Magnetars are neutron stars with the strongest magnetic fields known in the Universe, observed as high-energy galactic sources. The formation of these objects is one of the most studied scenarios to explain some of the most violent explosions: superluminous supernovae, hypernovae, and gamma-ray bursts. In recent years, our team has succeeded in numerically reproducing magnetic fields of magnetar-like intensities by simulating dynamo amplification mechanisms that develop in the proto-neutron star during the first seconds after the collapse of the progenitor core. However, most observational manifestations of magnetars require the magnetic field to survive over much longer timescales (from a few weeks for super-luminous supernovae to thousands of years for Galactic magnetars). This thesis will consist of developing 3D numerical simulations of magnetic field relaxation initialized from different dynamo states previously calculated by the team, extending them to later stages after the birth of the neutron star when the dynamo is no longer active. The student will thus determine how the turbulent magnetic field generated in the first few seconds will evolve to eventually reach a stable equilibrium state, whose topology will be characterized and compared with observations.

The Sun and solar-type stars possess rich and variable magnetism. In our recent work on turbulent convective dynamos in this type of star, we have been able to highlight a magneto-rotational history of their secular evolution. Stars are born active with short magnetic cycles, then slow down due to braking by their magnetized particle wind, their magnetic cycle lengthens to become commensurate with that of the Sun (lasting 11 years) and finally, for stars that live long enough, they end up with a loss of cycle and a so-called anti-solar rotation (slow equator/fast poles). The agreement with observations is excellent, but we are missing an essential element to conclude: What role do sunspots/starspots play in the organization of the magnetism of these stars, and are they necessary for the appearance of a stellar magnetic cycle, e.g. the so-called “paradox of spotty dynamos”? Indeed, our HPC simulations of solar dynamos do not have yet the angular resolution to resolve the spots, and yet we do observe cycles in our simulations of stellar dynamos for Rossby numbers < 1. So, are the spots simply a surface manifestation of an internal self-organization of the cyclic magnetism of these stars, or do they play a decisive role? Furthermore, how do the latitudinal flux emergence and the size and intensity of the spots forming on the surface evolve during the magneto-rotational evolution of these stars? To answer these key questions in stellar and solar magnetism in support of the ESA space missions Solar Orbiter and PLATO, in which we are involved, new HPC simulations of stellar dynamos must be developed, allowing us to get closer to the surface and thus better describe the process of magnetic flux emergence and the possible formation of sun/starspots. Recent tests showing that magnetic concentrations inhibiting local surface convection form in simulations with a higher magnetic Reynolds number and smaller-scale surface convection strongly encourage us to continue this project beyond the ERC Whole Sun project (ending in April 2026). Thanks to the Dyablo-Whole Sun code that we are co-developing with IRFU/Dedip, we wish to study in detail the convective dynamo, the emergence of magnetic flux, and the self-consistent formation of resolved spots, using its adaptive mesh refinement capability while varying global stellar parameters such as rotation rate, convective zone thickness, and surface convection intensity to assess how their number, morphology and latitude of emergence change and if they contribute or not to the closing of the cyclic dynamo loop.

Launched in 2023, the Euclid satellite is surveying the sky in optical and infrared wavelengths to create an unprecedented map of the Universe's large-scale structure. A cornerstone of its mission is the measurement of weak gravitational lensing—subtle distortions in the shapes of distant galaxies. This phenomenon is a powerful cosmological probe, capable of tracing the evolution of dark matter and helping to distinguish between dark energy and modified gravity theories.
Traditionally, cosmologists have analyzed weak lensing data using second-order statistics (like the power spectrum) paired with a Gaussian likelihood model. This established approach, however, faces significant challenges:
- Loss of Information: Second-order statistics fully capture information only if the underlying matter distribution is Gaussian. In reality, the cosmic web is highly structured, with clusters, filaments, and voids, making this approach inherently lossy.
- Complex Covariance: The method requires estimating a covariance matrix, which is both cosmology-dependent and non-Gaussian. This necessitates running thousands of computationally intensive N-body simulations for each model, a massive and often impractical undertaking.
- Systematic Errors: Incorporating real-world complications—such as survey masks, intrinsic galaxy alignments, and baryonic feedback—into this framework is notoriously difficult.

In response to these limitations, a new paradigm has emerged: likelihood-free inference via forward modelling. This technique bypasses the need for a covariance matrix by directly comparing real data to synthetic observables generated from a forward model. Its advantages are profound: it eliminates the storage and computational burden of massive simulation sets, naturally incorporates high-order statistical information, and can seamlessly integrate systematic effects. However, this new method has its own hurdles: it demands immense GPU resources to process Euclid-sized surveys, and its conclusions are only as reliable as the simulations it uses, potentially leading to circular debates if simulations and observations disagree.

A recent breakthrough (Tinnaneni Sreekanth, 2024) offers a compelling path forward. This work provides the first theoretical framework to directly predict key wavelet statistics of weak lensing convergence maps—exactly the kind Euclid will produce—for any given set of cosmological parameters. It has been shown in Ajani et al (2021) that the wavelet coefficient L1-norm is extremely powerful to constraint the cosmological parameters. This innovation promises to harness the power of advanced, non-Gaussian statistics without the traditional computational overhead, potentially unlocking a new era of precision cosmology. We have demonstrated that this theoretical prediction can be used to build a highly efficient emulator (Tinnaneri Sreekanth et al, 2025), dramatically accelerating the computation of these non-Gaussian statistics. However, it is crucial to note that this emulator, in its current stage, provides only the mean statistic and does not include cosmic variance. As such, it cannot yet be used for full statistical inference on its own. 

This PhD thesis aims to revolutionize the analysis of weak lensing data by constructing a complete, end-to-end framework for likelihood-free cosmological inference. The project begins by addressing the core challenge of stochasticity: we will first calculate the theoretical covariance of wavelet statistics, providing a rigorous mathematical description of their uncertainty. This model will then be embedded into a stochastic map generator, creating realistic mock data that captures the inherent variability of the Universe.
To ensure our results are robust, we will integrate a comprehensive suite of systematic effects—such as noise, masks, intrinsic alignments, and baryonic physics—into the forward model. The complete pipeline will be integrated and validated within a simulation-based inference framework, rigorously testing its power to recover unbiased cosmological parameters. The culmination of this work will be the application of our validated tool to the Euclid weak lensing data, where we will leverage non-Gaussian information to place competitive constraints on dark energy and modified gravity.

References
V. Ajani, J.-L. Starck and V. Pettorino, "Starlet l1-norm for weak lensing cosmology", Astronomy and Astrophysics,  645, L11, 2021.
V. Tinnaneri Sreekanth, S. Codis, A. Barthelemy, and J.-L. Starck, "Theoretical wavelet l1-norm from one-point PDF prediction", Astronomy and Astrophysics,  691, id.A80, 2024.
V. Tinnaneri Sreekanth, J.-L. Starck and S. Codis, "Generative modeling of convergence maps based in LDT theoretical prediction", Astronomy and Astrophysics,  701, id.A170, 2025.