Limits of quasistatic approximation in modifiedgravity cosmologies
Abstract
We investigate the limits of applicability of the quasistatic approximation in cosmologies featuring general models of dark energy or modified gravity. We show that, at best, the quasistatic approximation breaks down outside of the sound horizon of the darkenergy, rather than the cosmological horizon as is frequently assumed. When the sound speed of dark energy is significantly below that of light, the quasistatic limit is only valid in a limited range of observable scales and this must be taken into account when computing effects on observations in such models. As an order of magnitude estimate, in the analysis of data from today's weaklensing and peculiarvelocity surveys, dark energy can be modeled as quasistatic only if the sound speed is larger than order 1% of that of light. In upcoming surveys, such as Euclid, it should only be used when the sound speed exceeds around 10% of the speed of light. In the analysis of the cosmic microwave background, the quasistatic limit should never be used for the integrated SachsWolf effect and for lensing only when the sound speed exceeds 10% of the speed of light.
 Publication:

Physical Review D
 Pub Date:
 October 2015
 DOI:
 10.1103/PhysRevD.92.084061
 arXiv:
 arXiv:1503.06831
 Bibcode:
 2015PhRvD..92h4061S
 Keywords:

 04.50.Kd;
 04.80.Cc;
 98.80.Jk;
 Modified theories of gravity;
 Experimental tests of gravitational theories;
 Mathematical and relativistic aspects of cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 6 pages, 1 table. v2 reflects version accepted for publication in PRD. More detailed discussion of CMB lensing and evolution during sound horizon crossing added