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Neutron stars (NSs) are excellent natural laboratories to constrain gravityon strong field regime and nuclear matter in extreme conditions. Motivated bythe recent discovery of a compact object with $2.59^{+0.08}_{-0.09} M_\odot$ inthe binary merger GW190814, if this object was a NS, it serves as a strongconstraint on the NS equation of state (EoS), ruling out several soft EoSsfavored by GW170817 event. In this work, we revisit the question of the maximummass of NSs considering a chameleon screening (thin-shell effect) on the NSmass-radius relation, where the microscopic physics inside the NS is given byrealistic soft EoSs. We find that from appropriate and reasonable combinationof modified gravity, rotation effects and realistic soft EoSs, that it ispossible to achieve high masses and explain GW190814 secondary component, andin return also NSs like PSR J0740+6620 (the most NS massive confirmed to date).It is shown that gravity can play an important role in estimating maximum massof NSs, and even with soft EoSs, it is possible to generate very high masses.Therefore, in this competition on the hydrostatic equilibrium between gravityand EoS, some soft EoSs, in principle, cannot be completely be ruled outwithout first taking into account gravitational effects.

Weighing massive neutron star with screening gravity: A look on PSR J0740+6620 and GW190814 secondary component