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

Abstract

Abstract We apply quadratic f ( R ) = R + ϵR 2 field equations, where ϵ has a dimension [L 2 ], 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 ϵ ≈ ± 3 km 2 . 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 r 2 ( ρ - ρ 1 ) and p r ≈ v t 2 ( ρ - ρ 2 ), where v r ( v t ) is the sound speed in radial (tangential) direction, ρ 1 = ρ s (surface density) and ρ 2 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 = 2 GMR s -1 c -2 , which satisfies the f ( R ) modified Buchdahl limit. Remarkably, the quadratic f ( R ) gravity with negative ϵ naturally restricts the maximum compactness to values lower than Buchdahl limit, unlike the GR or f ( R ) gravity with positive ϵ 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 × 10 14 g/cm 3 , 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.