A Nearly Scale Invariant Spectrum of Gravitational Radiation from Global Phase Transitions

TL;DR

Using a large N sigma model approximation, the power spectrum of gravitational waves arising from a global phase transition in the early Universe is calculated and it is confirmed that it is scale invariant, implying an observation of such a spectrum may not be a unique feature of inflation.

Abstract

Using a large N sigma model approximation we explicitly calculate the power spectrum of gravitational waves arising from a global phase transition in the early universe and we confirm that it is scale invariant, implying an observation of such a spectrum may not be a unique feature of inflation. Moreover, the predicted amplitude can be over 3 orders of magnitude larger than the naive dimensional estimate, implying that even a transition that occurs after inflation may dominate in Cosmic Microwave Background polarization or other gravity wave signals.

Figures (2)

• Figure 1: Plot of gravitational radiation power vs $p \tau$ where $p$ is the wave-vector and $\tau$ is the conformal time, computed assuming the scale factor appropriate for matter domination. The plot may be interpreted to show the variation in power with time for modes of a fixed wave-vector or the variation in power with wave-vector for fixed time. The points are obtained by numerical integration of eq (\ref{['eq:monster']}). The dashed curve is a guide to the eye. The solid line shows an asymptotic approximation $C_{\beta} (p \tau)^3$ valid for small $p \tau$. The numerical data are consistent with a $1/(p \tau)^4$ tail for large $p \tau$. The peak value 11,600 occurs at $p \tau \approx 3.7$.
• Figure 2: Plot of the gravitational power vs $\tau/\tau_*$ at wavevector $p = 1/\tau$. $\tau_*$ is the time of crossover from radiation to matter domination. The spectrum is flat for $\tau \gg \tau_*$ and again for $\tau \ll \tau_*$; thus except at the crossover, it is essentially scale invariant. The points are calculated by numerical integration of eq (\ref{['eq:monster']}); the dashed curve is a guide to the eye.