Speaker
Description
A locally rotationally symmetric Bianchi type-I model has been analyzed with a perfect fluid within the framework of ( f(R, \mathcal{L}m) ) gravity. The exact field equations were derived, the variable deceleration parameter ( q(t) = \alpha - \frac{\beta}{H} ) has been used here. The cosmological parameters such as energy density, pressure, equation of state, spatial volume, the Hubble parameter, expansion scalar, deceleration parameter, anisotropy parameter, and shear scalar were evaluated. The best-fit curve for ( H(z) ) was determined using 57 observational data points and evaluated through the ( R^2 )-test, achieving an ( R^2 ) value of 0.9321. The best-fit parameters obtained were ( \alpha = 0.542^{+0.019}{-0.022} ), ( \beta = 52.9^{+2.3}{-2.7} ), and ( c_1 = -0.877^{+0.055}{-0.058} ), with a Hubble constant ( H_0 = 64.39^{+0.04}_{-0.47} \, \text{km/s/Mpc} ). Our results show that the model closely matches the (\Lambda)CDM model.
Additionally, we calculated and plotted the evolution of energy density ( \rho(z) ), pressure ( p(z) ), and the equation of state parameter ( \omega(z) ). The results indicate a rapid increase in density at higher redshifts and negative pressure, consistent with dark energy driving the accelerated expansion of the universe. The statefinder diagnostics with ( (r, s) = (1, 0) ) confirm alignment with the (\Lambda)CDM model, while ( r < 1 ) and ( s > 0 ) suggest a quintessence-like behavior. These findings underscore the model's compatibility with current cosmological observations and the need for precise parameter determination to further enhance our understanding of cosmic evolution. The ( \Omega(z) ) plot shows close alignment with the (\Lambda)CDM model at higher redshifts, with rapid expansion changes near ( z = 0 ). As redshift increases, the model stabilizes, reflecting uniform expansion and reduced uncertainties. The evolution of the Strong, Weak, Null, and Dominant Energy Conditions has been discussed.
