Sensitivity to a frequency-dependent circular polarization in an isotropic stochastic gravitational wave background

We calculate the sensitivity to a circular polarization of an isotropic stochastic gravitational wave background (ISGWB) as a function of frequency for ground- and space-based interferometers and observations of the cosmic microwave background. The origin of a circularly polarized ISGWB may be due to exotic primordial physics (i.e., parity violation in the early universe) and may be strongly frequency dependent. We present calculations within a coherent framework which clarifies the basic requirements for sensitivity to circular polarization, in distinction from previous work which focused on each of these techniques separately. We find that the addition of an interferometer with the sensitivity of the Einstein Telescope in the southern hemisphere improves the sensitivity of the ground-based network to circular polarization by about a factor of two. The sensitivity curves presented in this paper make clear that the wide range in frequencies of current and planned observations (${10}^{-18}\mathrm{Hz}\lesssim f\lesssim 100\mathrm{Hz}$) will be critical to determining the physics that underlies any positive detection of circular polarization in the ISGWB. We also identify a desert in circular polarization sensitivity for frequencies between ${10}^{-15}\mathrm{Hz}\lesssim f\lesssim {10}^{-3}\mathrm{Hz}$, given the inability for pulsar timing arrays and indirect-detection methods to distinguish the gravitational wave polarization.

Figure 1

The gravitational wave power spectrum $S_h$ is shown for left- (red, dashed) and right-circular (blue, solid) polarizations in a gauge-flation scenario. The power spectrum for a single polarization in an equivalent slow-roll inflationary scenario is also shown (yellow, solid). The normalization of the vertical axis is arbitrary. There is a wave number $k_{*}$ set by the parameters of the model; at wave numbers $k\ll k_{*}$ the spectrum is chirally symmetric with a slight red tilt, $n_T<0$; at wave numbers $k\gg k_{*}$ the chiral symmetry is broken and one hand dominates over the other with a blue tilt, $n_T\simeq 0.2$ in the case shown above.

Figure 2

A schematic figure showing the geometry of the four detectors we are considering in this calculation.

Figure 3

Two equal arm Michelson interferometers rotated by 180 degrees and separated by a distance $D$.

Figure 4

Left panel: The minimum detectable ${\mathrm{\Omega }}_{\mathrm{gw}}^{(I,V)}$ as a function of the separation between the two observatories for LISA; sensitivity to the intensity $I$ is shown in solid blue, sensitivity to the circular polarization $V$ is shown in dashed orange. Right panel: The minimum detectable ${\mathrm{\Omega }}_{\mathrm{gw}}^{(I,V)}$ as a function of the separation between the two observatories for BBO; sensitivity to the intensity $I$ is shown in blue, sensitivity to the circular polarization $V$ is shown in orange. In both cases we have assumed a ten-year-long observation.

Figure 5

Left panel: The sensitivity curve for ${\mathrm{\Omega }}_{\mathrm{gw}}^{(I,V)}$ for LISA assuming a separation between the two observatories of $D/L=7$, and a 10-year-long observation. The solid blue curve shows the sensitivity to the intensity and the dashed orange curve shows the sensitivity to the circularly polarized background. Note that the sensitivity curve for $V$ has a smaller opening angle. Right panel: The same as in the left panel but for BBO and $D/L=2$.

Figure 6

Left panel: The sensitivity of currently built ground-based observatories (LIGO Hanford and Livingston, Virgo). The solid blue and dashed orange curves show the sensitivity to the intensity and circular polarization. Right panel: The sensitivity curve for the five current and planned ground-based observatories listed in Table 3 and a 10-year-long observation.

Figure 7

Left panel: The sensitivity of the Einstein Telescope (ET). Since the ET consists of phase measurements at the vertices of an equilateral triangle, it is not intrinsically sensitive to the level of circular polarization in the ISGWB. Right panel: When we correlate the ET signal with other current and planned ground-based gravitational wave observatories the network is sensitive to the circular polarization, shown in the dashed-orange curve.

Figure 8

The sensitivity of CMB observations to the intensity (solid blue) and circular polarization (dashed orange) for both Planck (left panel) and CMBpol (right panel). Our noise model and parameters for these two instruments are specified in Appendix pp3.

Figure 9

A collection of all of the sensitivity curves calculated in this paper with solid blue giving the sensitivity to the intensity and dashed orange to the level of circular polarization. We have also included the sensitivity to the ISGWB from pulsar timing array from Ref. [59] and indirect limits coming from CMB measurements of the radiative energy density of the universe [60, 61].