The fine tuning of the cosmological constant in a conformal model

TL;DR

This paper explores a conformal scalar field model that predicts a zero cosmological constant and discusses fine tuning issues, proposing solutions involving super-Planckian fields or a strongly coupled hidden sector.

Contribution

It introduces a conformal model with two scalar fields that naturally predicts zero cosmological constant and addresses fine tuning problems with novel solutions.

Findings

The model predicts exactly zero cosmological constant.

Fine tuning issues can be resolved with super-Planckian scalar fields.

A strongly coupled hidden sector can dynamically break conformal invariance.

Abstract

We consider a conformal model involving two real scalar fields in which the conformal symmetry is broken by a soft mechanism and is not anomalous. One of these scalar fields is representative of the standard model Higgs. The model predicts exactly zero cosmological constant. In the simplest version of the model, some of the couplings need to be fine tuned to very small values. We formulate the problem of fine tuning of these couplings. We argue that the problem arises since we require a soft mechanism to break conformal symmetry. The symmetry breaking is possible only if the scalar fields do not evolve significantly over the time scale of the Universe. We present two solutions to this fine tuning problem. We argue that the problem is solved if the classical value of one of the scalar fields is super-Planckian, i.e. takes a value much larger than the Planck mass. The second solution involves introduction of a strongly coupled hidden sector that we call hypercolor. In this case the conformal invariance is broken dynamically and triggers the breakdown of the electroweak symmetry. We argue that our analysis applies also to the case of the standard model Higgs multiplet.