Stochastic backgrounds in alternative theories of gravity: overlap reduction functions for pulsar timing arrays

TL;DR

This paper explores how pulsar timing arrays can detect various gravitational wave polarizations predicted by alternative gravity theories, highlighting increased sensitivity to non-transverse modes especially at small angular separations.

Contribution

It calculates overlap reduction functions for alternative gravity theories and demonstrates enhanced sensitivity to non-transverse gravitational wave modes in pulsar timing arrays.

Findings

Sensitivity to non-transverse modes exceeds that to transverse modes.

Small angular separations greatly increase sensitivity to longitudinal modes.

Specific pulsar pairs can be up to 10^4 times more sensitive to longitudinal components.

Abstract

In the next decade gravitational waves might be detected using a pulsar timing array. In an effort to develop optimal detection strategies for stochastic backgrounds of gravitational waves in generic metric theories of gravity, we investigate the overlap reduction functions for these theories and discuss their features. We show that the sensitivity to non-transverse gravitational waves is greater than the sensitivity to transverse gravitational waves and discuss the physical origin of this effect. We calculate the overlap reduction functions for the current NANOGrav Pulsar Timing Array (PTA) and show that the sensitivity to the vector and scalar-longitudinal modes can increase dramatically for pulsar pairs with small angular separations. For example, the J1853+1303-J1857+0943 pulsar pair, with an angular separation of about 3 degrees, is about 10^4 times more sensitive to the longitudinal component of the stochastic background, if it is present, than the transverse components.