negligible during slow-roll inflation. They argue that this mechanism could only be con- sidered as a phenomenological idea that still lacks some theoretical support and an explicit regime where this can be realized. There could be many more light fields during inflation, they could collectively assist inflation by increasing the effective friction term for all the individual fields [157, 285, 286, 548–551]. This idea can be illustrated with the help of ′ m ′ identical scalar fields with an exponential potentials [157]: For a particular solution; where all the scalar fields are equal: φ$_{1}$ = φ$_{2}$ = · · · = φ$_{m}$ . so the expansion rate is a ∝ t ˜ $^{p}$, provided that ˜ p > 1 / 3. The expansion becomes quicker the more scalar fields there are. In particular, potentials with p < 1, which for a single field are unable to support inflation, can do so as long as there are enough scalar fields to make mp > 1. In order to calculate the density perturbation produced in multi-scalar field models, we recall the results from [213]: where P R is the spectrum of the curvature perturbation R , N is the number of e -foldings of inflationary expansion remaining, and there is a summation over i and j . Since N = − ∫ H dt , we have ∂N ˙ φ$_{i}$ = H , (193) V ( φ$_{i}$ ) = V$_{0}$ exp ( − √ 2 p φ$_{i}$ M$_{P}$ ) . (188) H 2 = 1 3 M 2 P m [ V ( φ$_{1}$ ) + 1 2 ˙ φ 2 1 ] ; (189) ¨ φ$_{1}$ = − 3 H ˙ φ$_{1}$ − dV ( φ$_{1}$ ) dφ$_{1}$ . (190) ˜ φ 2 1 = m φ 2 1 ; ˜ V = m V ; ˜ p = mp , (191) P R = ( H 2 π ) 2 ∂N ∂φ$_{i}$ ∂N ∂φ$_{j}$ δ$_{ij}$ , (192) These can be mapped to the equations of a model with a single scalar field ˜ φ by the redefi- nitions 4. Assisted inflation