We investigate the limits of applicability of the quasi-static approximation in cosmologies featuring general models of dark energy or modified gravity. We show that the quasi-static approximation always breaks down outside of the sound horizon of the dark-energy, rather than the cosmological horizon as is frequently assumed. When the sound speed of dark energy is significantly below that of light, the quasi-static 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. In particular, in the analysis of data from today's weak-lensing and peculiar-velocity surveys, dark energy can be modelled as quasi-static 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.

## Address

Département de Physique Théorique

Université de Genève

24, quai Ernest Ansermet

1211 Genève 4

Switzerland

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