The backreaction of inhomogeneities

For more info about our services contact : help@bestpfe.com

Table of contents

1 Introduction 
1.1 The 3+1 and 1+3 formalisms of general relativity
1.2 The standard model of cosmology
1.3 The backreaction of inhomogeneities
1.4 Newtonian cosmology
1.5 Strategy of the thesis
References
2 1+3-Newton-Cartan system and Newton-Cartan cosmology 
2.1 Why Newton-Cartan?
2.2 Galilean spacetimes
2.3 The 1+3-Newton-Cartan equations
2.4 Space expansion in Newton-Cartan
2.5 Gravitational field and cosmological equations in Newton-Cartan
2.6 Observers in the Newton-Cartan theory
2.7 Conclusion
References
3 On non-Euclidean Newtonian theories and their global backreaction
3.1 Introduction of a spatial Ricci curvature
3.2 Poisson equation approach
3.3 The Newton-Cartan approach
3.4 Lorentzian manifold from a solution of the Newton’s equations
3.5 Conclusion
References
4 Galilean limit of general relativity
4.1 Motivations
4.2 Galilean limit of Lorentzian structures
4.3 The (Euclidean) Newtonian limit
4.4 The non-Euclidean Newtonian limit
4.5 Backreaction from post-Newtonian terms
4.6 Conclusion
References
5 Towards non-Euclidean relativistic simulations
5.1 Lattice cosmology
5.2 Relativistic numerical cosmology with fluid models
5.3 Probing the effect of topology with the BSSN formalism
5.4 Which topology to choose?
5.5 Conclusion
References
6 Conclusion and perspectives