# Gauge dependence of gravitational waves generated from scalar perturbations

## TL;DR

This paper investigates the gauge dependence of gravitational waves generated from scalar perturbations in cosmology, revealing that their power spectrum varies with gauge choice and can dominate primordial signals during matter domination.

## Contribution

It demonstrates that second-order induced tensor perturbations are gauge dependent and emphasizes the importance of proper modeling for observational strategies.

## Key findings

- Induced tensor modes depend on the gauge choice for scalar perturbations.
- During matter domination, induced modes can surpass primordial gravitational waves for certain scales.
- Proper gauge-specific modeling is crucial for interpreting gravitational wave measurements from large-scale structure.

## Abstract

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.