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From neutron stars to quark stars in mimetic gravity

Artyom V. Astashenok¹ and Sergei D. Odintsov^2,3,4

¹I. Kant Baltic Federal University, Institute of Physics, Mathematics and Information Technologies, 4 Nevskogo Street 14, 236041 Kaliningrad, Russia
²Instituciò Catalana de Recerca i Estudis Avançats (ICREA), P. Luis Companyus 23, 08010 Barcelona, Spain
³Institute of Space Sciences (IEEC-CSIC), C. Can Magrans s/n, 08193 Barcelona, Spain
⁴Tomsk State Pedagogical University, 634061 Tomsk, Russia and Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050 Tomsk, Russia

Phys. Rev. D 94, 063008 – Published 19 September, 2016

DOI: https://doi.org/10.1103/PhysRevD.94.063008

Abstract

Realistic models of neutron and quark stars in the framework of mimetic gravity with a Lagrange multiplier constraint are presented. We discuss the effect of a mimetic scalar aiming to describe dark matter on the mass-radius relation and the moment of inertia for slowly rotating relativistic stars. The mass-radius relation and moment of inertia depend on the value of the mimetic scalar in the center of the star. This fact leads to the ambiguity in the mass-radius relation for a given equation of state. Such ambiguity allows us to explain some observational facts better than in standard general relativity. The case of mimetic potential $V (ϕ) \sim A e^{C ϕ^{2}}$ is considered in detail. The relative deviation of the maximal moment of inertia is approximately twice as large as the relative deviation of the maximal stellar mass. We also briefly discuss the mimetic $f (R)$ gravity. In the case of $f (R) = R + a R^{2}$ mimetic gravity, it is expected that the increase of maximal mass and maximal moment of inertia due to the mimetic scalar becomes much stronger with bigger parameter $a$ . The influence of the scalar field in mimetic gravity can lead to the possible existence of extreme neutron stars with large masses.

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