Exacerbating the cosmological constant problem with interacting dark energy
M. C. David Marsh
TL;DR
This paper analyzes how the cosmological constant problem (c.c.p.) is affected by models with varying fundamental parameters, focusing on both cosmological variations of the fine-structure constant $\alpha$ and multi-field interacting dark energy scenarios. It shows that even modest variations of $\alpha$ introduce additional fine-tuning into the vacuum energy, quantified by $\mathfrak{f}_{\rm tot}=\mathfrak{f}_{\Lambda}\,\mathfrak{f}_{\delta \alpha}$, and provides numerical estimates demonstrating substantial amplification of the c.c.p. Yet these effects remain below the large flux-vacua counts $N_{\rm vac} \sim {\cal O}(10^{272{,}000})$ in simple cases. The authors then generalize to a class of multi-field models where dark-matter masses depend on dark-energy fields, deriving a multi-field fine-tuning expression $f_{\rm tot}=f_{\Lambda} f_{\delta m}$ that grows rapidly with the number of varying masses and the domain dimensionality $p$, showing that even modest multi-field variations can yield astronomically large fine-tuning, e.g. $f_{\rm tot} \sim 10^{10^{6}}$ for $p=3$ and three masses and even larger for $p=4$. They discuss observational prospects, highlighting very weak dark-matter-photon couplings that would produce decays $\phi_i\to \gamma\gamma$ with line energies $E_i(t,\mathbf{x})=m_i(\chi_{\alpha})/2$, which future gamma-ray observatories could detect, potentially mapping a 3D mass-parameter domain and thus testing multi-field scenarios. The paper concludes that if such models are realized in nature, they undermine anthropic solutions to the c.c.p. in finite-vacua theories and offer a concrete avenue for falsifying aspects of the string-theory flux landscape, unless a mechanism (e.g., supersymmetry) provides cancellations to restore naturalness.
Abstract
Future cosmological surveys will probe the expansion history of the universe and constrain phenomenological models of dark energy. Such models do not address the fine-tuning problem of the vacuum energy, i.e. the cosmological constant problem (c.c.p.), but can make it spectacularly worse. We show that this is the case for 'interacting dark energy' models in which the masses of the dark matter states depend on the dark energy sector. If realised in nature, these models have far-reaching implications for proposed solutions to the c.c.p. that require the number of vacua to exceed the fine-tuning of the vacuum energy density. We show that current estimates of the number of flux vacua in string theory, $N_{\rm vac} \sim {\cal O}(10^{272,000})$, is far too small to realise certain simple models of interacting dark energy \emph{and} solve the cosmological constant problem anthropically. These models admit distinctive observational signatures that can be targeted by future gamma-ray observatories, hence making it possible to observationally rule out the anthropic solution to the cosmological constant problem in theories with a finite number of vacua.