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I would like to ask you some questions I have about some interesting work I was reading (https://arxiv.org/abs/1205.4238 & https://academic.oup.com/mnras/article/527/4/11962/7457744) where the authors analysed the effects of dark energy in the shape and evolution of voids

Apparently, they established a relation between dark energy, voids' ellipticity and tidal forces. I have a question about this, since it was not entirely clear to me:

Does it mean that dark energy (or the accelerated expansion of the universe) contributes to increase the ellipticity of voids? Then, does dark energy increase the tidal forces of the void (so that a greater dark energy density in the universe would result in more intense tidal forces in the void)?

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    $\begingroup$ Why not ask the authors of the paper? $\endgroup$ Commented Feb 12 at 17:58
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    $\begingroup$ @MariusLadegårdMeyer I did, but they did not answer back :) $\endgroup$
    – vengaq
    Commented Feb 13 at 11:37

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If you would ask me, tidal fields (they are not really forces I think due to gravity not being a force) of the large-scale structure (LSS) are most prominently artifacts of gravity. The tidal fields are extremely important for the formation of the LSS (this is a key idea throughout the works of Van de Weygaert), and even contain so much information that the primordial tidal fields are sufficient to construct a high-resolution nonlinear description of the recent epoch LSS (I think some of the recent papers of Van de Weygaert & Feldbrugge point this out). It then makes sense that the tidal fields have a concrete effect on how voids evolve, see e.g. Equations (3) to (8) of Bos & Van de Weygaert et al. (2012).

Regarding the ellipticity, its PDF is described by Eq. (6), which depends on the filter scale $R_L$ being a measure for the size of the void. The size of the void is depended on local behavior of dark energy, see e.g. Sheth & Van de Weygaert (2004).

Regarding dark energy affecting the tidal forces, this is fundamentally evident from the expression of the tidal field components in their Eq. (3): they are the second derivatives of the gravitational potential $\phi$, and dark energy does affect $\phi$. In last sentence of the paragraph above this Eq. (3), they are able to write "In turn, the evolution of the tidal forces are directly dependent on the nature of the dark energy content of the universe. This offers a path towards measuring the cosmological parameters."

Please let me know if this helped, otherwise I can contact one of the authors myself for you. If so, please do elucidate your question.

Best wishes, Dave

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