Tensor-scalar gravity and binary-pulsar experiments

TL;DR

The paper analyzes nonperturbative strong-field effects in tensor--scalar gravity, focusing on spontaneous scalarization in neutron stars that can produce order-unity deviations from general relativity even when the weak-field coupling $\alpha_0$ is small. It develops a slow-rotation formalism in the Einstein frame to compute gravitational form factors $\alpha_A$, $\beta_A$, and $K_A^B$, which enter binary-pulsar timing observables such as $\gamma$ through inertia-moment variations. By applying these results to PSR 1913+16, PSR 1534+12, and PSR 0655+64, the authors derive exclusion regions in the $(\alpha_0,\beta_0)$ plane, showing that pulsar data can be more constraining than solar-system tests in certain regimes, particularly ruling out $\beta_0 \lesssim -5$. They present exclusion plots and discuss limitations (EOS choice, cosmological evolution of $\varphi_0$) and future work to refine the confrontation between tensor--scalar theories and pulsar observations.

Abstract

Some recently discovered nonperturbative strong-field effects in tensor-scalar theories of gravitation are interpreted as a scalar analog of ferromagnetism: "spontaneous scalarization". This phenomenon leads to very significant deviations from general relativity in conditions involving strong gravitational fields, notably binary-pulsar experiments. Contrary to solar-system experiments, these deviations do not necessarily vanish when the weak-field scalar coupling tends to zero. We compute the scalar "form factors" measuring these deviations, and notably a parameter entering the pulsar timing observable gamma through scalar-field-induced variations of the inertia moment of the pulsar. An exploratory investigation of the confrontation between tensor-scalar theories and binary-pulsar experiments shows that nonperturbative scalar field effects are already very tightly constrained by published data on three binary-pulsar systems. We contrast the probing power of pulsar experiments with that of solar-system ones by plotting the regions they exclude in a generic two-dimensional plane of tensor-scalar theories.

Figures (9)

• Figure 1: Effective scalar coupling strength $-\alpha_A\equiv \omega_A/m_A$ versus baryonic mass $\overline m_A$, for the model $A(\varphi) = \exp(-3 \varphi^2)$. The solid line corresponds to the maximum value of $\varphi_0$ allowed by solar-system experiments, and the dashed lines to $\varphi_0 = 0$ ("zero-mode"). The dotted lines correspond to unstable configurations of the star.
• Figure 2: Critical baryonic mass $\overline m_{\rm cr}$ versus the curvature parameter $\beta$ within the quadratic models $A(\varphi) = \exp({1\over 2}\beta \varphi^2)$.
• Figure 3: Dependence upon the baryonic mass $\overline m_A$ of the coupling parameters $\alpha_A$, $\beta_A$, the inertia moment $I_A$, and its derivative $\partial\ln I_A/\partial\varphi_0$. These plots correspond to the model $A(\varphi) = \exp(-3 \varphi^2)$ and the maximum value of $\varphi_0$ allowed by solar-system experiments. As in Fig. \ref{['fig1']}, the dotted lines correspond to unstable configurations of the star.
• Figure 4: Parameter $K^A_A = -\alpha_A(\partial \ln I_A/\partial \varphi_0)$ versus the Einstein inertial mass $m_A$, within the model $A(\varphi) = \exp(-3 \varphi^2)$. The solid line corresponds to the maximum value of $\varphi_0$ allowed by solar-system experiments, and the dashed line to a ten-fold smaller value of $\varphi_0$ ( i.e, a 100 times smaller value of the Eddington parameter $\gamma_{\rm Edd}-1$).
• Figure 5: The $(\dot\omega\hbox{-}\gamma\hbox{-}\dot P_b)_{1913+16}$ test for general relativity (GR), the Jordan--Fierz--Brans--Dicke theory (JFBD), and the quadratic model $A(\varphi) = \exp(+3 \varphi^2)$ [corresponding to a positive curvature parameter $\beta = +6$]. The widths of the three $\dot P$ lines correspond to 1-$\sigma$ standard deviations. The $\dot \omega^{\rm th} = \dot \omega^{\rm exp}$ and $\gamma^{\rm th}=\gamma^{\rm exp}$ lines are wider than 1-$\sigma$ errors, and cannot be distinguished for the three theories.