Dark Energy, the Swampland and the Equivalence Principle

TL;DR

This work investigates how dark energy can couple to dark matter in ways that remain compatible with swampland conjectures and current cosmological data. It analyzes both conformal and derivative (disformal) couplings, with a focus on a coupling function $C(\phi)$ that possesses a minimum at $\phi_*=1 M_Pl$, enabling a suppressed early coupling and a late-time onset of DM-DE interactions. The study shows that such a minimum allows an enhanced effective gravitational constant $G_{eff}$ today and a DE equation of state $w_DE$ close to, or slightly below, $-1$ without conflicting with CMB/LSS constraints, and it extends to disformal couplings in which the coupling is time- and density-dependent. The results motivate searching for equivalence-principle violations in the dark sector and monitoring the evolution of $w_DE(z)$ and $G_{eff}(z)$, especially on non-linear and intermediate scales, to test these swampland-inspired scenarios.

Abstract

It has recently been argued that string theory does not admit de Sitter vacua. This would imply that the current accelerated expansion of the universe is not driven by a cosmological constant (or vacuum energy) but by other means such as a quintessential scalar field. Such a scalar field is in general expected to couple to at least some matter species, such as dark matter. Cosmological observations already constrain such dark matter couplings strongly. We argue that there are a number of interesting scenarios to be explored, such as coupling functions which possess a minimum at finite field values. In these theories, the effective gravitational coupling between dark matter particles grows with time and are consistent with observations of the anisotropies in the cosmic microwave background radiation and large scale structures. We argue that such couplings might also help to alleviate the tension between the swampland conjectures and the properties of the quintessential potential. Observational signatures of violations of the equivalence principle in the dark sector are expected in the non-linear regime on intermediate or small scales.

Figures (6)

• Figure 1: Upper figure: Evolution of the equation of state of dark energy $w_{\rm DE}$, defined in Eq. (\ref{['weff']}), for models M1 ($\alpha = 3, \lambda = 0.5$) and M2 ($\alpha = 5, \lambda = 0.6$). Lower figure: The evolution of the effective gravitational constant, defined in Eq. (\ref{['effgrav']}), in both models.
• Figure 2:
• Figure 3: The CMB anisotropy power spectrum for models M1 and M2, compared to the $\Lambda$CDM model.
• Figure 4: Upper plot: The predictions for the linear matter power spectrum for different initial conditions for the scalar field. For both curves, we have chosen $\lambda = 0.5$ and $\alpha = 3$. Lower plot: Evolution of the effective gravitational constant $G_{\rm eff}$ for different initial conditions for the scalar field. The evolution of $G_{\rm eff}$ is essentially the same in both models for redshifts below $z=200$, but differs substantially at higher redshifts.
• Figure 5: The evolution of the inflaton field $\chi$ and the DE field $\phi$ during the first 10 e--folds during inflation, for the potential $U(\chi)$ given by eq. (\ref{['infexample']}). In this example, we have chosen $b=10$ and $U_0 = 10^{-5}M_{\rm Pl}^4$ for the parameter in the potential and $\alpha = 5$ in the coupling function. Inflation lasts more than 50 e--folds. The field $\phi$ is driven quickly to the minimum value $\phi_*$, whereas $\chi$ rolls down its potential.