dark energy, WFIRST has the more robust and powerful approach. WFIRST should make significant advances in dark energy research beyond Euclid’s own contributions.

In the report of the NWNH Science Frontiers Panel on Cosmology and Fundamental Physics, that panel noted that the key requirements for studying cosmic acceleration were measurements over a wide redshift range, rather than an emphasis on a redshift z < 1.13 There have been no observational results since NWNH that argue for a major deviation from that panel’s conclusions. There are three primary, complementary techniques for studying dark energy: weak gravitational lensing, three-dimensional clustering of galaxies, and supernova measurements. Only WFIRST will use all three, including the supernova technique used by U.S. astronomers and their colleagues in their Nobel Prize-winning discovery of cosmic acceleration. Supernova measurements complement the other two techniques and currently provide the strongest dark energy constraints; all three are needed for a robust dark energy program.

Both Euclid and WFIRST plan to use measurements of the three-dimensional distribution of galaxies to trace the geometry of the universe. During the first 400,000 years after the Big Bang, sound waves in the cosmic fluid imprint a structure known as baryon acoustic oscillations in the threedimensional distribution of galaxies. Measurements of these BAO features provide a “standard ruler” for measuring the expansion rate of the universe as a function of time (or equivalently, redshift). According to the current plans of both missions, the Euclid mission would cover a wider area of the sky than the WFIRST mission.14Because the WFIRST mission delivers a higher number density of galaxies, the effective volume of its survey is larger; thus it will be better able to make the key measurement of the relationship between distance and redshift (z). The proposed WFIRST BAO survey will make significantly more accurate distance measurements than the Euclid BAO survey at redshifts z > 1, when the universe was approximately half its present age, and nearly an order of magnitude better at z = 2.15 With its higher number density of galaxies, WFIRST will be better able to use redshift distortions to measure the growth rate of structure. The combination of growth rate measurements and geometry measurements tests whether cosmic acceleration is due to dark energy or the breakdown of general relativity.

Weak gravitational lensing, the distortion of the observed shapes of distant galaxies due to the bending of light rays by the clumpy distribution of matter, is a potentially powerful technique for tracing its large-scale distribution. The measurement of weak gravitational lensing is a primary objective of both the Euclid and the WFIRST missions. For Euclid this involves measuring the shapes of galaxies with optical CCDs. WFIRST measures the shapes of galaxies in the infrared, where galaxies are brighter and smoother. The WFIRST reference mission, as described in the interim report of the WFIRST SDT,16 allocates 1 year of survey time for a wide-area weak gravitational lensing program in comparison to 6.25 years for Euclid. If limited by statistical errors, then the expected weak gravitational lensing dark energy science return will be somewhat greater from Euclid than WFIRST.17 The weak gravitational lensing signal is very subtle, however, and its detection is vulnerable to systematic errors introduced by the instrument,18 by the atmosphere (when observed from the ground), and by astrophysical effects such as intrinsic alignments.19 The WFIRST multiband approach to weak gravitational lensing is more robust than Euclid’s single very broad band, which is potentially vulnerable to galaxy color gradients.20,21 Because WFIRST measures lensing in three passbands, its data can be internally cross-correlated to help mitigate systematic measurement error. Since the WFIRST approach to weak gravitational lensing measurement appears to be more robust, it may produce better constraints on dark energy properties.

Euclid’s and WFIRST’s measurements are not duplicative and the combinations will be more powerful than any single measurement. Combining WFIRST with Euclid and with ground-based data sets, such as that expected from LSST,22 should further enable astronomers to address the systematic challenges that previous ground-based weak gravitational lensing measurements have experienced.23 These combined data sets will likely overcome systematic limitations and realize the full potential of this powerful technique.

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