bins, are well fitted by a flat Λ cold dark matter (ΛCDM) cosmological model with matter density parameter Ω_m = 0.27. Our analysis hence indicates that this model provides a self-consistent description of the growth of cosmic structure through large-scale
perturbations and the homogeneous cosmic expansion mapped by supernovae and baryon acoustic oscillations. We achieve robust results by systematically comparing our data with
several different models of the quasi-linear growth of structure including empirical models, fitting formulae calibrated to N-body simulations, and perturbation theory techniques. We extract the first measurements of the power spectrum of the velocity divergence field, P_(θθ) (k),
as a function of redshift (under the assumption that P_(gθ) (k) = − √P_(gg)(k)P_(θθ) (k), where g is the galaxy overdensity field), and demonstrate that the WiggleZ galaxy–mass cross-correlation is consistent with a deterministic (rather than stochastic) scale-independent bias model for WiggleZ galaxies for scales k < 0.3 h Mpc^(−1). Measurements of the cosmic growth rate from
the WiggleZ Survey and other current and future observations offer a powerful test of the physical nature of dark energy that is complementary to distance–redshift measures such as supernovae and baryon acoustic oscillations.

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The WiggleZ Dark Energy Survey: the growth rate of cosmic structure since redshift z=0.9

We present an improved prescription for the matter power spectrum in redshift space taking proper account of both nonlinear gravitational clustering and redshift distortion, which are of particular importance for accurately modeling baryon acoustic oscillations (BAOs). Contrary to the models of redshift distortion phenomenologically introduced but frequently used in the literature, the new model includes the corrections arising from the nonlinear coupling between the density and velocity fields associated with two competitive effects of redshift distortion, i.e., Kaiser and Finger-of-God effects. Based on the improved treatment of perturbation theory for gravitational clustering, we compare our model predictions with the monopole and quadrupole power spectra of $N$-body simulations, and an excellent agreement is achieved over the scales of BAOs. Potential impacts on constraining dark energy and modified gravity from the redshift-space power spectrum are also investigated based on the Fisher-matrix formalism, particularly focusing on the measurements of the Hubble parameter, angular diameter distance, and growth rate for structure formation. We find that the existing phenomenological models of redshift distortion produce a systematic error on measurements of the angular diameter distance and Hubble parameter by 1%--2% , and the growth-rate parameter by $\ensuremath{\sim}5%$, which would become non-negligible for future galaxy surveys. Correctly modeling redshift distortion is thus essential, and the new prescription for the redshift-space power spectrum including the nonlinear corrections can be used as an accurate theoretical template for anisotropic BAOs.

Baryon Acoustic Oscillations in 2D: Modeling Redshift-space Power Spectrum from Perturbation Theory

We report on a measurement of the quadrupole power spectrum in the two degree field (2dF) QSO redshift (2QZ) survey. The analysis used an algorithm parallel to that for estimating the standard monopole power spectrum without first requiring computation of the correlation function or the anisotropic power spectrum. The error on the quadrupole spectrum was rather large, but the best-fit value of the bias parameter from the quadrupole spectrum is consistent with that from previous investigations of the 2dF data.

A Measurement of the Quadrupole Power Spectrum in the Clustering of the 2dF QSO Survey

An acoustic oscillation of the primeval photon-baryon fluid around the decoupling time imprints a characteristic scale in the galaxy distribution today, known as the baryon acoustic oscillation (BAO) scale. Several on-going and/or future galaxy surveys aim at detecting and precisely determining the BAO scale so as to trace the expansion history of the universe. We consider nonlinear and redshift-space distortion effects on the shifts of the BAO scale in $k$-space using perturbation theory. The resulting shifts are indeed sensitive to different choices of the definition of the BAO scale, which needs to be kept in mind in the data analysis. We present a toy model to explain the physical behavior of the shifts. We find that the BAO scale defined as in Percival et al. (2007) indeed shows very small shifts ($\\lesssim$ 1%) relative to the prediction in {\\it linear theory} in real space. The shifts can be predicted accurately for scales where the perturbation theory is reliable.

Characteristic Scales of Baryon Acoustic Oscillations from Perturbation Theory: Nonlinearity and Redshift-Space Distortion Effects

An acoustic oscillation of the primeval photon-baryon fluid around the decoupling time imprints a characteristic scale in the galaxy distribution today, known as the baryon acoustic oscillation (BAO) scale. Several on-going and/or future galaxy surveys aim at detecting and precisely determining the BAO scale so as to trace the expansion history of the universe. We consider nonlinear and redshift-space distortion effects on the shifts of the BAO scale in $k$-space using perturbation theory. The resulting shifts are indeed sensitive to different choices of the definition of the BAO scale, which needs to be kept in mind in the data analysis. We present a toy model to explain the physical behavior of the shifts. We find that the BAO scale defined as in Percival et al. (2007) indeed shows very small shifts ($\lesssim$ 1%) relative to the prediction in {\it linear theory} in real space. The shifts can be predicted accurately for scales where the perturbation theory is reliable.

Masashi Nakamichi

Papers

A Measurement of the Quadrupole Power Spectrum in the Clustering of the 2dF QSO Survey

Characteristic Scales of Baryon Acoustic Oscillations from Perturbation Theory: Nonlinearity and Redshift-Space Distortion Effects

Characteristic Scales of Baryon Acoustic Oscillations from Perturbation Theory: Non-linearity and Redshift-Space Distortion Effects