Cosmic Rulers
  We derive general covariant expressions for the six independent observable
modes of distortion of ideal standard rulers in a perturbed
Friedmann-Robertson-Walker spacetime. Our expressions are gauge-invariant and
valid on the full sky. These six modes are most naturally classified in terms
of their rotational properties on the sphere, yielding two scalars, two vector
(spin-1), and two tensor (spin-2) components. One scalar corresponds to the
magnification, while the spin-2 components correspond to the shear. The vector
components allow for a polar/axial decomposition analogous to the
E/B-decomposition for the shear. Scalar modes do not contribute to the axial
(B-)vector, opening a new avenue to probing tensor modes. Our results apply,
but are not limited to, the distortion of correlation functions (of the CMB,
21cm emission, or galaxies) as well as to weak lensing shear and magnification,
all of which can be seen as methods relying on "standard rulers".
