Symmetry analysis in multi scalar-torsion cosmological model with quantum description

Abstract A detailed symmetry analysis has been done for the present multi scalar-torsion gravity theory in the background of flat Friedmann Lema $$\hat{\text{ i }}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mrow> <mml:mspace/> <mml:mtext>i</mml:mtext> <mml:mspace/> </mml:mrow> <mml:mo>^</mml:mo> </mml:mover> </mml:math> tre Robertson Walker (FLRW) space-time. Not only the Noether symmetry from the invariance of the Lagrangian has been determined and associated conserved quantities are evaluated, but also the conformal symmetry of the physical metric (i.e., metric of the kinetic part) has been investigated to evaluate homothetic and killing vector fields. Finally, a through study of quantum cosmology both by canonical approach and by considering quantum trajectories has been presented.