Comprehensive analysis of dark energy stars in R-squared gravity

Abstract This study examines the structure and stability of dark energy stars within the context of $$R^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> gravity, with the gravity model defined by $$f(R) = R + a R^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> <mml:mi>a</mml:mi> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> (the Starobinsky model). Specifically, dark energy is a mysterious force that can prevent the gravitational collapse of compact objects to singularities. To characterize dark energy, we consider modified Chaplygin fluid as an equation of state (EoS) of matter and study its mass-radius relation for different model parameters. By numerically solving the modified Tolman–Oppenheimer–Volkoff (TOV) equations, our primary objective is to examine the influence of variations in the $$R^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> gravity parameter a on the energy density, pressure, mass-radius and mass-central density relationships of dark energy stars. Our findings reveal that the variation of a does not significantly impact on the $$(M-R)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>M</mml:mi> <mml:mo>-</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> relations but comfortably exceeds the 2 $$M_{\odot }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:math> limit. Additionally, we examine the dynamical stability of these stars by evaluating the static stability criterion, adiabatic index, and sound speed. Finally, we compare our results with various astrophysical observational data and discuss future observations that could validate the predictions of our model.

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