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With an effective chiral model, we investigate how the mesonic crosscouplings $\sigma-\rho$ and $\omega-\rho$ affect the density content of thesymmetry energy and its higher-order slope parameters. Earlier mentionedcross-couplings are crucial to controlling the density content of symmetryenergy. For this purpose, we did a case study for different values of thesymmetry energy $J_1$, defined at density 0.1 fm$^{-3}$ in the range (23.4 -25.2) for a fixed value of the slope of the symmetry energy $L_0 = 60$ MeV atsaturation density and investigate its effect on the higher-order coefficientsand their influence on the underlying equation of state. We found that themodel with $J_1= 24.6$ MeV is more favorable with the pure neutron matter (PNM)constraints obtained from $\chi$EFT calculations. In addition, we show that allof our models predict a monotonically increasing speed of sound up to fourtimes the saturation density. The speed of sound decreases/saturates above thatpoint and approaches the conformal limit approximately $\sqrt{1/3}~c$ at thecenter of the maximum mass star.

High-Density behavior of symmetry energy and speed of sound in the dense matter within an effective chiral model