  Cosmological probes constructed in large-scale surveys are independent of the
underlying theory of gravity, and their relativistic descriptions are indeed
applicable to any theory of gravity. It was shown that the presence of
fluctuations with wavelength much larger than the characteristic scales of the
surveys has no impact on cosmological probes, if the matter content is
adiabatic and the Einstein equations are used. In this paper we study the
sensitivity of cosmological probes to infrared fluctuations in Horndeski
theory. We find that the extra degree of freedom in the Horndeski scalar field
can induce sensitivity to infrared fluctuations in the cosmological probes,
even when the matter components are adiabatic on large scales. A generalized
adiabatic condition including the extra dof, in contrast, guarantees that
cosmological probes are devoid of infrared sensitivity, and this solution
corresponds to the adiabatic modes \`a la Weinberg in Horndeski theory, which
can be removed by a coordinate transformation in the infrared limit. We discuss
the implications of our findings and the connections to the initial conditions.
