Dynamics of a lattice Universe : the dust approximation in cosmology
- Bruneton, J-P, Larena, Julien
- Authors: Bruneton, J-P , Larena, Julien
- Date: 2012
- Language: English
- Type: Article
- Identifier: vital:6789 , http://hdl.handle.net/10962/d1006941
- Description: We find a solution to Einstein field equations for a regular toroidal lattice of size L with equal masses M at the centre of each cell; this solution is exact at order M/L. Such a solution is convenient to study the dynamics of an assembly of galaxy-like objects. We find that the solution is expanding (or contracting) in exactly the same way as the solution of a Friedman–Lemaître–Robertson–Walker Universe with dust having the same average density as our model. This points towards the absence of backreaction in a Universe filled with an infinite number of objects, and this validates the fluid approximation, as far as dynamics is concerned, and at the level of approximation considered in this work.
- Full Text:
- Date Issued: 2012
- Authors: Bruneton, J-P , Larena, Julien
- Date: 2012
- Language: English
- Type: Article
- Identifier: vital:6789 , http://hdl.handle.net/10962/d1006941
- Description: We find a solution to Einstein field equations for a regular toroidal lattice of size L with equal masses M at the centre of each cell; this solution is exact at order M/L. Such a solution is convenient to study the dynamics of an assembly of galaxy-like objects. We find that the solution is expanding (or contracting) in exactly the same way as the solution of a Friedman–Lemaître–Robertson–Walker Universe with dust having the same average density as our model. This points towards the absence of backreaction in a Universe filled with an infinite number of objects, and this validates the fluid approximation, as far as dynamics is concerned, and at the level of approximation considered in this work.
- Full Text:
- Date Issued: 2012
The fitting problem in a lattice Universe
- Authors: Larena, Julien
- Date: 2012
- Language: English
- Type: Text
- Identifier: vital:6780 , http://hdl.handle.net/10962/d1012405
- Description: We present a regular cubic lattice solution to Einstein field equations that is exact at second order in a small parameter. We show that this solution is kinematically equivalent to the Friedmann-Lemaitre-Robertson-Walker (FLRW) solution with the same averaged energy density. This allows us to discuss the fitting problem in that framework: are observables along the past lightcone of observers equivalent to those in the analogue FLRW model obtained by smoothing spatially the distribution of matter? We find a criterion on the compacity of the objects that must be satisfied in order for the answer to this question to be positive and given by perturbative arguments. If this criterion is not met, the answer to this question must be addressed fully non perturbatively along the past lightcone, even though the spacetime geometry can be described perturbatively. , Prepared for the Proceedings of the conference 'Relativity and Gravitation: 100 years after Einstein in Prague', Prague, 25-29th June 2012.
- Full Text:
- Date Issued: 2012
- Authors: Larena, Julien
- Date: 2012
- Language: English
- Type: Text
- Identifier: vital:6780 , http://hdl.handle.net/10962/d1012405
- Description: We present a regular cubic lattice solution to Einstein field equations that is exact at second order in a small parameter. We show that this solution is kinematically equivalent to the Friedmann-Lemaitre-Robertson-Walker (FLRW) solution with the same averaged energy density. This allows us to discuss the fitting problem in that framework: are observables along the past lightcone of observers equivalent to those in the analogue FLRW model obtained by smoothing spatially the distribution of matter? We find a criterion on the compacity of the objects that must be satisfied in order for the answer to this question to be positive and given by perturbative arguments. If this criterion is not met, the answer to this question must be addressed fully non perturbatively along the past lightcone, even though the spacetime geometry can be described perturbatively. , Prepared for the Proceedings of the conference 'Relativity and Gravitation: 100 years after Einstein in Prague', Prague, 25-29th June 2012.
- Full Text:
- Date Issued: 2012
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