What if X-ray bursts ticked (the tensor field theory of) General Relativity away?

A mimetic scalar field in the core of neutron stars? 
2015 saw the celebration of the 100th anniversary of General Relativity. May this new year give us opportunity to go beyond and work on, read about or learn more from a recent extension called mimetic gravity that has gained some momentum recently. I choose to focus today on astrophysics instead of cosmology:
Number of modified gravity theories which may describe accelerating universe has been intensively studied in the recent years (for a review, see [1]). In the framework of these theories it is possible to obtain the accelerated expansion of Universe [2–4] without using of inflaton for inflation and/or scalars, fluids or cosmological constant for dark energy. Some cosmological bounds also favour the modified gravity [1]. However, one can not discriminate between the ΛCDM model or the modified gravity using only cosmological bounds. The study of alternative gravities on the astrophysical level, e.g. using the relativistic stars, allows for an alternative way of discrimination between General Relativity (GR) from its possible modifications [5]. The fundamental question is the existence of stable neutron stars in given f(R) theory [6, 7]. Secondly, one needs to compare the mass-radius relation, moment of inertia, quadrupole moment, Love number and other relevant characteristics of stars in GR and f(R) gravity [8]. Finally, it is interesting to consider the possible emergence of new stellar structures in modified gravities (stable stars with large central densities or/and with large magnetic fields, (super)massive stars etc.). The discovery of such structures will constitute a powerful signature for the Extended Gravity [9, 10]. The structure of compact stars in perturbative f(R) gravity was investigated recently in refs.[11–13]. In this approach the scalar curvature R is defined by Einstein equations at zeroth order on the small parameter, i.e. R∼T , where T is the trace of energy-momentum tensor. Non-perturbative studies are also available for non-rotating, slowly and fast rotating compact star models [14, 15]. In this paper we investigate relativistic stars in mimetic gravity with scalar potential V (φ) (mimetic potential) and with Lagrange multiplier β(φ). This theory was recently proposed in ref.[17] for eventual geometric description of dark matter... 
The ambiguity of mass-radius (M−R) relation is determined by the free parameter φ(0) which can explain some inconsistencies in M−R relation from observations and theoretical considerations. For example, from the study of longer X-ray bursters [23, 24] it follows that neutron stars with masses M∼1−1.4M have large radii R > 14.0 km. However, the analysis of both transiently accreting and bursting sources [25] suggests that the radius of a 1.4M neutron star should not exceed the 12.9 km. These contradictions may indicate that the neutron star mass is determined not only by the Equation Of State (EOS) of the dense matter but also by other parameters. In mimetic gravity these free parameters are present. Of course, there are many other EOS for which neutron stars can have larger radius for the typical 1.4M models. However, our main point is that even EoS which is considered to be not fully realistic due to discovery of large mass neutron mass, may still be viable in modified gravity! The results presented here provide hint that unique discrimination between General Relativity and mimetic gravity can be made once we know in detail the equation of state...

The mass-radius diagram (left panel) and dependence of neutron star mass on the central density (right panel) for neutron stars in mimetic GR with V (φ) = Aφ−2 (A = 0.005) in comparison with GR by using a SLy4 equation of state for various values of φ(0).
In the present paper we considered realistic neutron and quark stars in simple mimetic gravity with mimetic scalar potential. We obtained the mass-radius relations and examined the dependence of inertial characteristics from stellar mass. For simple potentials of the form V(φ) = Aφ−2 the mass-radius relation for compact stars can considerably deviate from the mass-radius relation in General Relativity. For neutron stars this deviation occurs for stellar configurations with any mass whereas for quark stars the mass-radius relation deviates only for large masses. The deviation from GR depends on the value of mimetic scalar in the center of star. For values of φ(0) smaller than a specific critical value φcrit there exist no stable stellar configurations. The parameter φcrit depends on equation of state and the form of potential. Due to the contribution of mimetic scalar the maximum mass and the corresponding moment of inertia may increase. This increase is considerably larger for quark stars in comparison with the neutron stars. It should be noted that the presence of mimetic scalar offers the possibility for the existence of stars with low central densities ρ < 1015g/cm3 but large masses M > M. In mimetic gravity there exists a free parameter (the value of mimetic scalar in the center of the star as initial condition). This freedom leads to ambiguity of mass-radius relation for given equation of state. This ambiguity can potentially explain some contradictions between observations and theoretical modelling of compact stars in General Relativity. The relative deviation of the maximal moment of inertia is approximately two times larger than the relative deviation of maximal stellar mass. Even for negligible increase of mass lying within equation of state uncertainty the increase of moment of inertia (if measured) can help to discriminate between GR and mimetic gravity. Eventually, the future observations of moment of inertia of compact stars will set constraints on the models of mimetic gravity and/or convenient modified gravity.
A.V. Astashenok, S.D. Odintsov (Submitted on 22 Dec 2015)