N-flation: Multifield inflationary dynamics and perturbations

We carry out numerical investigations of the dynamics and perturbations in the Nflation model of Dimopoulos et al. (2005). This model features large numbers of scalar fields with different masses, which can cooperate to drive inflation according to the assisted inflation mechanism. We extend previous work to include random initial conditions for the scalar fields, and explore the predictions for density perturbations and the tensor-to-scalar ratio. The tensor-to-scalar ratio depends only on the number of $e$-foldings and is independent of the number of fields, their masses, and their initial conditions. It therefore always has the same value as for a single massive field. By contrast, the scalar spectral index has significant dependence on model parameters. While normally multifield inflation models make predictions for observable quantities which depend also on the unknown field initial conditions, we find evidence of a “thermodynamic“ regime whereby the predicted spectral index becomes independent of initial conditions if there are enough fields. Only in parts of parameter space where the mass spectrum of the fields is extremely densely packed is the model capable of satisfying the tight observational constraints from WMAP3 observations.

Figure 1

The evolution of 11 of the fields in a 1000 field simulation, where the field initial conditions are randomly chosen. The simulation started at $N=0$.

Figure 2

The evolution of 11 fields from a 1000 field simulation with different masses, with $\sigma =100$ and $N_{\mathrm{f}}=1000$. The fields shown are $j=0,100,\cdots ,900$ and 999. The more massive fields exit slow-roll first.

Figure 3

The mass $m$ of the lightest field, determined from the normalization of the power spectrum. This is shown as a function of the number of fields $N_{\mathrm{f}}$ for a range of values of $\sigma$ (from bottom to top, $\sigma =100$, 150, 200, 300, 500, 1000 and 2000).

Figure 4

The predicted average value of the spectral index as a function of the number of fields $N_{\mathrm{f}}$, shown for a range of values of $\sigma$ (from bottom to top, $\sigma =100$, 150, 200, 300, 500, 1000 and 2000). The left-hand edge of the graph roughly corresponds to the minimum number of fields needed to achieve sufficient inflation, and the dotted line shows the observational lower limit on $n_{\mathrm{S}}$ from WMAP3.