Baryon acoustic scale at $z_{\eff} = 0.166$ with the SDSS blue galaxies

The Baryon Acoustic Oscillations (BAO) phenomenon provides a unique opportunity to establish a standard ruler at any epoch in the history of the evolving universe. The key lies in identifying a suitable cosmological tracer to conduct the measurement. In this study, we focus on quantifying the sound horizon scale of BAO in the Local Universe. Our chosen cosmological tracer is a sample of blue galaxies from the SDSS survey, positioned at the effective redshift $z_{{\eff}} = 0.166$. Utilizing Planck-CMB input values for redshift-to-distance conversion, we derive the BAO scale $s_{\scalebox{0.65}{\rm BAO}} = 100.28 ^{+10.79} _{-22.96}$ Mpc$/h$ at the 1$\sigma$ confidence level. Subsequently, we extrapolate the BAO signal scale in redshift space: $\Delta z_{\scalebox{0.6}{\rm BAO}}(z_{\rm eff}=0.166)=0.0361^{+0.00262}_ {-0.0055}$. This measurement holds the potential to discriminate among dark energy models within the Local Universe. To validate the robustness of our methodology for BAO scale measurement, we conduct three additional BAO analyses using different cosmographic approaches for distance calculation from redshifts. These tests aim to identify possible biases or systematics in our measurements of $s_{\scalebox{0.65}{\rm BAO}}$. Encouragingly, our diverse cosmographic approaches yield results in statistical agreement with the primary measurement, indicating no significant deviations. Conclusively, our study contributes with a novel determination of the BAO scale in the Local Universe, at $z_{{\eff}} = 0.166$, achieved through the analysis of the SDSS blue galaxies cosmic tracer.