Cosmo-Blow-Up · Deflating the blow-up: controlling infinities in cosmic fluid descriptions
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2018-12-01 → 2020-11-30
- EU contribution
- €185,076
- Participants
- 1
- Scheme
- MSCA-IF-EF-ST
Lines connect the coordinator with its partners.
Results in brief
Deflating the blow-up: controlling infinities in cosmic fluid descriptions
The main objective of this action was to mathematically analyse shell-crossings in our Universe, which is the instance when dark matter particle trajectories cross for the first time. This instance is accompanied with formally infinite matter densities and is thus highly relevant for the process of cosmic structure formation; resolving these infinities in a tractable manner constitutes a major challenge in the field of mathematical cosmology. The scientific tasks were essentially three-fold, namely (1) to provide the theoretical framework that allows to solve the underlying cosmic fluid equations to arbitrary high precision, (2) to numerically implement these theoretical findings, thereby establishing a simulation of the dark matter fluid for random initial conditions, from which shell-crossings are detected, and (3) to further exploit the theoretical findings by establishing exact analytical shell-crossing solutions for simplified initial conditions. All those three tasks were successfully executed and lead to the anticipated deliverables and milestones, which are scientific papers. Specifically, building up on previous works of myself, we were able to complete the underlying theory. Thanks to the expertise provided at the Lagrange Institute, we implemented these findings in a computationally highly efficient way (full support of parallel computing), from which we were able to detect shell-crossings to extremely high accuracy. This numerical implementation is publicly available and can be directly exploited by the wider cosmological audience, e.g. for generating highly accurate initial conditions of heavily used cosmological N-body simulations. I discovered also new exact analytical solutions for nonlinear matter collapse models, and we were able to exploit the matter collapse in the presence of massive neutrinos. As a side product, we performed highly efficient two-fluid simulations that include neutrino clustering. The deliverables and milestones have been published in peer reviewed papers with high impact factor.
Data: CORDIS, © European Union
Project objective
According to the standard model of cosmology, we are witnesses of an epic battle: While dark energy leads to an accelerated expansion, matter and particularly the dark matter, opposes this trend, leading to the observed large-scale structure of the Universe. Since the pioneering discovery of dark energy that lead to a Nobel Prize in Physics, the nature of dark matter is still shrouded in mystery. What we know is that matter can be described as a fluid on macrophysical scales, and that the fluid has, at early times, no overlapping matter trajectories. Yet, matter trajectories do eventually begin to intersect (""shell-crossing""), which marks the starting point of very complex computations in the phase-space on the one side, and the birth of our cluttered Universe on the other side. Understanding the collapse and shell-crossing is quite a challenge that is usually tackled by utterly opposing means, either by (approximative) analytical models or by cosmological N-body simulations. With this Marie-Curie fellowship, I will close this gap and get full control of the instant of shell-crossing in two complementary ways. I will develop full-fledged numerical simulations of the cosmological fluid equations and develop certain matter collapse models, that, at their heart, determine the matter trajectories by exact analytical descriptions until the instance of shell-crossing, where infinities become real and the solutions ""blow up"". Detecting blow-ups is one of the most challenging and rewarding problems in mathematical physics; by resolving them, precious information will be gained which we will use to improve (heavily used) N-body simulations at the critical vicinity of shell-crossing. The department Lagrange (host institute) is a unique place in Europe that houses both world experts in numerical cosmology and in mathematical analysis, thereby complementing exactly my expertise (exact analytical models). This allows us to solve outstanding problems in interdisciplinary fields.""
Original text from CORDIS.
Participants
- CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS · ParisCoordinatorFrance
Links
- View on CORDIS
- DOI: 10.3030/795707
- https://web.archive.org/web/20201129104738/https://www.oca.eu/fr/group
Data: CORDIS, © European Union