Gauge-flation trajectories in Chromo-Natural Inflation

TL;DR

Chromo-Natural Inflation couples an axion to SU(2) gauge fields to realize slow-roll inflation on steep potentials. The gauge-field vacuum expectation value provides damping that flattens the effective potential, with an attractor psi_min = ((mu^4 * sin(X/f)) / (3 * gtilde * lambda * H))^(1/3). Gauge-flation emerges as a special case of CNI when the axion is integrated out, with kappa = 3 lambda^2 / mu^4, notably near the minimum X ≈ pi f; CNI thus subsumes GF but offers much richer dynamics with two additional parameters. The authors show that viable inflation is achievable for a broad parameter range (e.g., large lambda) and that GF trajectories are recovered in the final 60 e-folds, motivating a full perturbation analysis to assess observational signatures and discriminate among regimes.

Abstract

We provide a detailed discussion of the multifield trajectories and inflationary dynamics of the recently proposed model of Chromo-Natural inflation, which allows for slow roll inflation on a steep potential with the aid of classical non-Abelian gauge fields. We show that slow roll inflation can be achieved across a wide range of the parameter space. We demonstrate that Chromo-Natural Inflation includes trajectories that match those found in Gauge-flation and describe how the theories are related.

Figures (4)

• Figure 1: The behaviour of the gauge field during inflation for the choice of parameters $\{\mu,f,\tilde{g}, \lambda\} = \{3.16 \times 10^{-4}, 0.01, 2.0 \times10^{-6}, 200\}$. In the left panel we show the phase portrait of the gauge field. The solid black curve corresponds to the period of exponential expansion, inflation. The red curve is the $\sim 8$ observable efoldings, 50 efoldings before the end of inflation, where the cosmic microwave background fluctuations are produced. Inflation ends where the dashed black line begins, and the gauge field decays. In the right hand panel we show the behavior of the gauge field as inflation proceeds, the observable window 50 efoldings before the end of inflation is shown in red. Plotted in blue is the value of the gauge field that minimizes its effective potential, Eqn. (\ref{['eqn:psimin']}).
• Figure 2: The part of the bare axion potential traversed 50 efoldings before inflation ends (upper panel) is shown in red over the top of the parts of the potential that are probed by the axion during the entire period of inflation for the choice of parameters $\{\mu,f,\tilde{g}, \lambda\} = \{3.16 \times 10^{-4}, 0.01, 2.0 \times10^{-6}, 200\}$. In the lower panel we show the full range of values the axion takes during inflation as a function of the efolding number. The axion's position in between 50 - 42 efoldings before the end of inflation is shown in red.
• Figure 3: We show the number of efoldings of inflation produced as the various parameters of Chromo-Natural Inflation are varied. In the upper left panel, we show how the total amount of inflation varies as we vary the energy scale of the axion's potential, $\mu$. In the upper right panel we show how the total amount of inflation varies as we vary the gauge field coupling strength $\tilde{g}$. In the lower left panel, we show that the number of efoldings of inflation is kept constant if the parameters gauge field strength and the axion energy scale are covaried while keeping the ratio $2\tilde{g}/\mu^2$ constant. We also show the effect of these variations at various values of the coupling strength between the gauge and axion sectors, $\lambda$. In the lower right panel, we show the effect of varying $\lambda$ while keeping the remaining parameters fixed. Unless otherwise noted, all other parameters are fixed at the values $\{\mu,f,\tilde{g}, \lambda\} = \{3.16 \times 10^{-4}, 0.01, 2.0 \times10^{-6}, 200\}$. This parameter set is one that we estimate will give the appropriate level of cosmological perturbations. In this figure, however, deviations from this set are not guaranteed to generate the appropriate level of perturbations, and generically will not.
• Figure 4: The behaviour of the gauge field during inflation for the choice of parameters that corresponds to the Gauge-flation model of Maleknejad:2011jw$\{\mu,f,\tilde{g}, \lambda\} = \{4 \times 10^{-2}, 0.01, 2.5 \times10^{-3}, 12158\}$. In the left panel we show a phase portrait of the gauge field. The solid black curve corresponds to the period of exponential expansion, inflation. The red curve shows the final $\sim 60$ efoldings of inflation and Chromo-Natural inflation ends at the end of the red curve here where the gauge field decays. The dashed blue line here (which begins 60 efoldings before the end of inflation, and thus includes the red curve) shows the result of evolving the equations that follow from the action after the axion has been integrated out, Eqn. (\ref{['eqn:actionGF']}), where $\{\tilde{g}, \kappa\} = \{2.5\times10^{-3}, 1.73\times 10^{14}\}$. In the inset panel we show in more detailed the post-inflationary region. In the right hand panel we show the full range of the axion as Chromo-Natural inflation proceeds. In blue we show the region that corresponds to the gaugeflation regime, which for these parameters is occurring for 60 efoldings. In the inset panels we show the region of the evolution of the axion where the two theories overlap.