1. Theory group
Michael Joyce *

2. Plan Le groupe et ses collaborations Cadre général de recherche
Quelques resultats récents
Perspectives

3. Members and collaborations
1 permanent (MJ) + doctorants (quatre depuis 2007)
+ External french collaborations: LPTMC(UPMC), Université de Nice
+ External non-french collaborations: Rome, Copenhagen (NBI)

4. Overview of research

5. The problem of structure formation
Principal Motivation:
The problem of structure formation ?? 
WMAP : the universe aged ~105 years… SDSS : the universe today (1010 years)
Density fluctuations ~ Fluctuations >> 1
How do these structures come from these initial conditions ?
Theory furnishes predictions also for other observations
(weak lensing, dark matter searches…)

6. Cosmological structure formation
Overview
Cosmological structure formation
Linear Regime: simple and resolved analytically
Non-linear regime: intractable, essentially numerical resolution

7. Structure formation in the standard cosmological model: millenium
Millenium simulations:

8. Cosmological simulations: limitations
Overview
Cosmological simulations: limitations
Numerical simulations
(still) have limited spatial resolution
use approximate (N-body) methods, precision is not established
They lead to purely phenomenological descriptions (e.g halo models)
Even if « dissipationless» (i.e. gravity only) poor understanding of physics

9. Goals of research Overview
To improve understanding of physics of non-linear regime of clustering
[ To improve accuracy of our description of non-linear clustering for comparison with observations ]
Recent years:
Mostly purely self-gravitating systems
Broad framework  statistical mechanics of long-range systems

10. Thèses récentes François SICARD
Out of equilibrium dynamics of infinite one dimensional self-gravitating systems soutenue décembre 2010
Tirawut WORRAKITPOONPON
Relaxation of isolated self-gravitating systems in one and three dimensions, soutenue juin 2011
David BENHAIEM
Self-similarity and stable clustering in scale-free cosmological models in one and three dimensions soutenue décembre 2013
Jules MORAND
Dynamics of long-range interacting systems beyond the Vlasov limit soutenue décembre 2014

11. Some recent publications
D. Benhaiem and M. Joyce,
Self-similarity and stable clustering in a family of scale-free cosmologies
Mon. Not. R. Astron. Soc. 394, 791 (2014)
I. Carucci, M. Sparre, S. Hansen and M.Joyce
Particle ejection during mergers of dark matter halos
JCAP 06, 57 (2014)
M. Joyce, P. Viot and J. Morand
Scaling Quasistationary States in Long-Range Systems with Dissipation
Phys. Rev. Lett., 112, (2014)
A. Gabrielli, M. Joyce and J. Morand,
Finite-N corrections to Vlasov dynamics and the range of pair interactions,
Phys. Rev. E90, (2014)

12. Some recent results

13. Non-linear clustering in scale-free cosmologies
David Benhaiem, MJ and Bruno Marcos
Mon. Not. R. Astron. Soc. (2014)
Equations of motion of N-body simulations (in general):
Can be recast in new “time” variable as
where
i.e. self gravitating particles subjected to a fluid damping

14. Effective damping in standard cosmology

15. scale-free cosmologiesIf
Initial power spectrum P(k) ~ kn
« Damping coefficient » kappa independent of time
the model is « scale-free »
Only one relevant characteristic scale
 clustering must be « self-similar »
temporal evolution = trivial rescaling of coordinates
Provides very powerful control on numerical simulation

16. Effect of expansion rate on structure formation
small damping large damping

17. dependence of NL clustering on cosmology
Scale-free models:
dependence of NL clustering on cosmology

18. resolution and stable clustering
Scale-free models:
resolution and stable clustering

19. self-similarity tests: some conclusions
Resolution improves in time in a strongly model-dependent way
The analytical prediction of stable clustering provides a very good approximation to the well resolved non-linear regime
Currently in preparation:
Halo profiles in this family of cosmologies…universality of halos (NFW)?
Conclusions:
universality broken in large part of model space
slope of outer part of profile is clearly model dependent

20. Application to dark energy models?
A very large family of dark energy models can be approximated as interpolations through our scale-free family:
 Construction of semi-analytical approximations for clustering statistics

21. Perspectives

22. Perspectives
Short-term focus on consolidating and developing external collaborations (no thesis student recruted this year). Sabbatical MJ next year?
Medium-long term: focus more on cosmological orientation or statistical mechanics ?
Stat mech: possibility of collaboration with experimental group at NTU Singapore
Recrutement of post-doc (Comité théorie in2p3?) with numerical orientation would greatly boost cosmological aspects