Charged vector inflation

We present a model of inflation in which the inflaton field is charged under a triplet of $U(1)$ gauge fields. The model enjoys an internal $O(3)$ symmetry supporting the isotropic FRW solution. With an appropriate coupling between the gauge fields and the inflaton field, the system reaches an attractor regime in which the gauge fields furnish a small constant fraction of the total energy density. We decompose the scalar perturbations into the adiabatic and entropy modes and calculate the contributions of the gauge fields into the curvature perturbations power spectrum. We also calculate the entropy power spectrum and the adiabatic-entropy cross-correlation. In addition to the metric tensor perturbations, there are tensor perturbations associated with the gauge field perturbations that are coupled to metric tensor perturbations. We show that the correction in the primordial gravitational tensor power spectrum induced from the matter tensor perturbation is a sensitive function of the gauge coupling.

Figure 1

Left: The phase space plot of $(\varphi ,\dot{\varphi })$ for the potential $V=\frac{1}{2}{m}^2{\varphi }^2$ with parameters $m={10}^{-6}{M}_P$, $\varphi (0)=12M_P$, and $\dot{\varphi }(0)=0$. We have fixed $\mathbf{e}=0.01$ and varied the parameter $c$ with three values $c=1$, 2, and 2.2. The latter two values of $c$ are too large to generate a scale-invariant power spectrum, but we have chosen them for better visualizations of the effects of gauge fields on inflation dynamics. Right: The three-dimensional plot of $(\varphi ,\dot{\varphi })$ with respect to $N$ for the same parameters as in the left figure.

Figure 2

Left: The phase space plot of $(\varphi ,\dot{\varphi })$ with $c$ held fixed at $c=2$, while varying $\mathbf{e}$ with $\mathbf{e}=0$, 0.001, and 0.01. Other parameters are the same as in the top figures. Right: The three-dimensional plot of $(\varphi ,\dot{\varphi })$ with respect to $N$ for the same parameters as in left figure.