## Research Overview

Cosmology can be described as the search for two numbers: the current values of the Hubble parameter and the deceleration parameter. The former describes the speed at which space-time of the universe is expanding on the largest scales. The latter describes how quickly that seed is changing (i.e., the acceleration of the expansion of space). Our current cosmological paradigm states that both the speed and acceleration have evolved over time: about seven billion years after the Big Bang, we have evidence that the universe stopped slowing down in its expansion and started to speed up. We do not know what started this acceleration, we do not know how it evolved, and we do not know how it will end. Our current theories explore a large range of physical explanations, from a constant term (or perhaps not) added to Einstein’s field equations, to a more generalized approach to the field equations themselves, to new theories of gravity which aim to combine gravity and quantum mechanics. An observational time-evolving characterization of the expansion of space-time would have a profound impact on constraining the theories of its causation.

Galaxy clusters trace the expansion of the Universe in three different ways

*Number count:*Galaxy clusters are identified as peaks above a threshold in the underlying dark matter density field. Galaxies attract onto those peaks over time until gravity loses the battle against the accelerating expansion of space. The number and masses of galaxy clusters over time are sensitive to the expansion history of the Universe as well as the total amount of matter in the Universe. By measuring the cluster abundance, we constrain cosmology.*Spatial distribution:*The primordial power spectrum of the matter density fluctuations in the Universe was imprinted into the spatial distribution of clusters. Due to the presence of baryons, this power spectrum has features called the “Baryon Acoustic Oscillations (BAO). The BAO become “standard-rulers,” which map the length-scale of the sound horizon of the Universe through time. Statistical measures like the two-point correlation function and the cluster power spectrum can be used to trace the scale of the BAO and the expansion history of the Universe.*Escape velocity:*The radius-velocity phase-space of galaxies within clusters has a sharp edge with traces the escape velocity of galaxies from clusters. This escape velocity is derived from the local Newtonian gravitational potential and the acceleration of the expansion of the Universe. In an accelerating Universe, galaxy escape speeds are slowed because they need to escape only to a distance where the pull of the expanding space-time overcomes gravity. Photo-based weak-lensing cluster potentials are free from this effect and can be used jointly with the dynamical measures to constrain cosmology.

This project will conduct a meta-analysis which combines the cosmological constraints from the above techniques. This will lay the foundation for a future, larger effort using the next generation large-scale astronomy survey data from the Large Synoptic Survey Telescope and the Dark Energy Spectroscopic Instrument.