Gauge dependence of gravitational waves generated from scalar
  perturbations
  A tensor-type cosmological perturbation, defined as a transverse and
traceless spatial fluctuation, is often interpreted as the gravitational waves.
While decoupled from the scalar-type perturbations in linear order, the tensor
perturbations can be sourced from the scalar-type in the nonlinear order. The
tensor perturbations generated by the quadratic combination of linear
scalar-type cosmological perturbation are widely studied in the literature, but
all previous studies are based on zero-shear gauge without proper
justification. Here, we show that, being second order in perturbation, such an
induced tensor perturbation is generically gauge dependent. In particular, the
gravitational wave power spectrum depends on the hypersurface (temporal gauge)
condition taken for the linear scalar perturbation. We further show that,
during the matter-dominated era, the induced tensor modes dominate over the
linearly evolved primordial gravitational waves amplitude for
$k\gtrsim10^{-2}~[h/{\rm Mpc}]$ even for the gauge that gives lowest induced
tensor modes with the optimistic choice of primordial gravitational waves
($r=0.1$). The induced tensor modes, therefore, must be modeled correctly
specific to the observational strategy for the measurement of primordial
gravitational waves from large-scale structure via, for example, parity-odd
mode of weak gravitational lensing, or clustering fossils.
