My research focuses on developing and applying novel dynamical methods to measure galaxy cluster masses and probe cosmological parameters. By analyzing galaxy velocities and positions in cluster phase spaces, I work to extract fundamental information about dark matter, gravity, and the expansion history of the universe.
The centerpiece of my work involves measuring galaxy cluster masses using escape velocity profiles—the maximum velocities at which galaxies remain bound to clusters. Unlike traditional methods that rely on equilibrium assumptions (such as velocity dispersion or X-ray temperature), the escape velocity technique provides an instantaneous snapshot of the gravitational potential, similar to how weak gravitational lensing maps mass through light deflection.
In my recent publication in The Astrophysical Journal (Rodriguez et al. 2024), I developed a rigorous framework for inferring cluster masses from escape velocity profiles, accounting for observational effects including sparse galaxy sampling, projection effects, and measurement uncertainties. A key innovation was modeling the statistical suppression of observed velocity profiles measured in Action-based galaxy modelling architecture (AGAMA) rather than simulations, which proved essential for unbiased mass estimation.
My most significant result demonstrates excellent agreement between escape velocity masses and weak gravitational lensing masses for 46 galaxy clusters spanning redshifts 0.05 < z < 0.3 and masses 10^14.4 to 10^15.4 solar masses. Published in The Astrophysical Journal (Rodriguez et al. 2025), this work resolved a long-standing discrepancy in the field: previous caustic-based dynamical masses showed poor correlation with lensing masses, but our improved methodology reveals a strong correlation (0.68) and negligible bias (0.02 dex).
This concordance validates both techniques and demonstrates that dynamical and lensing mass estimates are fundamentally compatible in ΛCDM cosmology—a critical consistency check for our understanding of structure formation. The observed scatter (0.17 dex) matches expectations from individual measurement uncertainties, with no evidence for additional intrinsic scatter.
The mass-velocity dispersion relation is a cornerstone of cluster cosmology, enabling mass estimates for the thousands of clusters in spectroscopic surveys where only dispersions are readily measurable. While this relation has been extensively studied in simulations, observational confirmations have been troubled by conflicting results—some studies report unexpectedly large scatter while others find artificially tight correlations. These inconsistencies have raised concerns about whether we truly understand the relationship between cluster masses and their velocity structure.
My work provides a crucial observational test by comparing escape velocity masses—measured independently from the phase-space boundary—with velocity dispersions. Unlike previous dynamical methods that are calibrated against dispersions, escape velocities offer genuinely independent mass measurements across a statistically meaningful sample. The observed correlation and scatter between escape masses and dispersions reveals the true intrinsic relationship and offers the strongest evidence that the mass-dispersion relation observed in simulations can be re-produced in observations.
A unique aspect of escape velocity measurements is their direct sensitivity to the expansion history of the universe through the deceleration parameter q(z). The escape velocity depends on both the cluster's gravitational potential and the outward acceleration from cosmic expansion—creating a competition between infall and expansion that directly constrains q(z)H²(z).
This capability is particularly timely given recent results from the Dark Energy Spectroscopic Instrument (DESI), which suggest possible deviations from the standard ΛCDM cosmological model. DESI data hint that the universe may have transitioned differently between deceleration and acceleration phases than predicted by a cosmological constant, with the evolution of q(z) potentially showing dynamical dark energy behavior rather than a static cosmological constant.
Escape velocity measurements provide an independent dynamical probe of this expansion history—one that is completely independent of the angular diameter distance and luminosity distance measurements used by standard cosmological probes (CMB, baryon acoustic oscillations, Type Ia supernovae). My ongoing work is using galaxy cluster phase spaces to reconstruct q(z) as a function of redshift, offering a novel test of whether the DESI hints of cosmic deceleration in the recent past are supported by dynamical evidence. Preliminary results show we can constrain qH²/H₀² to ~20-30%, providing meaningful constraints on the acceleration history over the past several billion years.
In addition to probing the expansion history, escape velocity measurements can constrain present-day cosmological parameters, particularly the Hubble constant H₀ and matter density Ωₘ. These parameters enter directly into the escape velocity calculation through the balance point where gravitational attraction equals cosmic expansion.
This offers a rare dynamical measurement of H₀—independent of the distance ladder and early-universe physics that underlie the current "Hubble tension" between local (Cepheids + Type Ia supernovae) and early-universe (CMB) measurements. Using Fisher matrix forecasts, I have demonstrated that samples of ~50-100 clusters with high-quality spectroscopy can achieve percent-level constraints on H₀ and ~10% constraints on Ωₘ.
Broader Implications
This research has several important applications:
Modified Gravity Tests: Escape velocity profiles offer rare tests of general relativity on megaparsec scales, as modifications to gravity (such as f(R) theories) would alter the relationship between mass and velocity profiles.
Cosmological Tensions: As the only known dynamical probe of both expansion history and present-day cosmological parameters, escape velocities offer unique leverage on current tensions in cosmology, providing measurements that are independent of both early-universe physics and traditional distance measurements.
Cluster Mass Estimates: Accurate dynamical masses are essential for understanding galaxy clusters. The escape velocity provides crucial cross-validation for other methods like weak lensing or velocity dispersions.