Quark stars in massive gravity might be candidates for the mass gap objects

We have investigated the structural properties of strange quark stars (SQSs) in a modified theory of gravity known as massive gravity. In order to obtain the equation of state (EOS) of strange quark matter, we have employed a modified version of the Nambu-Jona-Lasinio model (MNJL) which includes a combination of NJL Lagrangian and its Fierz transformation by using weighting factors ($1-\alpha $) and $\alpha$. Additionally, we have also calculated dimensionless tidal deformability ($\Lambda$) in massive gravity. To constrain the allowed values of the parameters appearing in massive gravity, we have imposed the condition $\Lambda_{1.4 {M}_{\odot }}\lesssim580 $. Notably, in the MNJL model, the value of $\alpha$ varies between zero and one. As $\alpha$ increases, the EOS becomes stiffer, and the value of $\Lambda$ increases accordingy. We have demonstrated that by softening the EOS with increasing the bag constant, one can obtain objects in massive gravity that not only satisfy the constraint $\Lambda_{1.4 {M}% _{\odot }}\lesssim580$, but they also fall within the unknown mass gap region ($2.5{M}_{\odot}-5{M}_{\odot }$). To establish that the obtained objects in this region are not black holes, we have calculated Schwarzschild radius, compactness, and $\Lambda_{{M_{TOV}}}$ in massive gravity.