Long gradient mode and large-scale structure observables I: linear order
  We study the effect of long gradient modes on large scale observables. When
defined correctly, genuine observables should not only be gauge invariant but
also devoid of any gauge artifacts. One such gauge artifact is a pure gradient
mode. Using the relativistic formulation of large scale observables, we confirm
that a long gradient mode which is still outside observer's horizon leaves no
imprint on the large scale observables at first order. These include the cosmic
rulers and the number counts. This confirms the existing method for
relativistically defined observables. The general relativistic bias relation
for the halos and galaxies is also invariant under the presence of a long
gradient mode perturbation. The observed power spectrum is not affected by this
long mode.
