We prove the universality of predictions for linear perturbations from the entire class of models of inflation driven by a pseudoscalar field coupled to an SU(N) gauge boson, where SU(2) subgroups in the SU(N) crossed with the background spatial SO(3) spontaneously break into a single SO(3). The effect of which SU(2) subgroup in SU(N) acquires a vacuum expectation value through spontaneous symmetry breaking can be quantified by a single parameter λ, which always appears in combination with the gauge coupling constant g. In the linear perturbations, as well as the background system, the same dynamics and predictions as in the chromo-natural inflation hold for its SU(N) extension by replacing g→gλ. The latter class of models thereby draws the same prediction curve on the ns-r plane as the former at the tree level as long as gλ stays constant during inflation. We briefly discuss possible transitions from one value of λ to another during inflation and the observational prospects.
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