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Similar

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2011
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F. Bezrukov, A. Magnin, M. Shaposhnikov, and S. Sibiryakov, “Higgs inflation: consistency and generalisations,” JHEP
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S. Ferrara, R. Kallosh, A. Linde, A. Marrani, and A. Van Proeyen, “Superconformal Symmetry, NMSSM, and Inflation,” Phys. Rev
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Then

Y. Hamada, H. Kawai, K.-y. Oda, and S. C. Park, “Higgs Inflation is Still Alive after the Results from BICEP2,” Phys. Rev. Lett
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F. Bezrukov, J. Rubio, and M. Shaposhnikov, “Living beyond the edge: Higgs inflation and vacuum metastability,” Phys. Rev
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2017

Unitarity and predictiveness in new Higgs inflation

Fumagalli, Jacopo, Mooij, Sander, Postma, Marieke

Understand

In new Higgs inflation the Higgs kinetic terms are non-minimally coupled to the Einstein tensor, allowing the Higgs field to play the role of the inflaton.

The new interaction is non-renormalizable, and the model only describes physics below some cutoff scale.
Even if the unknown UV physics does not affect the tree level inflaton potential significantly, it may still enter at loop level and modify the running of the Standard Model (SM) parameters.
This is analogous to what happens in the original model for Higgs inflation.