Tests of gravitational scalar polarization and constraints of chameleon $f(R)$ gravity from comprehensive analysis of binary pulsars

TL;DR

This paper investigates how chameleon $f(R)$ gravity affects binary pulsar orbital dynamics, using PK parameters and simulations to constrain deviations from general relativity and find no evidence of additional polarization states.

Contribution

It provides a detailed analysis of PK effects in chameleon $f(R)$ gravity and establishes observational constraints using binary pulsar data, enhancing tests of alternative gravity theories.

Findings

Orbital decay faster than GR due to dipole radiation.

No evidence of additional polarization states beyond GR.

PSR J1738+0333 provides the strongest constraints.

Abstract

Chameleon $f(R)$ gravity is equivalent to a class of scalar-tensor theories of gravity with chameleon screening mechanism allowing the theory to satisfy local tests of gravity. Within the framework of chameleon $f(R)$, we study the impact of the chameleon mechanism on the orbital evolution of binary pulsars, and calculate in detail the post-Keplerian (PK) effects (periastron advance, Einstein delay, Shapiro delay, orbital period decay and eccentricity decay) of binary orbit. The differences in PK effects between general relativity (GR) and chameleon $f(R)$ are elegantly quantified by a combination of star's compactness and theory parameter. We use the mass-radius relation to break the degeneracy between these two parameters, thus allowing us to constrain the theory. We simulate the temporal evolution of the orbital period and eccentricity of neutron star (NS) - white dwarf (WD) binaries, and the results indicate that the orbital evolution is typically faster than in GR due to the emission of dipole radiation in chameleon $f(R)$. We use the observables of PK parameters from the three NS-WD binary pulsars to place constraints on chameleon $f(R)$ and possible deviations from GR by performing Monte-Carlo simulations. We find that PSR J1738$+$0333 is the most constraining test of chameleon $f(R)$ in these systems. Our results show no solid evidence of the existence of helicity-0 or helicity-1 polarization states inducing dipole radiation, exclude significant strong-field deviations and confirm that GR is still valid for strong-field asymmetric systems.