Prof. David Alonso

Abstract:

We investigate the three-dimensional clustering of sources emitting electromagnetic pulses traveling through cold electron plasma, whose radial distance is inferred from their dispersion measure. As a distance indicator, dispersion measure is systematically affected by inhomogeneities in the electron density along the line of sight and special and general relativistic effects, similar to the case of redshift surveys. We present analytic expressions for the correlation function of fast radio bursts (FRBs) and for the galaxy-FRB cross-correlation function, in the presence of these dispersion measure-space distortions. We find that the even multipoles of these correlations are primarily dominated by nonlocal contributions (e.g., the electron density fluctuations integrated along the line of sight), while the dipole also receives a significant contribution from the Doppler effect, one of the major relativistic effects. A large number of FRBs, O(105-106), expected to be observed in the Square Kilometre Array, would be enough to measure the even multipoles at very high significance, S/N≈100, and perhaps to make a first detection of the dipole (S/N≈10) in the FRB correlation function and FRB-galaxy cross correlation function. This measurement could open a new window to study and test cosmological models.

Abstract:

We assess the usefulness of gradient-based samplers, such as the no-U-turn sampler (NUTS), by comparison with traditional Metropolis–Hastings (MH) algorithms, in tomographic 3 × 2 point analyses. Specifically, we use the Dark Energy Survey (DES) Year 1 data and a simulated dataset for the Large Synoptic Survey Telescope (LSST) survey as representative examples of these studies, containing a significant number of nuisance parameters (20 and 32, respectively) that affect the performance of rejection-based samplers. To do so, we implement a differentiable forward model using JAX-COSMO, and we use it to derive parameter constraints from both data sets using the NUTS algorithm implemented in NUMPYRO, and the Metropolis–Hastings algorithm as implemented in COBAYA. When quantified in terms of the number of effective number of samples taken per likelihood evaluation, we find a relative efficiency gain of O(10) in favour of NUTS. However, this efficiency is reduced to a factor ∼ 2 when quantified in terms of computational time, since we find the cost of the gradient computation (needed by NUTS) relative to the likelihood to be ∼ 4.5 times larger for both experiments. We validate these results making use of analytical multivariate distributions (a multivariate Gaussian and a Rosenbrock distribution) with increasing dimensionality. Based on these results, we conclude that gradient-based samplers such as NUTS can be leveraged to sample high-dimensional parameter spaces in Cosmology, although the efficiency improvement is relatively mild for moderate (O(50)) dimension numbers, typical of tomographic large-scale structure analyses.