We discuss the difference between various gauge-invariant quantities typically used in single-field inflation, namely synchronous ζs, comoving ζc, and unitary ζu curvatures. We show that conservation of ζc outside the horizon is quite restrictive on models as it leads to conservation of ζs and ζu, whereas the reverse does not hold. We illustrate the consequence of these differences with two inflationary models: ultra-slow-roll (USR) and braiding-ultra-slow-roll (BUSR). In USR, we show that out of the three curvatures, only ζs is conserved outside the horizon, and we connect this result to the concepts of a separate universe and the usage of the δ N formalism. We find that even though ζs is conserved, there is still a mild violation of the separate universe approximation in the continuity equation. Nevertheless, the δ N formalism can still be applied to calculate the primordial power spectrum of some gauge-invariant quantities such as ζu, although it breaks down for others such as the uniform-density curvature. In BUSR, we show that both ζu and ζs are conserved outside the horizon, but take different values. Additionally, since ζu≠ζc, we find that the prediction for observable curvature fluctuations after inflation does not reflect ζc at the horizon crossing during inflation and moreover involves not just ζu at that epoch but also the manner in which the braiding phase ends.
Physical Review D
- Pub Date:
- December 2019
- General Relativity and Quantum Cosmology;
- Astrophysics - Cosmology and Nongalactic Astrophysics;
- High Energy Physics - Theory
- Phys. Rev. D 100, 123507 (2019)