Composite Nambu–Jona-Lasinio inflation near infrared fixed point of the Hořava-Lifshitz theory

In this work, we first propose a cosmological scenario inherently based on the effective Nambu--Jona-Lasio (NJL) model near the infrared (IR) limit of the Ho\v{r}ava-Lifshitz (HL) theory. Having used the one-loop correction, we employ the NJL framework in the ultraviolet (UV) limit of the HL theory, with critical exponent $z=3$, to demonstrate in the IR limit that the symmetry of the potential at the critical coupling value is broken at $z=1$. We also derive the effective Higgs-like potential in the low energy regimes. Here the symmetry of the effective potential will be broken near $z=1$ at a certain value of the critical coupling. In our scenario, the scalar channel of the NJL model plays the role of a composite inflaton. We find that the Lorentz invariance (LI) appears at the IR regime of the HL theory and employ the standard inflationary (slow-roll) paradigm as a probe of physics at very high energy. We compute inflationary parameters and compare them with recent Planck 2015 data. Interestingly, we discover that the predictions of the model are in perfect agreement with the Planck analysis. Our salient feature is that we used inflation to quantify the IR and UV fixed points of the underlying theory. We discover that the IR fixed point of HL gravity is compatible with the grand unified energy scale; whilst the UV fixed point is the Planck energy scale.
Comment: v3: 15 pages, 2 figures, texts modified, references added, version accepted for publication by Physics Letters B