Beyond standard large-scale structure: optimising cosmological probes and primordial feature detections

Abstract

The current and forthcoming generation of galaxy surveys will provide data with unprecedented precision. To take full advantage of this opportunity, similar advances on the theoretical side are required. However, unlike the modelling of the Cosmic Microwave Background (CMB), these late-time cosmological probes are more susceptible to non-linear gravitational collapse dynamics: this sets a limit on the extent to which one can describe the large-scale distribution of galaxies analytically. Even though it is challenging, efforts to understand these complex dynamics pay off: the 3D nature of galaxy maps implies that the number of modes sampled scales with ∼ k3, in contrast to the quadratic scaling of the CMB.

Over the last few decades, these considerations have motivated the development of cosmological perturbation theory for structure formation. The state-of-the-art model employs tools borrowed from quantum field theory, such as field renormalisation, counter-terms, cut-off scales, the renormalisation group, and so on. These tools are at the heart of the Standard Model of particle physics, the holy grail of theoretical physics, which remarkably explains Nature up to energy scales of ∼ 1 TeV. Their use in structure formation, therefore, highlights the maturity and robustness of the model, indicating an awareness of why the model works and, perhaps more importantly, its limitations. These mathematical tools are used extensively throughout this dissertation. A succinct introduction to these techniques can be found in Chapter 1, alongside a list of relevant references for further reading.

On the data-analysis side, we developed a pipeline to search for primordial physics (i.e., inflationary signals) in galaxy clustering datasets. In Chapter 2, we pedagogically demonstrate how these signals can be studied using spectroscopic survey data and show the pipeline’s robustness by performing a joint analysis of the BOSS DR12 galaxy sample and the eBOSS quasar sample. This pipeline was validated with mock catalogues and led to the tightest constraints to date on some of the models considered. We are currently working on a follow-up project in which we extend this analysis using the DESI Y1 data and consider new inflationary models.

On theoretical grounds, there are two main ideas developed in this thesis. In Chapter 3, we demonstrate why galaxy samples should be split into subpopulations before any perturbation model is applied. This idea relies on the fact that different tracers of the cosmic web occupy different environments. For instance, red galaxies are expected to populate denser regions, whereas blue galaxies are expected to reside in halo outskirts. This implies that their nonlinear response to cosmic dynamics differs. Hence, by combining them into a single tracer, the resulting clustering signal becomes the outcome of an average over different dynamics, making it harder to model. Using synthetic datasets, we show that splitting the data can lead to measurements of cosmological parameters with error bars ∼ 40% smaller than in the combined case.

Although the idea of splitting the data is well-motivated, a long-standing question in the field is how this split should be performed, which variables should be used, and how many splits are optimal. One way to answer this question is presented in Chapter 4. We cast the multi-tracer problem as an optimisation problem, in which we seek the optimal number of splits and weights used to define the sub-samples. We showcase its application in a one-dimensional case and prove that the problem is indeed formally defined: it is possible to optimise the information we extract from correlation functions of the cosmic fields by selecting the right number and type of weights. The further development of such a model in three dimensions is work in progress.