  We investigate the gauged Nambu-Jona-Lasinio model in curved spacetime at the
large $N_c$ limit and in slow-roll approximation. The model can be described by
the renormalization group corrected gauge-Higgs-Yukawa theory with the
corresponding compositeness conditions. Evaluating the renormalization group
(RG) improved effective action, we show that such model can produce CMB
fluctuations and find inflationary parameters: spectral index,
tensor-to-scalar-ratio and running of the spectral index. We demonstrate that
the model can naturally satisfy the Planck 2015 data and maybe considered as an
alternative candidate for Higgs inflation.
