Observables in a lattice Universe : the cosmological fitting problem
- Bruneton, J-P, Larena, Julien
- Authors: Bruneton, J-P , Larena, Julien
- Date: 2013
- Language: English
- Type: Article
- Identifier: vital:6790 , http://hdl.handle.net/10962/d1006943
- Description: We explore observables in a lattice Universe described by a recently found solution to Einstein field equations. This solution models a regular lattice of evenly distributed objects of equal masses. This inhomogeneous solution is perturbative, and, up to second order in a small parameter, it expands at a rate exactly equal to the one expected in a dust dominated Friedmann-Lema^itre-Robertson-Walker (FLRW) model with the equivalent, smoothed, energy density. Therefore, the kinematics of both cosmologies are identical up to the order of perturbation studied. Looking at the behaviour of the redshift and angular distance, we find a condition on the compactness of the objects at the centre of each cell under which corrections to the FLRW observables remain small, i.e. of order of a few percents at most. Nevertheless, we show that, if this condition is violated, i.e. if the objects are too compact, our perturbative scheme breaks down as far as the calculations of observables are concerned, even though the kinematics of the lattice remains identical to its FLRW counter-part (at the perturbative order considered). This may be an indication of an actual fitting problem, i.e. a situation in which the FLRW model obtained from lightcone observables does not correspond to the FLRW model obtained by smoothing the spatial distribution of matter. Fully non-perturbative treatments of the observables will be necessary to answer that question.
- Full Text:
- Date Issued: 2013
- Authors: Bruneton, J-P , Larena, Julien
- Date: 2013
- Language: English
- Type: Article
- Identifier: vital:6790 , http://hdl.handle.net/10962/d1006943
- Description: We explore observables in a lattice Universe described by a recently found solution to Einstein field equations. This solution models a regular lattice of evenly distributed objects of equal masses. This inhomogeneous solution is perturbative, and, up to second order in a small parameter, it expands at a rate exactly equal to the one expected in a dust dominated Friedmann-Lema^itre-Robertson-Walker (FLRW) model with the equivalent, smoothed, energy density. Therefore, the kinematics of both cosmologies are identical up to the order of perturbation studied. Looking at the behaviour of the redshift and angular distance, we find a condition on the compactness of the objects at the centre of each cell under which corrections to the FLRW observables remain small, i.e. of order of a few percents at most. Nevertheless, we show that, if this condition is violated, i.e. if the objects are too compact, our perturbative scheme breaks down as far as the calculations of observables are concerned, even though the kinematics of the lattice remains identical to its FLRW counter-part (at the perturbative order considered). This may be an indication of an actual fitting problem, i.e. a situation in which the FLRW model obtained from lightcone observables does not correspond to the FLRW model obtained by smoothing the spatial distribution of matter. Fully non-perturbative treatments of the observables will be necessary to answer that question.
- Full Text:
- Date Issued: 2013
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
Does the growth of structure affect our dynamical models of the Universe? The averaging, backreaction, and fitting problems in cosmology
- Clarkson, C, Ellis, G, Larena, Julien, Umeh, O
- Authors: Clarkson, C , Ellis, G , Larena, Julien , Umeh, O
- Date: 2011
- Language: English
- Type: Article
- Identifier: vital:6791 , http://hdl.handle.net/10962/d1006944
- Description: Structure occurs over a vast range of scales in the Universe. Our large-scale cosmological models are coarse-grained representations of what exists, which have much less structure than there really is. An important problem for cosmology is determining the influence the small-scale structure in the Universe has on its large-scale dynamics and observations. Is there a significant, general relativistic, backreaction effect from averaging over structure? One issue is whether the process of smoothing over structure can contribute to an acceleration term and so alter the apparent value of the cosmological constant. If this is not the case, are there other aspects of concordance cosmology that are affected by backreaction effects? Despite much progress, this 'averaging problem' is still unanswered, but it cannot be ignored in an era of precision cosmology, for instance it may affect aspects of baryon acoustic oscillation observations.
- Full Text:
- Date Issued: 2011
- Authors: Clarkson, C , Ellis, G , Larena, Julien , Umeh, O
- Date: 2011
- Language: English
- Type: Article
- Identifier: vital:6791 , http://hdl.handle.net/10962/d1006944
- Description: Structure occurs over a vast range of scales in the Universe. Our large-scale cosmological models are coarse-grained representations of what exists, which have much less structure than there really is. An important problem for cosmology is determining the influence the small-scale structure in the Universe has on its large-scale dynamics and observations. Is there a significant, general relativistic, backreaction effect from averaging over structure? One issue is whether the process of smoothing over structure can contribute to an acceleration term and so alter the apparent value of the cosmological constant. If this is not the case, are there other aspects of concordance cosmology that are affected by backreaction effects? Despite much progress, this 'averaging problem' is still unanswered, but it cannot be ignored in an era of precision cosmology, for instance it may affect aspects of baryon acoustic oscillation observations.
- Full Text:
- Date Issued: 2011
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