Beyond general relativity: Designing a template-based search for exotic gravitational wave signals

Accurate waveform models describing the complete evolution of compact binaries are crucial for the maximum likelihood detection framework, testing the predictions of general relativity (GR) and investigating the possibility of an alternative theory of gravity. Deviations from general relativity could manifest in subtle variations of the numerical value of the gravitational wave signal’s phasing coefficients. Once the search pipelines confirm an unambiguous signal detection, deviations of the signal phasing coefficients at various post-Newtonian orders are routinely measured and reported. As the search templates themselves do not incorporate any deviations from general relativity, they may miss astrophysical signals carrying a significant departure from GR. We present a parametrized template-based search for exotic gravitational-wave signals beyond general relativity by incorporating deviations to the signal’s phasing coefficients at different post-Newtonian orders in the search templates. We present critical aspects of the new search, such as improvements in search volume and its effect on various parts of the parameter space. In particular, we demonstrate a twofold increase in search sensitivity (at a fixed false-alarm rate) to beyond-GR exotic signals by using search templates that admit a range of departures from general relativity. We also present the results from a reanalysis of ten days long duration of LIGO data from the first science run that includes the epoch of the GW150914 event.

Figure 1

Combined posterior distribution for the deviation parameters $\delta {\widehat{\phi }}_i$. We are considering only those events that have FAR $\mathrm{FAR}<(1000\mathrm{yr}{)}^{-1}$ and exceed SNR threshold ($>6$) in inspiral regime (GW150914, GW151226, GW170104, GW170608, and GW170814). The SNR constraint is due to fact that the PN approximation is not very effective beyond inspiral regime. The dashed line corresponds to the value predicted by GR. And the vertical bar show the 90% credible interval. This figure is reproduced by using the results from [8].

Figure 2

Cumulative distribution of fitting factors shown for three different cases: GR template bank against the GR injections (blue curve), GR template bank against the non-GR injections (red curve), non-GR template bank against the non-GR injections (orange curve). The gray dashed line corresponds to the fitting factor of 0.97, which was also the minimal match at which our banks were constructed.

Figure 3

Fitting factor plots in total mass and mass ratio plane for three cases. The color bar shows the lowest fitting factor in the respective hexagonal bin. The left, middle, and right panels show the performance of the GR bank for GR injections, GR bank for non-GR injections, and non-GR bank for non-GR injections, respectively. We see that the GR bank has a low fitting factor in the region of mass ratio $\ge 4.5$ and total mass $\in [15,50]$ for detecting the non-GR signals.

Figure 4

The scatter plot of found and missed instances of the non-GR signal which had lowest fitting factor against the GR bank. The cross ticks and solid circles indicate missed and found instances, respectively. The color of the circles indicates the inverse false alarm rate (ifar) of the found injections, and their values are depicted in the color bar. These results are produced using the three weeks of LIGO’s O1 data starting from September 22, 2015 (GPS start time 1126989824). The vertical white bands in the triggers indicate the time of data excluded from the analysis by applying a data quality veto.

Figure 5

Comparison of sensitivity distance as a function of ifar between non-GR bank and GR bank for searching the non-GR signals. These plots were made by performing injection over a reduced range of parameters: $M\in [15,50]$ and $q\in [4.5,10]$. The top-left panel shows the results for worst fitting injection, where the non-GR waveform has maximum deviation from GR. For this type of injections, we can see the non-GR bank can observe two times larger distance than the GR bank. The remaining three panels are correspond to the randomly distributed injections binned in total mass. The solid line shows the median of the distribution and the shaded region shows the $\pm 1\sigma$ width of the uncertainty. The sensitivity of a non-GR bank compared to the GR bank decreases with the total mass of the binaries.

Figure 6

Comparison of search results between the non-GR bank and GR bank obtained using the ten days of O1 data surrounding the time of GW150914 event. The false alarm rate is shown as a function of the detection statistic used by the search. The solid black and dashed black lines show the background of false positive detections when the search is performed using a GR bank and a non-GR bank, respectively. The blue and red markers show the search results obtained using a GR bank and a non-GR bank, respectively.