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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 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.
References
Barreira A, Li B, Hellwing WA, Baugh CM, Pascoli S (2013) JCAP 10:027. https://doi.org/10.1088/1475-7516/2013/10/027, http://adsabs.harvard.edu/abs/2013JCAP...10.027B
Bose S, Hellwing WA, Li B (2015) JCAP 2:034. https://doi.org/10.1088/1475-7516/2015/02/034, http://adsabs.harvard.edu/abs/2015JCAP...02.034B
Brax P, van de Bruck C, Davis A-C, Khoury J, Weltman A (2004) Phys D Rev 70:123518. https://doi.org/10.1103/PhysRevD.70.123518, http://adsabs.harvard.edu/abs/2004PhRvD.70l3518B
Brax P, van de Bruck C, Davis A-C, Shaw D (2010) Phys Rev D 82:063519. https://doi.org/10.1103/PhysRevD.82.063519
Brax P, Davis A-C, Li B, Winther HA (2012) Phys D Rev 86:044015. https://doi.org/10.1103/PhysRevD.86.044015, http://adsabs.harvard.edu/abs/2012PhRvD.86d4015B
Cai Y-C, Li B, Cole S, Frenk CS, Neyrinck M (2014) MNRAS 439:2978. https://doi.org/10.1093/mnras/stu154, http://adsabs.harvard.edu/abs/2014MNRAS.439.2978C
Carroll SM, de Felice A, Duvvuri V, Easson DA, Trodden M, Turner MS (2005) Phys D Rev 71:063513. https://doi.org/10.1103/PhysRevD.71.063513, http://adsabs.harvard.edu/abs/2005PhRvD.71f3513C
Cautun MC, van de Weygaert R (2011) The DTFE public software: the delaunay tessellation field estimator code, Astrophysics source code library. arXiv:1105.0370
Clifton T, Ferreira PG, Padilla A, Skordis C (2012) Phys Rep 513:1. https://doi.org/10.1016/j.physrep.2012.01.001, http://adsabs.harvard.edu/abs/2012PhR...513....1C
Colombi S, Jaffe A, Novikov D, Pichon C (2009) MNRAS 393:511. https://doi.org/10.1111/j.1365-2966.2008.14176.x, http://adsabs.harvard.edu/abs/2009MNRAS.393.511C
Courant R, Friedrichs K, Lewy H (1928) Math Ann 100:32. https://doi.org/10.1007/BF01448839, http://adsabs.harvard.edu/abs/1928MatAn.100...32C
Deffayet C, Esposito-Farèse G, Vikman A (2009) Phys D Rev 79:084003. https://doi.org/10.1103/PhysRevD.79.084003, http://adsabs.harvard.edu/abs/2009PhRvD.79h4003D
Dvali G, Gabadadze G, Porrati M (2000) Phys Lett B 485:208. https://doi.org/10.1016/S0370-2693(00)00669-9, http://adsabs.harvard.edu/abs/2000PhLB..485..208D
Hagala R, Llinares C, Mota DF (2017) Phys Rev Lett 118:101301. https://doi.org/10.1103/PhysRevLett.118.101301, http://adsabs.harvard.edu/abs/2017PhRvL.118j1301H
He J-H, Li B, Jing YP (2013) Phys D Rev 88:103507. https://doi.org/10.1103/PhysRevD.88.103507, http://adsabs.harvard.edu/abs/2013PhRvD.88j3507H
Hellwing WA, Juszkiewicz R, van de Weygaert R (2010) Phys D Rev 82:103536. https://doi.org/10.1103/PhysRevD.82.103536, http://adsabs.harvard.edu/abs/2010PhRvD.82j3536H
Hellwing WA, Li B, Frenk CS, Cole S (2013) MNRAS 435:2806. https://doi.org/10.1093/mnras/stt1430, http://adsabs.harvard.edu/abs/2013MNRAS.435.2806H
Hellwing WA, Barreira A, Frenk CS, Li B, Cole S (2014) Phys Rev Lett 112:221102. https://doi.org/10.1103/PhysRevLett.112.221102, http://adsabs.harvard.edu/abs/2014PhRvL.112v1102H
Hinshaw G et al (2013) APJS 208:19. https://doi.org/10.1088/0067-0049/208/2/19, http://adsabs.harvard.edu/abs/2013ApJS.208...19H
Hinterbichler K, Khoury J (2010) Phys Rev Lett 104:231301. https://doi.org/10.1103/PhysRevLett.104.231301, http://adsabs.harvard.edu/abs/2010PhRvL.104w1301H
Hu W, Sawicki I (2007) Phys D Rev 76:064004. https://doi.org/10.1103/PhysRevD.76.064004, http://adsabs.harvard.edu/abs/2007PhRvD.76f4004H
Jennings E, Baugh CM, Pascoli S (2011) MNRAS 410:2081. https://doi.org/10.1111/j.1365-2966.2010.17581.x, http://adsabs.harvard.edu/abs/2011MNRAS.410.2081J
Khoury J (2010). arXiv:1011.5909
Li B, Barrow JD (2011a) Phys D Rev 83:024007. https://doi.org/10.1103/PhysRevD.83.024007, http://adsabs.harvard.edu/abs/2011PhRvD.83b4007L
Li B, Barrow JD (2011b) MNRAS 413:262. https://doi.org/10.1111/j.1365-2966.2010.18130.x, http://adsabs.harvard.edu/abs/2011MNRAS.413.262L
Li B, Zhao G-B, Teyssier R, Koyama K (2012) JCAP 1:051. https://doi.org/10.1088/1475-7516/2012/01/051, http://adsabs.harvard.edu/abs/2012JCAP...01.051L
Li B, Barreira A, Baugh CM, Hellwing WA, Koyama K, Pascoli S, Zhao G-B (2013a) JCAP 11:012. https://doi.org/10.1088/1475-7516/2013/11/012, http://adsabs.harvard.edu/abs/2013JCAP...11.012L
Li B, Hellwing WA, Koyama K, Zhao G-B, Jennings E, Baugh CM (2013b) MNRAS 428:743. https://doi.org/10.1093/mnras/sts072, http://adsabs.harvard.edu/abs/2013MNRAS.428.743L
Llinares C, Mota DF (2014a) Phys D Rev 89:084023. https://doi.org/10.1103/PhysRevD.89.084023, http://adsabs.harvard.edu/abs/2014PhRvD.89h4023L
Llinares C, Mota DF (2014b) Phys D Rev 89:084023. https://doi.org/10.1103/PhysRevD.89.084023, http://adsabs.harvard.edu/abs/2014PhRvD.89h4023L
Mota DF, Shaw DJ (2007) Phys D Rev 75:063501. https://doi.org/10.1103/PhysRevD.75.063501, http://adsabs.harvard.edu/abs/2007PhRvD.75f3501M
Nicolis A, Rattazzi R, Trincherini E (2009) Phys D Rev 79:064036. https://doi.org/10.1103/PhysRevD.79.064036, http://adsabs.harvard.edu/abs/2009PhRvD.79f4036N
Perlmutter S et al (1999) ApJ 517:565. https://doi.org/10.1086/307221, http://adsabs.harvard.edu/abs/1999ApJ...517.565P
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2002) Numerical recipes in C++ : the art of scientific computing
Riess AG et al (1998) AJ 116: 1009. https://doi.org/10.1086/300499, http://adsabs.harvard.edu/abs/1998AJ....116.1009R
Schaap WE, van de Weygaert R (2000) A&A 393:L29. http://adsabs.harvard.edu/abs/2000A%26A...363L..29S
Schmidt F, Vikhlinin A, Hu W (2009b) Phys D Rev 80:083505. https://doi.org/10.1103/PhysRevD.80.083505, http://adsabs.harvard.edu/abs/2009PhRvD.80h3505S
Teyssier R (2002) A&A 385:337. https://doi.org/10.1051/0004-6361:20011817, http://adsabs.harvard.edu/abs/2002A%26A...385.337T
van Daalen MP, Schaye J, McCarthy IG, Booth CM, Dalla Vecchia C (2014) MNRAS 440:2997. https://doi.org/10.1093/mnras/stu482, http://adsabs.harvard.edu/abs/2014MNRAS.440.2997V
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-96761-5_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-96760-8
Online ISBN: 978-3-319-96761-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)