Quintessence and the Higgs Portal in the Carroll limit

A cosmological model based on two scalar fields is proposed. The first of these, $\varphi$, has mass $\mu$, while the second, $\chi$, is massless. The pair are coupled through a ``Higgs portal''. First, we show how the model reproduces the Friedmann equations if the square of the mass of the $\varphi$ field is proportional to the cosmological constant and $\chi$ represents the quintessence field. Quantum corrections break the conformal symmetry, and the $\chi$ field acquires a mass equal to $\sqrt{3g\Lambda}$. The perturbative approach with $g\ll 1$ is consistent with the bounds for $m_\chi$; moreover, by using dimensional analysis, we estimate $m_\chi \ll H_0\approx 10^{-33}$ eV, which is in accordance with what is expected in the quintessence scenario. The acceleration of the universe is proportional to $\chi^2$, we conclude that for very long times, the solution of the equation of motion approaches $\langle \chi\rangle \sim {m_\chi}/{{\sqrt\lambda}}$ and the universe continues to accelerate, with a constant acceleration.