Master II Interniship proposals

Description: Theoretical and observational advances in cosmology offer a unique opportunity to explore subtle relativistic properties hidden in the folds of the cosmic web. In the coming years, big data will allow small effects to be measured and, in turn, the most minute details will be of utmost importance to gain insights into, and perhaps solve, great cosmological puzzles such as the physical nature of those still elusive cosmic components called dark matter and dark energy.
With this proposal we intend to develop analytical approaches to study the linear evolution of cosmological perturbations in non-Newtonian regimes, i.e., on spatial and temporal scales where general relativistic corrections are no longer negligible. According to the standard picture, each perturbation mode in the matter distribution enters the ’cosmic horizon’ (its physical length becomes shorter than Hubble’s length) and begins to grow in amplitude. We expect this transition to introduce fine structure corrections to the Newtonian scenario, such as, for example, scale-dependent modulations in the growth of linear perturbations of matter, and in general, deviations from simple predictions obtained using quasi-static approximation, which are valid only in regimes where the temporal derivatives of perturbations are negligible compared to spatial ones.
The aim is to investigate the potential existence of tricky relativistic effects, emerging on large cosmological scales, which may allow solving a long-standing issue in observational cosmology: the discrepancy between the measurement of the amplitudes of dark matter fluctuations made in our local outskirts with those made in the early universe, when cosmic structures were much younger.

Deadline: -

Description: This three-month internship project will focus on forecasting the ability of future scientific experiments to test whether cosmological perturbations, particularly the growth of structure in the universe, are compatible with the predictions of General Relativity (GR) and the ΛCDM model. The candidate will investigate the potential of combining gravitational-wave angular power spectra with galaxy surveys in tomographic redshift bins to test cosmological perturbations at late cosmic times.

Objective: The main goal of this project is to assess the ability of cross-correlation measurements between gravitational-wave data (from advanced interferometers like Einstein Telescope and Cosmic Explorer) and galaxy surveys (such as Euclid) to constrain the underlying cosmological model, specifically the evolution of perturbations and their compatibility with GR and the ΛCDM paradigm. The candidate will focus on testing whether the large-scale structure and perturbation evolution inferred from these observables are consistent with the standard cosmological model, and how the data can be used to distinguish deviations from GR.

Key Tasks:
-Modeling Cosmological Perturbations Beyond GR: Familiarise with theoretical models for cosmological perturbations, including density fluctuations and gravitational potentials, beyond the ΛCDM framework. Analyze how these perturbations affect the angular power spectrum in both gravitational-wave and galaxy surveys.
-Gravitational-Wave and Galaxy Survey Cross-Correlation: Perform numerical studies of the cross-correlation between the angular power spectra of gravitational waves and galaxy surveys, taking into account the perturbations’ evolution. Investigate the impact of perturbations on the gravitational-wave signal, and explore how this might provide insight into deviations from standard cosmology.
-Fisher Matrix Analysis: Use a Fisher matrix approach to evaluate how next-generation GW detectors (like Cosmic Explorer and Einstein Telescope) and galaxy surveys (such as Euclid) can be used to test the compatibility of cosmological perturbations with GR. The analysis will incorporate realistic source populations and errors specific to the next-generation detectors and survey configurations.
-Testing for Deviations from ΛCDM: investigate how departures from ΛCDM might appear in the data, and the constraining power of the latter. especially in the context of large-scale structure formation and gravitational-wave propagation.

Expected Outcomes: Assessment of the potential of next-generation detectors to test cosmological models beyond ΛCDM.
Establishment of the feasibility of using gravitational-wave and galaxy survey cross-correlations to probe deviations from GR.

Skills and Tools: The candidate will gain experience in the use of gravitational-wave data for cosmology, including the use of Fisher matrix techniques and numerical simulations.
The project will provide exposure to the theoretical modeling of cosmological perturbations
Familiarity with Python (and relevant libraries like NumPy, SciPy, Matplotlib), and simulation tools will be beneficial.

Importance of this Work: This project will contribute to testing the core assumptions of the ΛCDM model, and determine whether gravitational-wave astronomy, alongside large galaxy surveys, could be used to test fundamental aspects of cosmology. A successful analysis could lead to new constraints on the properties of cosmological perturbations and potentially reveal deviations from GR, providing a deeper understanding of the universe’s evolution.

Deadline: -

Description: This three-month internship project will focus on investigating the propagation of gravitational waves (GWs) and the constraints on complex gravitational-wave population models within a hierarchical Bayesian inference framework. The project will extend an approach developed in recent work of the group at CPT, which tackles the full hierarchical population posterior of merging black holes in gravitational-wave astronomy. The framework, developed using modern probabilistic programming languages and Hamiltonian Monte Carlo (HMC), is designed to fully sample the parameter space of both individual events (such as masses, spins, redshifts) and the underlying population hyperparameters.
The candidate will explore how this framework can be applied to investigate the propagation of GWs through the expanding universe to test its compatibility with General Relativity. The project will also explore how complex population models can be integrated into the framework for a more comprehensive understanding of the astrophysical and cosmological parameters that govern the merging binary population.

Objective: The goal of this project is to apply an existing Python-based hierarchical population inference framework to test the propagation of gravitational waves through the universe. We will assess the influence of cosmological parameters on the observed GW signals and populations, while taking advantage of the advanced sampling methods (HMC and probabilistic programming) to explore high-dimensional parameter spaces.

Key Tasks:
-Testing Gravitational-Wave Propagation: Use a hierarchical inference framework to investigate how the propagation of gravitational waves through the universe can be constrained.
-Population Modeling: Explore how the framework can be applied to model complex populations of gravitational-wave sources, incorporating both astrophysical parameters (such as masses, spins, and redshifts) and cosmological parameters. The candidate will study the correlations between individual event parameters and population-level hyperparameters.
-Full Parameter Sampling: The candidate will perform full hierarchical sampling of the merging black hole population, including direct sampling of both single-event parameters and population hyperparameters. This approach, which is different from traditional methods that marginalize over single-event parameters, will allow for a more detailed and accurate understanding of the population's underlying structure.
-Framework Enhancement: As part of the internship, the candidate will work with the supervisor's open-source Python implementation, which uses Hamiltonian Monte Carlo (HMC) and modern probabilistic programming techniques, to test the framework on models of modified gravitational-wave propagation and complex population structures.

Expected Outcomes: Extension of the hierarchical Bayesian framework to test gravitational-wave propagation.
Possible identification of key astrophysical or cosmological features that can be further constrained using future gravitational-wave surveys.

Skills and Tools: Python Programming: The candidate will work with Python-based tools for Bayesian inference, utilizing Hamiltonian Monte Carlo (HMC) methods and probabilistic programming libraries like PyMC3 or NumPyro.
Bayesian Inference Techniques: Practical experience with advanced sampling methods, including Markov Chain Monte Carlo (MCMC) and hierarchical models, will be beneficial.
Cosmological Modeling: Familiarisation with modern cosmological models, with a focus on how cosmological parameters can be incorporated into gravitational-wave data analysis.
Numerical Simulations: Practical experience running parameter inference in gravitational-wave astronomy.

Importance of this Work: This project will contribute to the growing field of gravitational-wave cosmology by advancing methods for testing the propagation of gravitational waves through the universe. By leveraging the framework developed in the supervisor’s open-source Python implementation, the candidate will gain a deeper understanding of the complex interactions between astrophysical populations and cosmological models. This research has the potential to contribute to the interpretation of future gravitational-wave catalogs, improving our understanding of the universe's expansion and testing key assumptions of General Relativity and the ΛCDM model.

Deadline: -