Galileon gravity is a robust theoretical alternative to general relativity with a cosmological constant for explaining cosmic acceleration, with interesting properties such as having second order field equations and a shift symmetry. While either its predictions for the cosmic expansion or growth histories can approach standard Lambda CDM, we demonstrate the incompatibility of both doing so simultaneously. Already current observational constraints can severely disfavor an entire class of Galileon gravity models that do not couple directly to matter, ruling them out as an alternative to Lambda CDM.
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