Published in Physics Reports, Volume 530, Issue 2,
p. 87-255, 2013.

http://arxiv.org/abs/1201.2434

For a PDF version of the article, click here.

**Abstract:** The accelerating expansion of the universe is the most
surprising cosmological discovery in many decades, implying that the
universe is dominated by some form of "dark energy" with exotic physical
properties, or that Einstein's theory of gravity breaks down on
cosmological scales. The profound implications of cosmic acceleration
have inspired ambitious efforts to understand its origin, with
experiments that aim to measure the history of expansion and growth of
structure with percent-level precision or higher. We review in detail
the four most well established methods for making such measurements:
Type Ia supernovae, baryon acoustic oscillations (BAO), weak
gravitational lensing, and the abundance of galaxy clusters. We pay
particular attention to the systematic uncertainties in these techniques
and to strategies for controlling them at the level needed to exploit
"Stage IV" dark energy facilities such as BigBOSS, LSST, *Euclid*,
and *WFIRST*. We briefly review a number of other approaches
including redshift-space distortions, the Alcock-Paczynski effect, and
direct measurements of the Hubble constant *H*_{0}. We
present extensive forecasts for constraints on the dark energy equation
of state and parameterized deviations from General Relativity,
achievable with Stage III and Stage IV experimental programs that
incorporate supernovae, BAO, weak lensing, and cosmic microwave
background data. We also show the level of precision required for
clusters or other methods to provide constraints competitive with those
of these fiducial programs. We emphasize the value of a balanced program
that employs several of the most powerful methods in combination, both
to cross-check systematic uncertainties and to take advantage of
complementary information. Surveys to probe cosmic acceleration produce
data sets that support a wide range of scientific investigations, and
they continue the longstanding astronomical tradition of mapping the
universe in ever greater detail over ever larger scales.

**Table of Contents**

- INTRODUCTION
- History
- Theories of Cosmic Acceleration
- Looking Forward

- OBSERVABLES, PARAMETERIZATIONS, AND METHODS
- Basic Equations
- Model Parameterizations
- CMB Anisotropies and Large Scale Structure
- Parameter Dependences and CMB Constraints
- Overview of Methods

- TYPE Ia SUPERNOVAE
- General Principles
- The Current State of Play
- Observational Considerations
- Systematic Uncertainties and Strategies for Amelioration
- Space vs. Ground
- Prospects

- BARYON ACOUSTIC OSCILLATIONS
- General Principles
- The Current State of Play
- Theory of BAO
- Linear Theory
- Non-linear Evolution and Galaxy Clustering Bias
- Reconstruction
- Fitting to Data

- Observational Considerations
- Statistical Errors
- From BAO to Dark Energy
- Sampling Density
- Spectroscopic vs. Photometric Redshifts
- Tracers of Structure

- Systematic Uncertainties and Strategies for
Amelioration
- Measurement Systematics
- Astrophysical Systematics
- Cosmological Systematics

- Space vs. Ground
- Prospects

- WEAK LENSING
- General principles: Overview
- Weak lensing principles: Mathematical
discussion
- Deflection of light in cosmology
- Cosmic shear, magnification, and flexion
- Power spectra and correlation functions*
- Method I: Cosmic Shear Power Spectrum*
- Method II: Power Spectrum Tomography*
- Method III: Galaxy-galaxy Lensing*
- Method IV: Cosmography*
- Method V: Non-Gaussian Statistics*

- The Current State of Play
- Cosmic shear
- Galaxy-galaxy lensing as a cosmological probe
- Lensing outside the optical bands

- Observational Considerations and Survey
Design
- Statistical Errors
- The Galaxy Population for Optical Surveys
- Photometric Redshifts and their Calibration
- Lensing in the Radio
- Lensing of the CMB

- Measuring Shears
- The Idealized Problem
- Shape Measurement Algorithms*
- Shape Measurement Errors*
- Noise Rectification and Selection Biases*
- Determining the PSF and Instrument Properties

- Astrophysical systematics
- Intrinsic Alignments*
- Theoretical uncertainties in the matter power spectrum*

- Systematic Errors and their Amelioration: Summary
- Advantages of a Space Mission
- Prospects

- CLUSTERS OF GALAXIES
- General Principles
- The Current State of Play
- Observational Considerations
- Expected Numbers and Cosmological Sensitivity
- Cluster Finding
- Calibrating the Observable-Mass Relation

- Systematic Uncertainties and Strategies for
Amelioration
- Redshift Uncertainties
- Contamination and Incompleteness: The Tails of P(X|M,z)
- Calibrating the Core of P(X|M,z)
- Theoretical Systematics

- Space vs. Ground
- Prospects

- ALTERNATIVE METHODS
- Measurement of the Hubble Constant at z ≈ 0
- Redshift-Space Distortions
- The Alcock-Paczynski Test
- Alternative Distance Indicators
- Standard Sirens
- The Lyα Forest as a Probe of Structure Growth
- Other Tests of Modified Gravity
- The Integrated Sachs-Wolfe Effect
- Cross-Correlation of Weak Lensing and Spectroscopic Surveys
- Strong Gravitational Lenses
- Galaxy Ages
- Redshift Drift
- Alternative Methods: Summary

- A BALANCED PROGRAM ON COSMIC ACCELERATION
- A Fiducial Program
- Forecasting Constraints
- Results: Forecasts for the Fiducial Program
and Variations
- Constraints in simple w(z) models
- Constraints on structure growth parameters
- Dependence on w(z) model and binning of data
- Constraints on w(z) in the general model

- Forecasts for Clusters
- Forecasts for Alternative Methods
- The Hubble constant
- The Alcock-Paczynski Test
- Redshift-space Distortions
- Distances

- Observables and Aggregate Precision
- Prospects with Many Probes

- CONCLUSIONS
- APPENDIX A. GLOSSARY OF ACRONYMS AND FACILITIES
- REFERENCES