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Within the effective field theory approach to cosmic acceleration, the background expansion can be specified separately from the gravitational modifications.
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J. Renk, M. Zumalacárregui and F. Montanari, Gravity at the horizon: on relativistic effects, CMB-LSS correlations and ultra-large scales in Horndeski’s theory, JCAP 1607 (2016) 040 [1604.03487]
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