Probing the gravitational wave signature from cosmic phase transitions at different scales

We present a new signature by which one could potentially discriminate between a spectrum of gravitational radiation generated by a self-ordering scalar field vs that of inflation, specifically a comparison of the magnitude of a flat spectrum at frequencies probed by future direct detection experiments to the magnitude of a possible polarization signal in the cosmic microwave background radiation. In the process we clarify several issues related to the proper calculation of such modes, focusing on the effect of post-horizon-crossing evolution.

Figure 1

Appropriately normalized power in Fourier modes with $p=x\tau$ as a function of $p\tau$. The solid curve represents a calculation including full scalar field dynamics down to $p\tau =10$, while the dotted curve cuts off sourcing at horizon crossing, $p\tau =1$.

Figure 2

The fractional energy density per logarithmic frequency interval as a function of frequency (normalized to the frequency of modes that cross the horizon at matter-radiation equality) for gravitational wave modes generated during inflation compared to that in modes generated by scalar field reordering, for transitions tuned to give the same gravitational wave amplitude for high frequency modes that enter the horizon during radiation domination.