Constraining quadratic f(R) gravity from astrophysical observations of the pulsar J0704+6620

We apply quadratic f(R) = R + R² field equations, where has a dimension [L²], to static spherical stellar model. We assume the interior configuration is determined by Krori-Barua ansatz and additionally the fluid is anisotropic. Using the astrophysical measurements of the pulsar PSR J0740+6620 as inferred by NICER and XMM observations, we determine ≈ ± 3 km². We show that the model can provide a stable configuration of the pulsar PSR J0740+6620 in both geometrical and physical sectors. We show that the Krori-Barua ansatz within f(R) quadratic gravity provides semi-analytical relations between radial, p_r, and tangential, p_t, pressures and density ρ which can be expressed as p_r ≈ v_r² (ρ-ρ₁) and p_r ≈ v_t² (ρ-ρ₂), where v_r (v_t) is the sound speed in radial (tangential) direction, ρ₁ = ρ_s (surface density) and ρ₂ are completely determined in terms of the model parameters. These relations are in agreement with the best-fit equations of state as obtained in the present study. We further put the upper limit on the compactness, C = 2GMR_s^-1c^-2, which satisfies the f(R) modified Buchdahl limit. Remarkably, the quadratic f(R) gravity with negative naturally restricts the maximum compactness to values lower than Buchdahl limit, unlike the GR or f(R) gravity with positive where the compactness can arbitrarily approach the black hole limit C → 1. The model predicts a core density a few times the saturation nuclear density ρ_nuc = 2.7 × 10¹⁴ g/cm³, and a surface density ρ_s > ρ_nuc. We provide the mass-radius diagram corresponding to the obtained boundary density which has been shown to be in agreement with other observations.