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There is a degeneracy between the equation of state (EOS) of superdenseneutron-rich nuclear matter and the strong-field gravity in understandingproperties of neutron stars. While the EOS is still poorly known, there arealso longstanding ambiguities in choosing General Relativity or alternativegravity theories in the not-so-well tested strong-field regime. Besidespossible appearance of hyperons and new phases, the most uncertain part of thenucleonic EOS is currently the density dependence of nuclear symmetry energy.To provide information that may help break the EOS-gravity degeneracy, weinvestigate effects of symmetry energy within its uncertain range determined byterrestrial nuclear laboratory experiments on the gravitational binding energyand spacetime curvature of neutron stars within GR and the scalar-tensor (ST)theory of gravity. In particular, we focus on effects of the followingparameters characterizing the EOS of neutron-rich nucleonic matter: (1) theincompressibility $K_0$ of symmetric nuclear matter, (2) the slope $L$ ofsymmetry energy at saturation density and (3) the high-density behavior ofsymmetry energy. We find that the variation of either the density slope $L$ orthe high-density behavior of symmetry energy leads to large changes in both thebinding energy and curvature of neutron stars while effects of varying the moreconstrained $K_0$ are negligibly small. The difference in predictions using theGR and the ST theory appears only for massive neutron stars, and issignificantly smaller than the differences resulting from variations in thesymmetry energy. We conclude that within the ST theory of gravity, theEOS-gravity degeneracy has been broken by the recent relativistic pulsarmeasurements, and that measurements of neutron star properties sensitive to thecompactness constrain mainly the density dependence of the symmetry energy.

Impact of the equation-of-state -- gravity degeneracy on constraining the nuclear symmetry energy from astrophysical observables