$H_0$ tension and the String Swampland

TL;DR

The paper confronts the $H_0$ tension through swampland-inspired cosmology by embedding the Agrawal-Obied-Vafa fading dark matter scenario into a six-dimensional Salam-Sezgin supergravity compactification on $M_4\times S^2$ with a monopole. The resulting 4D theory contains moduli $X$ and $Y$ with an exponential quintessence-type potential in $Y$ and a $Y$-dependent mass for $X$, yielding a tower of light states in the sense of the swampland distance conjecture and a CDM component sourced by $X$. Numerical fits show fading dark matter can raise the inferred $H_0$ toward local measurements (e.g., $h_0\approx0.69$ for certain parameter choices) but does not fully resolve the discrepancy, and outcomes depend on the late-time equation of state $w_{Y,0}$ and the fraction $ ho_X$ of CDM. The paper also discusses stringy embeddings, extra relativistic species, and future cosmological probes that could test the viability of this swampland-motivated framework, highlighting both potential alignment with data and current constraints from $\Delta N_{\rm eff}$.

Abstract

[Abridged] We realize the Agrawal-Obied-Vafa (AOV) swampland proposal of fading dark matter by the model of Salam-Sezgin and its string realization of Cvetic-Gibbons-Pope. The model describes a compactification of 6-dimensional supergravity with a monopole background on a 2-sphere. In 4 dimensions, there are 2 scalar fields, $X$ and $Y $, and the effective potential in the Einstein frame is an exponential with respect to $Y$ times a quadratic polynomial in the field $e^{-X}$. When making the volume of the 2-sphere large, namely for large values of $Y$, there appears a tower of states, which according to the infinite distance swampland conjecture becomes exponentially massless. If the standard model fields are confined on Neveu-Schwarz 5-branes the 6-dimensional gauge couplings are independent of the string dilaton in the string frame, and upon compactification to 4 dimensions the 4-dimensional gauge couplings depend on $X$ (rather than the dilaton $Y$) which is fixed at the minimum of the potential. This avoids direct couplings of the dilaton to matter suppressing extra forces competing with gravity. We show that this set up has the salient features of the AOV models, and ergo can potentially ameliorate the tension between local distance ladder and cosmic microwave background estimates of the Hubble constant $H_0$. Although the AOV proposal does not fully resolve the tension in $H_0$ measurements, it provides a dynamical dark energy model of cosmology that satisfies the de Sitter swampland conjecture. We comment on a viable solution to overcome the tension between low- and high-redshift observations within the AOV background and discuss the implications for the swampland program.

Figures (8)

• Figure 1: Allowed region in the $(h_0,w_{Y,0})$ parameter space, in terms of the ratio of present energy densities for the $X$-field and the total CDM. The star indicates the preferred $h_0$ value in the AOV analysis Agrawal:2019dlm.
• Figure 2: Evolution of $Y(u)$ and $Y'(u)$, for $a=0.178$ (left) and $a=0$ (right).
• Figure 3: Evolution of the density parameters $\Omega_r$, $\Omega_*$, $\Omega_X$, and $\Omega_Y$. We have taken $a=0.178$ (left) and $a=0$ (right).
• Figure 4: Evolution of the equation-of-state parameter for dark energy $w_Y$, for $a=0.178$ (left) and $a=0$ (right).
• Figure 5: Evolution of the acceleration parameter $-q$, for $a=0.178$ (left) and $a=0$ (right), showing the existence of an accelerated phase that asymptotically approaches a constant velocity expansion in the future.