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Structure Formation in Modified Gravity Cosmologies pp 147–170Cite as

Nonlinear Structure Formation in Nonlocal Gravity

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

Abstract

We now turn our attention to large scale structure formation in nonlocal gravity models. In these models, the modifications to gravity arise via the addition of nonlocal terms (i.e. which depend on more than one point in spacetime) to the Einstein field equations. These terms typically involve the inverse of the d’Alembertian operator, \(\Box ^{-1}\), acting on curvature tensors.

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Notes

  1. 1.

    The content in this chapter is based on the article Barreira et al. “Nonlinear structure formation in nonlocal gravity”, Journal of Cosmology and Astroparticle Physics, Volume 2014, Published 17 September 2014, ©IOP Publishing Ltd. Reproduced with permission. All rights reserved, http://dx.doi.org/10.1088/1475-7516/2014/09/031 (Ref. [1]).

  2. 2.

    For instance, in flat four-dimensional Minkowski space we have \(\Box = +\frac{\partial ^2}{\partial t^2} - \frac{\partial ^2}{\partial x^2} - \frac{\partial ^2}{\partial y^2} - \frac{\partial ^2}{\partial z^2}\).

  3. 3.

    In Eq. (6.24), \(\Delta G_{\mu \nu }\) also vanishes if \(\chi = 0\).

  4. 4.

    Here, \(\theta \) is the Fourier mode of the divergence of the peculiar physical velocity field v, defined as \(\theta (\mathbf {x}) = \nabla v(\mathbf {x})/H_0\).

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  1. Max Planck Institute for Astrophysics, Garching, Germany

    Alexandre Barreira

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Barreira, A. (2016). Nonlinear Structure Formation in Nonlocal Gravity. In: Structure Formation in Modified Gravity Cosmologies. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-33696-1_6

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