Reconstruction of symmteric teleparallel gravity with energy conditions

This research investigates the impact of modified gravity on cosmic scales, focusing on $f(Q)$ cosmology. By applying energy conditions, the study reconstructs various $f(Q)$ models, considering an accelerating Universe, quintessence, and a cosmological constant $\mathrm{\Lambda }$. Using up-to-date observational data, including the Supernova Pantheon sample and cosmic chronometer data, Hubble constants $H_0$ are estimated as $70.37_{-0.92}^{+0.84}$ km/sec/Mpc (from $H(z)$ data) and $70.02_{-0.25}^{+0.44}$ km/sec/Mpc (from pantheon compilation of SN Ia data). The matter energy density parameter (${\mathrm{\Omega }}_{0m}$) is calculated as $0.26_{-0.010}^{0.015}$(OHD) and $0.27_{-0.014}^{0.025}$(SN Ia). Furthermore, as a function of redshift $z$, explicit expressions of $f(Q)$ and the EOS parameter $\omega$ are produced, and their graphical analysis describes the late time acceleration of the Universe without the usage of dark energy.