# Constraining nonperturbative strong-field effects in scalar-tensor gravity by combining pulsar timing and laser-interferometer gravitational-wave detectors

## TL;DR

This paper combines pulsar timing and gravitational-wave data to constrain scalar-tensor gravity theories, demonstrating that future GW observations can significantly improve existing bounds and probe nonperturbative effects in neutron stars.

## Contribution

It provides the first combined analysis of pulsar timing and GW data to constrain nonperturbative scalarization in scalar-tensor gravity, highlighting the potential of future GW detectors.

## Key findings

- Current pulsar timing constrains scalar-tensor parameters but leaves scalarization windows open.
- Next-generation GW detectors can improve constraints across various neutron star equations of state.
- GW observations during neutron star inspirals can detect or further limit scalarization effects.

## Abstract

Pulsar timing and gravitational-wave (GW) detectors are superb laboratories to study gravity theories in the strong-field regime. Here we combine those tools to test the mono-scalar-tensor theory of Damour and Esposito-Far{\`e}se (DEF), which predicts nonperturbative scalarization phenomena for neutron stars (NSs). First, applying Markov-chain Monte Carlo techniques, we use the absence of dipolar radiation in the pulsar-timing observations of five binary systems composed of a NS and a white dwarf, and eleven equations of state (EOSs) for NSs, to derive the most stringent constraints on the two free parameters of the DEF scalar-tensor theory. Since the binary-pulsar bounds depend on the NS mass and the EOS, we find that current pulsar-timing observations leave scalarization windows, i.e., regions of parameter space where scalarization can still be prominent. Then, we investigate if these scalarization windows could be closed and if pulsar-timing constraints could be improved by laser-interferometer GW detectors, when spontaneous (or dynamical) scalarization sets in during the early (or late) stages of a binary NS (BNS) evolution. For the early inspiral of a BNS carrying constant scalar charge, we employ a Fisher matrix analysis to show that Advanced LIGO can improve pulsar-timing constraints for some EOSs, and next-generation detectors, such as the Cosmic Explorer and Einstein Telescope, will be able to improve those bounds for all eleven EOSs. Using the late inspiral of a BNS, we estimate that for some of the EOSs under consideration the onset of dynamical scalarization can happen early enough to improve the constraints on the DEF parameters obtained by combining the five binary pulsars. Thus, in the near future the complementarity of pulsar timing and direct observations of GWs on the ground will be extremely valuable in probing gravity theories in the strong-field regime.