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Structure Formation in Modified Gravity Cosmologies pp 91–116Cite as

Spherical Collapse in Galileon Gravity

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Part of the book series: Springer Theses ((Springer Theses))

Abstract

As we have mentioned in the previous chapters, the inclusion of data related to the growth of structure on scales \({\lesssim }10\,\mathrm{Mpc}\)/h in tests of Galileon gravity requires modelling of some physics which can only be tackled by going beyond linear theory.

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Notes

  1. 1.

    The content in this chapter is based on the article Barreira et al. “Spherical collapse in Galileon gravity: fifth force solutions, halo mass function and halo bias”, Journal of Cosmology and Astroparticle Physics, Volume 2013, Published 27 November 2013, © IOP Publishing Ltd. Reproduced with permission. All rights reserved, http://dx.doi.org/10.1088/1475-7516/2013/11/056 (Ref. [1]).

  2. 2.

    Note that \(\partial _r\varphi = \partial _r\delta \varphi \) is a perturbed quantity.

  3. 3.

    The Cubic Galileon model is also the best-fitting one to the WMAP9 \(+\) SNLS \(+\) BAO dataset, obtained with the strategy presented in Ref. [5]. The nonlinear structure formation in this model shall be studied in Chap. 5.

  4. 4.

    Near black holes, for instance, one can have larger metric perturbations \(\Psi \sim 1\).

  5. 5.

    We note that if we solve the model equations in perturbed Minkowski space (instead of FRW), then \(\dot{\varphi } = 0\) and \(G_\mathrm{eff} \rightarrow 1\), when \(\delta \gg 1\). We discuss this issue further in Chap. 6, when we encounter a similar problem in Nonlocal gravity models.

  6. 6.

    In the case of \(\delta _c\), we will avoid writing the subscript \(_\mathrm{lin}\) to ease the notation.

  7. 7.

    Note that one can use \(\Lambda \)CDM to compute the matter power spectrum of the Galileon model at the initial time, but one has to use the parameters given in Table 4.1.

  8. 8.

    Just like for \(\delta _c\), we will avoid writing the subscript \(_\mathrm{lin}\) in \(\delta _0\) to ease the notation.

  9. 9.

    Not to be confused with the initial times of Table 4.1.

  10. 10.

    Explicitly: \(\bar{\rho }_ma^3R^3 = \left( 1+\delta \right) \bar{\rho }_mr^3 \Rightarrow \delta = \left( aR/r\right) ^3 - 1 = y^{-3} - 1\).

  11. 11.

    In other words, if \(\delta _c\) is lower then the random walks first up-cross the barrier sooner (low S), rather than later (high S).

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  1. Max Planck Institute for Astrophysics, Garching, Germany

    Alexandre Barreira

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Barreira, A. (2016). Spherical Collapse in Galileon Gravity. In: Structure Formation in Modified Gravity Cosmologies. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-33696-1_4

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