Abstract
In recent years, theories of modified gravity have become a subject of great interest in alternative approaches to modelling the observed acceleration of the Universe. Einstein’s theory of General Relat6ivity (GR) has been the underlying gravity theory in the standard cosmological model of \(\varLambda \)CDM, the dark energy (\(\varLambda \)) and (cold) dark matter (CDM) components of which remain unresolved challenges to cosmologists.
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Notes
- 1.
The content of this chapter is based on the article Bose et al. ‘Testing the quasi-static approximation in f(R) gravity simulations’, Journal of Cosmology and Astroparticle Physics, Volume 2015, Issue 2, published 24 February 2015. Reproduced with permission. All rights reserved, https://doi.org/10.1088/1475-7516/2015/02/034.
- 2.
It is often argued that one should make \(|d^h|\) as small as practically possible, instead of stopping at \(|d^h|\sim \tau ^h/3\), to prevent the numerical errors in solving the differential equation at individual steps from accumulating over the many time steps of a simulation. While this is true to a certain extent, it is not clear that the discretisation error itself will not accumulate in this case (recall that, if \(d^h\) could be brought to zero, then the remaining error is completely from the discretisation). Again, the way to get away from this problem is to reduce the discretisation error by increasing the (spatial) resolution, and then check for convergence.
- 3.
The kick is by the sudden increase in the non-relativistic \(\rho _m\), as can be seen from \(\mathrm {d} V_{\mathrm {eff}} / \mathrm {d} f_R = -\left[ R - f_R R + 2 f(R) + 8\uppi G \rho _m\right] /3\) – because of the quick change in \(\rho _m\), \(f_{R,\mathrm{min}}\) is changed while the true \(f_R\) needs time to respond to this.
- 4.
Note that we can use \(a_e\) in the above expressions and estimates, because electrons are the last species of standard-model particles that become non-relativistic.
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Bose, S. (2018). Testing the Quasi-static Approximation in f(R) Gravity Simulations. In: Beyond ΛCDM . Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-96761-5_5
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