Ten years ago, the discovery that the expansion of the universe is accelerating put in place the last major building block of the present cosmological model, in which the universe is composed of 4% baryons, 20% dark matter, and 76% dark energy. At the same time, it posed one of the most profound mysteries in all of science, with deep connections to both astrophysics and particle physics. Cosmic acceleration could arise from the repulsive gravity of dark energy—for example, the quantum energy of the vacuum—or it may signal that general relativity (GR) breaks down on cosmological scales and must be replaced. We review the present observational evidence for cosmic acceleration and what it has revealed about dark energy, discuss the various theoretical ideas that have been proposed to explain acceleration, and describe the key observational probes that will shed light on this enigma in the coming years.

/pdf/dark-energy-and-the-accelerating-universe-5fgqpvodrw.pdf

Dark Energy and the Accelerating Universe

http://inspirehep.net/record/1084324/files/arXiv:1201.2434.pdf

Observational probes of cosmic acceleration

Based on a suite of state-of-the-art high-resolution N-body simulations, we revisit the so-called halofit model as an accurate fitting formula for the nonlinear matter power spectrum. While the halofit model has frequently been used as a standard cosmological tool to predict the nonlinear matter power spectrum in a universe dominated by cold dark matter, its precision has been limited by the low resolution of N-body simulations used to determine the fitting parameters, suggesting the necessity of an improved fitting formula at small scales for future cosmological studies. We run high-resolution N-body simulations for 16 cosmological models around the Wilkinson Microwave Anisotropy Probe best-fit cosmological parameters (one-, three-, five-, and seven-year results), including dark energy models with a constant equation of state. The simulation results are used to re-calibrate the fitting parameters of the halofit model so as to reproduce small-scale power spectra of the N-body simulations, while keeping the precision at large scales. The revised fitting formula provides an accurate prediction of the nonlinear matter power spectrum in a wide range of wavenumbers (k ? 30 h?Mpc?1) at redshifts 0 ? z ? 10, with 5% precision for k ? 1 h?Mpc?1 at 0 ? z ? 10 and 10% for 1 ? k ? 10 h?Mpc?1 at 0 ? z ? 3. We discuss the impact of the improved halofit model on weak-lensing power spectra and correlation functions, and show that the improved model better reproduces ray-tracing simulation results.

https://iopscience.iop.org/article/10.1088/0004-637X/761/2/152/pdf

Revising the Halofit Model for the Nonlinear Matter Power Spectrum

We review the problem of dark energy, including a survey of theoretical models and some aspects of numerical studies

Dark Energy

We describe the design and data analysis of the DEEP2 Galaxy Redshift Survey, the densest and largest high-precision redshift survey of galaxies at z ~ 1 completed to date. The survey was designed to conduct a comprehensive census of massive galaxies, their properties, environments, and large-scale structure down to absolute magnitude M_B = −20 at z ~ 1 via ~90 nights of observation on the Keck telescope. The survey covers an area of 2.8 deg^2 divided into four separate fields observed to a limiting apparent magnitude of R_(AB) = 24.1. Objects with z ≾0.7 are readily identifiable using BRI photometry and rejected in three of the four DEEP2 fields, allowing galaxies with z > 0.7 to be targeted ~2.5 times more efficiently than in a purely magnitude-limited sample. Approximately 60% of eligible targets are chosen for spectroscopy, yielding nearly 53,000 spectra and more than 38,000 reliable redshift measurements. Most of the targets that fail to yield secure redshifts are blue objects that lie beyond z ~ 1.45, where the [O ii] 3727 A doublet lies in the infrared. The DEIMOS 1200 line mm^(−1) grating used for the survey delivers high spectral resolution (R ~ 6000), accurate and secure redshifts, and unique internal kinematic information. Extensive ancillary data are available in the DEEP2 fields, particularly in the Extended Groth Strip, which has evolved into one of the richest multiwavelength regions on the sky. This paper is intended as a handbook for users of the DEEP2 Data Release 4, which includes all DEEP2 spectra and redshifts, as well as for the DEEP2 DEIMOS data reduction pipelines. Extensive details are provided on object selection, mask design, biases in target selection and redshift measurements, the spec2d two-dimensional data-reduction pipeline, the spec1d automated redshift pipeline, and the zspec visual redshift verification process, along with examples of instrumental signatures or other artifacts that in some cases remain after data reduction. Redshift errors and catastrophic failure rates are assessed through more than 2000 objects with duplicate observations. Sky subtraction is essentially photon-limited even under bright OH sky lines; we describe the strategies that permitted this, based on high image stability, accurate wavelength solutions, and powerful B-spline modeling methods. We also investigate the impact of targets that appear to be single objects in ground-based targeting imaging but prove to be composite in Hubble Space Telescope data; they constitute several percent of targets at z ~ 1, approaching ~5%–10% at z > 1.5. Summary data are given that demonstrate the superiority of DEEP2 over other deep high-precision redshift surveys at z ~ 1 in terms of redshift accuracy, sample number density, and amount of spectral information. We also provide an overview of the scientific highlights of the DEEP2 survey thus far.

https://escholarship.org/content/qt11f44236/qt11f44236.pdf?t=om6z9d

The DEEP2 Galaxy Redshift Survey: Design, Observations, Data Reduction, and Redshifts

We perform a systematic analysis of the effects of photometric redshift uncertainties on weak lensing tomography. We describe the photo-z distribution with a bias and Gaussian scatter that are allowed to vary arbitrarily between intervals of dz = 0.1 in redshift.While the mere presence of bias and scatter does not substantially degrade dark energy information, uncertainties in both parameters do. For a fiducial next-generation survey each would need to be known to better than about 0.003-0.01 in redshift for each interval in order to lead to less than a factor of 1.5 increase in the dark energy parameter errors. The more stringent requirement corresponds to a larger dark energy parameter space, when redshift variation in the equation of state of dark energy is allowed.Of order 10^4-10^5 galaxies with spectroscopic redshifts fairly sampled from the source galaxy distribution will be needed to achieve this level of calibration. If the sample is composed of multiple galaxy types, a fair sample would be required for each. These requirements increase in stringency for more ambitious surveys; we quantify such scalings with a convenient fitting formula. No single aspect of a photometrically binned selection of galaxies such as their mean or median suffices, indicating that dark energy parameter determinations are sensitive to the shape and nature of outliers in the photo-z redshift distribution.

https://arxiv.org/pdf/astro-ph/0506614.pdf

Effect of Photometric Redshift Uncertainties on Weak Lensing Tomography

We perform a systematic analysis of the effects of photometric redshift uncertainties on weak-lensing tomography. We describe the photo-z distribution with a bias and Gaussian scatter that are allowed to vary arbitrarily between intervals of δz = 0.1 in redshift. While the mere presence of bias and scatter does not substantially degrade dark energy information, uncertainties in both parameters do. For a fiducial next-generation survey each would need to be known to better than about 0.003-0.01 in redshift for each interval in order to lead to less than a factor of 1.5 increase in the dark energy parameter errors. The more stringent requirement corresponds to a larger dark energy parameter space, when redshift variation in the equation of state of dark energy is allowed. Of order 104-105 galaxies with spectroscopic redshifts fairly sampled from the source galaxy distribution will be needed to achieve this level of calibration. If the sample is composed of multiple galaxy types, a fair sample would be required for each. These requirements increase in stringency for more ambitious surveys; we quantify such scalings with a convenient fitting formula. No single aspect of a photometrically binned selection of galaxies such as their mean or median suffices, indicating that dark energy parameter determinations are sensitive to the shape and nature of outliers in the photo-z redshift distribution.

/pdf/effects-of-photometric-redshift-uncertainties-on-weak-3awh5ajeqs.pdf

Effects of Photometric Redshift Uncertainties on Weak-Lensing Tomography

Weak gravitational lensing surveys using photometric redshifts can have their cosmological constraints severely degraded by errors in the photo-z scale We explore the cosmological degradation versus the size of the spectroscopic survey required to calibrate the photo-z probability distribution Previous work has assumed a simple Gaussian distribution of photo-z errors; here, we describe a method for constraining an arbitrary parametric photo-z error model As an example we allow the photo-z probability distribution to be the sum of NG Gaussians To limit cosmological degradation to a fixed level, photo-z distributions comprised of multiple Gaussians require up to a 5 times larger calibration sample than one would estimate from assuming a single-Gaussian model This degradation saturates at NG ≈ 4 in the simple case where the fiducial distribution is independent of NG Assuming a single Gaussian when the photo-z distribution has multiple parameters underestimates cosmological parameter uncertainties by up to 35% The size of required calibration sample also depends on the shape of the fiducial distribution, even when the rms photo-z error is held fixed The required calibration sample size varies up to a factor of 40 among the fiducial models studied, but this is reduced to a factor of a few if the photo-z error distributions are forced to be slowly varying with redshift Finally, we show that the size of the required calibration sample can be substantially reduced by optimizing its redshift distribution We hope this study will help stimulate work on better understanding of photo-z errors

Size of Spectroscopic Calibration Samples for Cosmic Shear Photometric Redshifts

We modify the public PM code developed by Anatoly Klypin and Jon Holtzman to simulate cosmologies with arbitrary initial power spectra and the equation of state of dark energy. With this tool in hand, we perform the following studies on the matter power spectrum. With an artificial sharp peak at k ~ 0.2 h Mpc-1 in the initial power spectrum, we find that the position of the peak is not shifted by nonlinear evolution. An upper limit of the shift at the level of 0.02% is achieved by fitting the power spectrum local to the peak using a power law plus a Gaussian. We also find that the existence of a peak in the linear power spectrum would boost the nonlinear power at all scales evenly. This is contrary to what the HKLM scaling relation predicts, but roughly consistent with that of the halo model. We construct dark energy models with the same linear power spectra today but different linear growth histories. We demonstrate that their nonlinear power spectra differ at the level of the maximum deviation of the corresponding linear power spectra in the past. Similarly, two constructed dark energy models with the same growth histories result in consistent nonlinear power spectra. This is hinting, not a proof, that the linear power spectrum together with linear growth history uniquely determine the nonlinear power spectrum. Based on these results, we propose that linear growth history be included in the next-generation fitting formulae of the nonlinear power spectrum. Finally, we comment on the precision of existing fitting formulae when applied to dark energy models parametrized by w0 and wa.

/pdf/the-nonlinear-matter-power-spectrum-16pvhkh3q7.pdf

The Nonlinear Matter Power Spectrum

Accurate knowledge of the telescope's point-spread function (PSF) is essential for the weak gravitational lensing measurements that hold great promise for cosmological constraints. For space telescopes, the PSF may vary with time due to thermal drifts in the telescope structure, and/or due to jitter in the spacecraft pointing (ground-based telescopes have additional sources of variation). We describe and simulate a procedure for using the images of the stars in each exposure to determine the misalignment and jitter parameters, and reconstruct the PSF at any point in that exposure's field of view. As a case study, the simulation uses the design of the Supernova Acceleration Probe (SNAP) telescope. Stellar-image data in a typical exposure determines secondary-mirror positions as precisely as 20 nm. The PSF ellipticities and size, which are the quantities of interest for weak lensing are determined to 4.0 × 10^-4 and 2.2 × 10^-4 accuracies, respectively, in each exposure, sufficient to meet weak-lensing requirements. We show that, for the case of a space telescope, the PSF estimation errors scale inversely with the square root of the total number of photons collected from all the usable stars in the exposure.

/pdf/diagnosing-space-telescope-misalignment-and-jitter-using-3v6spic2ir.pdf

Zhaoming Ma

Papers

Effect of Photometric Redshift Uncertainties on Weak Lensing Tomography

Effects of Photometric Redshift Uncertainties on Weak-Lensing Tomography

Size of Spectroscopic Calibration Samples for Cosmic Shear Photometric Redshifts

The Nonlinear Matter Power Spectrum

Diagnosing Space Telescope Misalignment and Jitter Using Stellar Images