Constraining Cosmological Parameters with Galaxy Cluster Phase Spaces

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In 1914, Einstein brought forth his foundations for GeneralRelativity (GR) to explain gravity using the geometry of space andtime. Einstein's GR ushered in the beginning of a new scientificparadigm shift for the science of the origin and evolution of theuniverse ("Cosmology"). This is now a golden age, similar to thecenturies around Plato, Copernicus and Newton, and we are privilegedto be witnesses to this paradigm shift in real-time. All scientificparadigms go through a long period of intense testing, as the data andthe scientific methods push the theory to its limits. The Universe isso vast that there are physical scales on which GR should apply, butwhich have been difficult to test. Consider clusters of galaxies,which are the largest gravitationally bound objects in the Universe.Clusters entrap galaxies on scales of tens of millions of light years(i.e, 100 times larger than our own Milky Way). Does Einstein's GRstill apply over such large distances in space-time?The escape velocity from a galaxy cluster is a combination of thelocal Newtonian gravitational potential and the acceleration of theexpansion of the Universe. Weak lensing mass profiles of clusters canbe used to predict the escape velocity profile from the gravitationalNewtonian component and cosmology. This joint analysis provides a newdirect avenue to constrain the dynamics of the expanding Universe andcan simultaneously test GR and our standard Lambda CDM cosmologicalparadigm, time evolving dark energy, Chameleon gravity, and more. Wewill use the Michigan Magellan Fiber System (M2FS) to collect 100-200galaxy cluster member spectra for escape velocities of clusters withinthe Dark Energy Survey (DES) footprint. We will directly compare theweak-lensing predicted escape velocity profiles to the observedprofiles from the M2FS data in a likelihood analysis. Given a Hubbleconstant prior, this probe can achieve similar or better precision onthe dark energy equation of state parameters compared to supernovae orthe CMB.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.