# Constraining extra gravitational wave polarizations with Advanced LIGO, Advanced Virgo and KAGRA and upper bounds from GW170817

## TL;DR

This paper explores methods to distinguish and constrain extra gravitational wave polarization modes using a network of detectors, expanding previous techniques and applying them to real GW data to set upper bounds on non-standard modes.

## Contribution

It extends null stream methods to effectively suppress certain polarization modes, enabling separate tests for spin-1 and spin-0 modes with advanced detector networks.

## Key findings

- Null streams can effectively suppress spin-0 modes for certain sky positions.
- Upper bounds on spin-1 mode amplitude are established from GW170817 data.
- The method enhances the ability to test alternative gravity theories with GW observations.

## Abstract

General metric theories of gravity in four-dimensional spacetimes can contain at most six polarization modes (two spin-0, two spin-1 and two spin-2) of gravitational waves (GWs). It has been recently shown that, with using four GW non-coaligned detectors, a direct test of the spin-1 modes can be done in principle separately from the spin-0 and spin-2 modes for a GW source in particular sky positions [Hagihara et al., Phys. Rev. D 98, 064035 (2018)]. They have found particular sky positions that satisfy a condition of killing completely the spin-0 modes in a so-called null stream which is a linear combination of the signal outputs to kill the spin-2 modes. The present paper expands the method to discuss a possibility that the spin-0 modes are not completely but effectively suppressed in the null streams to test the spin-1 modes separately from the other modes, especially with an expected network of Advanced LIGO, Advanced Virgo and KAGRA. We study also a possibility that the spin-1 modes are substantially suppressed in the null streams to test the spin-0 modes separately from the other modes, though the spin-1 modes for any sky position cannot be completely killed in the null streams. Moreover, we find that the coefficient of the spin-0 modes in the null stream is significantly small for the GW170817 event, so that an upper bound can be placed on the amplitude of the spin-1 modes as $< 6 \times 10^{-23}$.