The alignments between galaxies, their underlying matter structures, and the cosmic web constitute vital ingredients for a comprehensive understanding of gravity, the nature of matter, and structure formation in the Universe. We provide an overview on the state of the art in the study of these alignment processes and their observational signatures, aimed at a non-specialist audience. The development of the field over the past one hundred years is briefly reviewed. We also discuss the impact of galaxy alignments on measurements of weak gravitational lensing, and discuss avenues for making theoretical and observational progress over the coming decade.

This paper presents the first application of 3D cosmic shear to a wide-field weak lensing survey. 3D cosmic shear is a technique that analyses weak lensing in three dimensions using a spherical harmonic approach, and does not bin data in the redshift direction. This is applied to CFHTLenS, a 154 square degree imaging survey with a median redshift of 0.7 and an effective number density of 11 galaxies per square arcminute usable for weak lensing. To account for survey masks we apply a 3D pseudo-C ℓ approach on weak lensing data, and to avoid uncertainties in the highly non-linear regime, we separately analyse radial wavenumbers k ≤ 1.5h Mpc −1 and k ≤ 5.0h Mpc −1 , and angular wavenumbers ℓ ≈ 400-5000. We show how one can recover 2D and tomographic power spectra from the full 3D cosmic shear power spectra and present a measurement of the 2D cosmic shear power spectrum, and measurements of a set of 2-bin and 6-bin cosmic shear tomographic power spectra; in doing so we find that using the 3D power in the calculation of such 2D and tomographic power spectra from data naturally accounts for a minimum scale in the matter power spectrum. We use 3D cosmic shear to constrain cosmologies with parameters Ω M , Ω B , σ 8 , h, n s , w 0 , w a . For a non-evolving dark energy equation of state, and assuming a flat cosmology, lensing combined with WMAP7 results in h = 0.78 ± 0.12, Ω M = 0.252 ± 0.079, σ 8 = 0.88 ± 0.23 and w = −1.16 ± 0.38 using only scales k ≤ 1.5h Mpc −1 . We also present results of lensing combined with first year Planck results, where we find no tension with the results from this analysis, but we also find no significant improvement over the Planck results alone. We find evidence of a suppression of power compared to LCDM on small scales 1.5 < k ≤ 5.0h Mpc −1 in the lensing data, which is consistent with predictions of the effect of baryonic feedback on the matter power spectrum.

The shapes of galaxies are not randomly oriented on the sky. During the galaxy formation and evolution process, environment has a strong influence, as tidal gravitational fields in the large-scale structure tend to align nearby galaxies. Additionally, events such as galaxy mergers affect the relative alignments of both the shapes and angular momenta of galaxies throughout their history. These "intrinsic galaxy alignments" are known to exist, but are still poorly understood. This review will offer a pedagogical introduction to the current theories that describe intrinsic galaxy alignments, including the apparent difference in intrinsic alignment between early-and late-type galaxies and the latest efforts to model them analytically. It will then describe the ongoing efforts to simulate intrinsic alignments using both N-body and hydrodynamic simulations. Due to the relative youth of this field, there is still much to be done to understand intrinsic galaxy alignments and this review summarises the current state of the field, providing a solid basis for future work.

Galaxy shapes are not randomly oriented, rather they are statistically aligned in a way that can depend on formation environment, history and galaxy type. Studying the alignment of galaxies can therefore deliver important information about the physics of galaxy formation and evolution as well as the growth of structure in the Universe. In this review paper we summarise key measurements of galaxy alignments, divided by galaxy type, scale and environment. We also cover the statistics and formalism necessary to understand the observations in the literature. With the emergence of weak gravitational lensing as a precision probe of cosmology, galaxy alignments have taken on an added importance because they can mimic cosmic shear, the effect of gravitational lensing by large-scale structure on observed galaxy shapes. This makes galaxy alignments, commonly referred to as intrinsic alignments, an important systematic effect in weak lensing studies. We quantify the impact of intrinsic alignments on cosmic shear surveys and finish by reviewing practical mitigation techniques which attempt to remove contamination by intrinsic alignments.

The Habitable-Exoplanet Observatory (HabEx) is a candidate flagship mission being studied by NASA and the astrophysics community in preparation of the 2020 Decadal Survey. The first HabEx mission concept that has been studied is a large (~4m) diffraction-limited optical space telescope, providing unprecedented resolution and contrast in the optical, with extensions into the near ulttraviolet and near infrared domains. We report here on our team's efforts in defining a scientifically compelling HabEx mission that is technologically executable, affordable within NASA's expected budgetary envelope, and timely for the next decade. We also briefly discuss our plans to explore less ambitious, descoped missions relative to the primary mission architecture discussed here.