Compact stars in alternative theories of gravity: Einstein-Dilaton-Gauss-Bonnet gravity

We develop a theoretical framework to study slowly rotating compact stars in a rather general class of alternative theories of gravity, with the ultimate goal of investigating constraints on alternative theories from electromagnetic and gravitational-wave observations of compact stars. Our Lagrangian includes as special cases scalar-tensor theories (and indirectly $f(R)$ theories) as well as models with a scalar field coupled to quadratic curvature invariants. As a first application of the formalism, we discuss (for the first time in the literature) compact stars in Einstein-Dilaton-Gauss-Bonnet gravity. We show that compact objects with central densities typical of neutron stars cannot exist for certain values of the coupling constants of the theory. In fact, the existence and stability of compact stars sets more stringent constraints on the theory than the existence of black hole solutions. This work is a first step in a program to systematically rule out (possibly using Bayesian model selection) theories that are incompatible with astrophysical observations of compact stars.

Figure 1

Compact star models in EDGB gravity for different values of the parameters $\alpha$ and $\beta$, using the APR EOS. In the bottom right panel we show the recent observation of a neutron star with $M\approx 2M_{\odot }$ and a possible future observation of the moment of inertia confirming general relativity within 10% [82]. Curves terminate when the condition (31) is not fulfilled (cf. also the exclusion plot in Fig. 5).

Figure 2

Compact star models in EDGB gravity for different values of the parameters $\alpha$ and $\beta$, using the FPS EOS. Curves terminate when the condition (31) is not fulfilled (cf. also the exclusion plot in Fig. 5).

Figure 3

Compact star models in EDGB gravity for different values of the parameters $\alpha$ and $\beta$, using a causal EOS. Curves terminate when the condition (31) is not fulfilled (cf. also the exclusion plot in Fig. 5).

Figure 4

Maximum mass as a function of the product $\alpha \beta$ of the EDGB coupling parameters, for different EOS models and in the nonrotating case (cf. the main text for details). To the left of the filled circle, this maximum mass corresponds to the radial stability criterion; to the right, it corresponds to the maximum central density for which we can construct static equilibrium models. The recent measurement [12] of a neutron star with $M\approx 2M_{\odot }$ is marked by a horizontal line. Only the combination $\alpha \beta$ is bounded, due to the approximation $\Phi \ll 1$ (cf. Eq. (29)).

Figure 5

Exclusion plot for the parameters $\alpha \beta$ in the small ${\Phi }_c$ limit and for nonrotating models. Only the combination $\alpha \beta$ is bounded, due to the approximation $\Phi \ll 1$ (cf. Eq. (29)). In the region above the dotted lines no compact star solution can be constructed (cf. Eq. (31)). In the region above the thick lines (marked as “RI,” Radial Instability), static configurations are unstable against radial perturbations (cf. the main text for details). Markers indicate the maximum central density of radially stable stars in general relativity.

Figure 6

Moment of inertia normalized by its value in general relativity for the APR EOS at fixed values of the gravitational mass. Curves terminate at the bounds listed in Table  (corresponding to the filled circles). The deviations from general relativity are always smaller than 5%.