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

TL;DR

This paper proposes a cosmological model based on the NJL framework near the IR fixed point of Hořava-Lifshitz gravity, demonstrating compatibility with Planck data and linking inflation to IR and UV fixed points.

Contribution

It introduces a novel inflationary scenario using composite NJL inflaton near the IR fixed point of HL gravity, connecting inflationary predictions with fixed points of the theory.

Findings

Model predictions align with Planck 2015 data.

IR fixed point corresponds to GUT scale, UV fixed point to Planck scale.

Scalar NJL channel acts as a composite inflaton.

Abstract

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.