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Gravitational wave (GW) constraints have recently been used to significantlyrestrict models of dark energy and modified gravity. New bounds arising from GWdecay and GW-induced dark energy instabilities are particularly powerful inthis context, complementing bounds from the observed speed of GWs. We discussthe associated linear cosmology for Horndeski gravity models surviving thesecombined bounds and compute the corresponding cosmological parameterconstraints, using CMB, redshift space distortion, matter power spectrum andBAO measurements from the Planck, SDSS/BOSS and 6dF surveys. The survivingtheories are strongly constrained, tightening previous bounds on cosmologicaldeviations from $\Lambda{}$CDM by over an order of magnitude. We also commenton general cosmological stability constraints and the nature of screening forthe surviving theories, pointing out that a raised strong coupling scale canensure compatibility with gravitational wave constraints, while maintaining afunctional Vainshtein screening mechanism on solar system scales. Finally, wediscuss the quasi-static limit as well as (constraints on) related observablesfor near-future surveys.

Cosmological constraints on dark energy in light of gravitational wave bounds