... clustering[*]
Appendices A-C are only available in electronic form at http://www.edpsciences.org 
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... density[*]
We have disregarded the infinities arising from the evaluation of the field  ${\vec{g}}({\vec{x}},t)$ at the particles' positions. These are artifacts of using point particles and are treated by smearing the particles over an infinitesimal size. For our formal manipulations, it suffices with the implicit understanding that the infinities can be dropped when they appear. 
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... fields[*]
Notice that this closure requires one to consider the energy or, equivalently, the thermodynamic temperature as another fundamental field on equal footing with $\varrho$ and ${\vec{u}}$. 
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...$\Pi_{ij} \approx 0$[*]
According to Eq. (13b), the same model is recovered if $F_i - a^{-1} \Pi_{ij,j} \approx 0$, i.e., when the corrections to the mean field are counterbalanced by velocity dispersion - we have not explored the physical meaning of such a balance condition. 
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... length[*]
The denomination "large-scale expansion'' used in Domínguez (2000) may lead to confusion. 
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...2001)[*]
Bharadwaj (1996) extended this claim to the case of multi-streamed initial conditions in the simplified model of free particles. This conclusion is, however, false because of a mathematical mistake in his Eq. (34). 
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...1999)[*]
In that work, only the particular case of a polytropic dependence, $p(\varrho) \propto \varrho^\gamma$, in an Einstein-de Sitter cosmological background was considered, but it can be checked that Eq. (35) holds generally. Also in that work, a minor mistake was made and the coefficient  ${\cal C}(t)$ quoted there is missing an extra time-dependent factor when $\gamma>13/6$. 
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... field[*]
If such conditions are imposed on the problem, ${\vec{T}}$ becomes a harmonic vector function which can be set to zero for periodic boundary conditions of the cosmological fields on some large scale (since then the only harmonic functions are spatially constant and can be set to zero due to the invariance of the basic equations with respect to spatially constant translations). 
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...${\vec{w}}$[*]
For details on the possibility and advantage of this choice, see Adler & Buchert (1999, Appendix A). 
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...J[*]
Of course, $\varrho$ solves Eq. (48), if ${\vec{P}}$ solves Eq. (47). 
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... time[*]
In this work we are not concerned with more general (non-Lagrangian) singularities in the velocity-gradient field, such as those that may occur in incompressible flows. 
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... model[*]
The weak solutions can be interpreted equivalently as solutions of the integral form of the balance equations for mass and momentum. 
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... variable[*]
As in the case of deriving Eq. (4), the formal definitions of the fields $\bu_{{\rm mic}}({\vec{q}})$, ${\vec{w}}_{{\rm mic}}({\vec{q}})$ can be regularized by smearing Dirac's delta function. 
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... state''[*]
This notion as well as the names attached to the different polytropic models (with the polytropic index n defined through $\gamma=:(n+1)/n$) is borrowed from thermodynamics. We emphasize that here we refer to dynamical stresses and do not imply thermal equilibrium. 
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Copyright ESO 2005