Effective Field Theories (EFTs) exploit a decoupling between high and low energy scales in order to make useful predictions of IR observables without appealing to the underlying UV physics. This is particularly important for cosmology and gravity, in which often no explicit UV completion is known.

However, not all UV information is lost - certain physical properties like causality, locality and unitarity manifest themselves as 'positivity constraints' on the low energy EFT. In this talk I will review these connections between IR and UV, and discuss how assumptions about the UV can constrain our IR model-building.

In particular, I will discuss the impact of positivity constraints on dark energy and the cosmological constant problem (namely on Galileons and massive gravity), as well as on recent spin-2 dark matter models.