String or M theory axion as a quintessence

TL;DR

The paper explores quintessence as a string/M-theory axion within 4D ${\cal N}=1$ supergravity, showing that achieving a dark-energy scale $V_Q$ as small as $(3\times10^{-3}\ { m eV})^4$ requires extreme $Q$-invariance of $K$, $W$, and $f_a$ to suppress non-derivative couplings. It identifies heterotic ${\rm M}$-theory or Type I string axions with large modulus VEVs ${\rm Re}(Z)\approx 32$ as plausible quintessence candidates, with the potential generated by membrane or D-brane instantons: $V_Q \sim e^{-2\pi \langle {\rm Re}(Z)\rangle} m_{3/2}^2 M_{\rm Pl}^2 \cos[2\pi {\rm Im}(Z)]$, and connects this to a near-GUT scale ${M_{\rm GUT}}$ when $\alpha_{GUT}\approx 1/25$. A major challenge is that the second slow-roll condition is violated, requiring the field to sit near the top of its potential today and implying severe initial-condition fine-tuning; the authors propose that nonperturbative enhancements to the Kähler metric or a late-time modular CP-invariant inflation phase could alleviate this. Overall, the work ties the dark-energy scale to high-energy modulus dynamics and unification scales, offering a concrete axion-based mechanism with distinctive implications for early-universe inflation and gauge coupling unification.

Abstract

A slow-rolling scalar field ($Q\equiv$ Quintessence) with potential energy $V_Q\sim (3\times 10^{-3} {\rm eV})^4$ has been proposed as the origin of accelerating universe at present. We investigate the effective potential of $Q$ in the framework of supergravity model including the quantum corrections induced by generic (nonrenormalizable) couplings of $Q$ to the gauge and charged matter multiplets. It is argued that the Kähler potential, superpotential and gauge kinetic functions of the underlying supergravity model are required to be invariant under the variation of $Q$ with an extremely fine accuracy in order to provide a working quintessence potential. Applying these results for string or $M$-theory, we point out that the heterotic $M$-theory or Type I string axion can be a plausible candidate for quintessence if (i) it does not couple to the instanton number of gauge interactions not weaker than those of the standard model and (ii) the modulus partner ${\rm Re}(Z)$ of the periodic quintessence axion ${\rm Im}(Z)\equiv {\rm Im}(Z)+1$ has a large VEV: ${\rm Re}(Z)\sim \frac{1}{2π}\ln(m_{3/2}^2 M_{Planck}^2/V_Q)$. It is stressed that such a large ${\rm Re}(Z)$ gives the gauge unification scale at around the phenomenologically favored value $3\times 10^{16}$ GeV. To provide an accelerating universe, the quintessence axion should be at near the top of its effective potential at present, which requires a severe fine tuning of the initial condition of $Q$ and $\dot{Q}$ in the early universe. We discuss a late time inflation scenario based on the modular and CP invariance of the moduli effective potential, yielding the required initial condition in a natural manner if the Kähler metric of the quintessence axion superfield receives a sizable nonperturbative contribution.

Figures (3)

• Figure 1: Two loop supergraph inducing the quadratically-divergent potential energy of $Y_{\alpha\beta\gamma}$.
• Figure 2: Quartically-divergent two loop supergraph for the potential energy of $H_{\alpha\beta}$ and $X_{\alpha\beta\bar{\gamma}}$.
• Figure 3: Three loop supergraph for the potential energy of $\Gamma_{\alpha\beta\gamma\delta}$ and $F_{a\alpha\beta}.$ For $F_{a\alpha\beta}$, two lines denote the gauge multiplets while the others are the charged matter multiplets.