Clarifying transfer function approximations for the large-scale gravitational wave background in $\Lambda$CDM

Understand

The primordial gravitational wave background (GWB) offers an exciting future avenue of discovery for new physics.

• Its information content encodes multiple eras in the early Universe's history, corresponding to many orders of magnitude in frequency and physical scale to be measured today.
• By numerically solving for the GW transfer functions we provide simple yet accurate formulas describing the average power of the large-scale energy spectrum of the GWB for arbitrary primordial tensor power spectra.
• In doing so we can pedagogically explain and clarify previous GWB literature, highlight the important cosmological parameters of various GWB features, and reveal multiple ways in which cancelling conceptual errors can give deceptively accurate results.