CFT driven cosmology and conformal higher spin fields

TL;DR

This paper explores how conformal higher spin fields influence cosmological initial conditions, potentially resolving hierarchy issues and connecting to inflation models like Starobinsky and Higgs, with implications for the energy scale of early universe physics.

Contribution

It demonstrates the role of conformal higher spin fields in setting initial conditions for inflation and establishes bounds on inflation scale based on their anomaly coefficients and polarizations.

Findings

CHS fields can resolve hierarchy problems in inflationary cosmology.

The inflation scale is bounded by the properties of CHS fields, notably $eta$ and $ extbf{N}$.

Predictions align with the energy scale of Starobinsky and Higgs inflation models.

Abstract

Conformal higher spin (CHS) field theory, which is a solid part of recent advanced checks of AdS/CFT correspondence, finds applications in cosmology. Hidden sector of weakly interacting CHS fields suggests a resolution of the hierarchy problem in the model of initial conditions for inflationary cosmology driven by a conformal field theory. These initial conditions are set by thermal garland type cosmological instantons in the sub-planckian energy range for the model of CHS fields with a large positive coefficient $\beta$ of the Gauss-Bonnet term in their total conformal anomaly and a large number of their polarizations $\mathbb{N}$. The upper bound of this range $M_P/\sqrt\beta$ is shown to be much lower than the gravitational cutoff $M_P/\sqrt\mathbb{N}$ which is defined by the requirement of smallness of the perturbatively nonrenormalizable graviton loop contributions. In this way we justify the approximation scheme in which the nonrenormalizable graviton sector is subject to effective field theory under this cutoff, whereas the renormalizable sector of multiple CHS fields is treated beyond perturbation theory and dynamically generates the bound on the inflation scale of the CFT cosmology $M_P/\sqrt\beta\ll M_P/\sqrt\mathbb{N}$. This confirms recent predictions for the origin of the Starobinsky $R^2$ and Higgs inflation models from the CHS cosmology, which occurs at the energy scale three or four orders of magnitude below the gravitational cutoff, $\sqrt{\mathbb{N}/\beta}\sim 10^{-3}\div 10^{-4}$. We also consider cosmological models dominated by fermionic CHS fields with a negative $\beta$ and anomaly free models of infinite towers of CHS fields with $\beta=0$ and briefly discuss the status of unitarity in CHS models.