We investigate inflation with a class of concave inflaton potentials of the form $$\sim \phi ^n$$∼ϕn$$(0<n<1)$$(0<n<1) in the Randall–Sundrum model with an infinite extra spatial dimension. We show that this class of models is much more in good agreement with observations compared to the standard inflation. We also find the range of the five-dimensional Planck scale ($$M_5$$M5) and show that large tensor-to-scalar ratios do not eliminate small-field inflation in braneworld cosmology.

In the first scenario, we revise the upper bound of the cutoff scale of the dimension-six potential Higgs operator required for a successful electroweak baryogenesis in the case of a modified expansion history caused by the existence of a noninteracting scalar field at the time phase transition happens. The upper bound 860[Formula: see text]GeV of the cutoff scale in the conventional case can be improved to 1[Formula: see text]TeV in the modified expansion case under certain conditions. In the second scenario, we consider the Randall–Sundrum type II model. We show that the lower bound of the five-dimensional Planck scale in this model, which is determined from the validity of Newtonian gravitational potential at small distance, turns out to be crucial in eliminating this model as a viable candidate to satisfy the sphaleron bound; however, again modifying the expansion history by including a noninteracting scalar field at the electroweak scale can then make this model satisfy the sphaleron bound with a certain parameter space.

Within the S P 2 , R symmetry, the two-time model (2T model) has six dimensions with two dimensions of time and the dilaton field that can be identified as inflaton in a warm inflation scenario with potential of the form ~ ϕ 4 . From that consideration, we derive the range of parameters for the Higgs-Dilaton potential, the coupling constant between Higgs and Dilaton ( α ) is larger than 0.0053 and the mass of Dilaton is smaller than 1 0 − 7  GeV. Therefore, the 2T model indirectly suggests that extra dimension can also be a source of inflation.