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We investigate the gauged Nambu-Jona-Lasinio model in curved spacetime at the large 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.

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