Paul and SenGupta (Eur Phys J C 79:591, 2019) have recently shown that the reason why torsion effects are not present in today s universe is that they are suppressed in the bulk of a 5D braneworld. In this case only curvature effects remain. In this paper our goals are to investigate how this idea applies in the 4D Brans–Dicke inflation in two cases: First in the spin-torsion energy density scaling as $$\sim {a^{-6}}$$ $\sim a^{-6}$ , whereas matter density scales at $$a^{-3}$$ $a^{-3}$ . Here a(t) is the cosmic evolution parameter in the cosmic time t. In this case when a is given by the de Sitter expansion spin-torsion density it is highly suppressed. the second is the inflation in the framework of Einstein–Cartan–Brans–Dicke (ECBD) gravity used here, to build an effective inflaton potential and computing the number of its e-folds. Spin-torsion density contributes to a decrease on the number of e-folds when the ratio of spin-torsion density to matter density is not suppressed as in Early Universe. At present universe it is easy to show that by the end of inflation, spin-torsion density is suppressed with respect to matter-curvature density with a ratio of $$a^{-3}$$ $a^{-3}$ or $$t^{-3}$$ $t^{-3}$ by the end of inflation. When torsion possesses dynamical degrees of freedom, contortion is also shown to be suppressed by the end of BD inflation. The Kalb–Ramond fields in the 5D braneworld are equivalent to torsion. At present universe we find $$K\sim {10^{-39}~\hbox {GeV}}$$ $K\sim {10}^{-39}\text{GeV}$ for contortion. Such an estimate is much more stringent than the value found by Russell et al. (Phys Rev Lett 100, 2008) from torsion Lorentz violation (LV) with dual masers experiment.