Tilted two forms of dark energy in f(T) theory of gravity

This study presents tilted two forms of dark energy in f(T) theory of gravity. f(T) gravity is the generalization of the teleparallel theory of gravity, where T is the torsion scalar. In this work, the tilted model is examined by using forms of dark energy consisting part of quintessence and cosmological constant (Dagwal and Pawar in MPLA 33:185213, 2018). The singular origin and non-singular origin of the models are discussed (Solanke et al. in IJGMMP 18:2150062, 2021). The Hubble parameter H0 and deceleration parameter q with the help of modern observational data are constrained.The reliability of the resultant model with observational parameter from the point of astrophysical miracle like as look-back time tL, angular-diameter distance d_A , distance modulus μ(z), luminosity distance d_L and proper distance d(z) are explored with SNeIa, H(z), WMAP7 + BAO + H(z) and WMAP7 with observational data (Kumar in MNRAA 422:2532, 2012 and Gumjudpai in MPLA 28:135022, 2013). (author)