Early dark sector, the Hubble tension, and the swampland

We consider the interplay of the early dark energy (EDE) model, the swampland distance conjecture (SDC), and cosmological parameter tensions. EDE is a proposed resolution of the Hubble tension relying upon a near-Planckian scalar field excursion, while the SDC predicts an exponential sensitivity of masses of other fields to such an excursion, $m\propto e^{-c|\mathrm{\Delta }\varphi |/M_{\mathrm{pl}}}$ with $c\sim \mathcal{O}(1)$. Meanwhile, EDE is in tension with large-scale structure (LSS) data, due to shifts in the standard $\mathrm{\Lambda }$ cold dark matter parameters necessary to fit the cosmic microwave background. One might hope that a proper treatment of the model, e.g., accounting for the SDC, may ameliorate the tension with LSSs. Motivated by these considerations, we introduce the early dark sector (EDS) model, wherein the mass of dark matter is exponentially sensitive to super-Planckian field excursions of the EDE scalar. The EDS model exhibits new phenomenology in both the early and late Universe, the latter due to an EDE-mediated dark matter self-interaction, which manifests as an enhanced gravitational constant on small scales. This EDE-induced dark-matter-philic “fifth force,” while constrained to be small, remains active in the late Universe and is not screened in virialized halos. We find that the new interaction with dark matter partially resolves the LSS tension. However, the marginalized posteriors are nonetheless consistent with $f_{\mathrm{EDE}}=0$ at 95% CL once the Dark Energy Survey year 3 measurement of $S_8$ is included. We additionally study constraints on the model from Atacama Cosmology Telescope data and find a factor of 2 improvement on the error bar on the SDC parameter $c$, along with an increased preference for the EDE component. We discuss the implications of these constraints for the SDC and find the tightest observational constraints to date on a swampland parameter, suggesting that an EDE description of cosmological data is in tension with the SDC.

Figure 1

Fiducial example background evolution of the scalar field, the energy density fraction $f_{\mathrm{EDE}}$, and the dark matter mass $m_{\mathrm{DM}}(\varphi )$. The vertical lines indicate the location of $z_c$. The scalar field indeed undergoes a Planckian field excursion (up to an order-1 factor), leading to an $\approx 0.3\%$ change to $m_{\mathrm{DM}}$ around $z_c$. See Eq. (17) for parameters.

Figure 2

Planck 2018 data residuals relative to the EDS best-fit model to the baseline dataset. Models with $\mathrm{\Delta }c=\pm 0.02$ around the best fit $-0.005$ with all other parameters fixed to their values in Eqs. (17) and (18) are shown for comparison. The blue vertical lines indicate the positions of the acoustic peaks in the best-fit EDS model.

Figure 3

Time evolution of Weyl potential, in units of the initial comoving curvature perturbation, and the dark matter mass for $\mathrm{\Delta }c=-0.02$ with respect to the best-fit EDS model. All the other parameters are fixed to their values in Eq. (17) and (18). The dashed vertical lines indicate locations of $k{r}_s(a)=\pi$ for each $k$ mode with the same color, where $r_s$ is the comoving sound horizon. The shaded area indicates the epoch between $z_c$ and recombination.

Figure 4

Comparison between the Planck $TT$ data and both the global best-fit EDS model where $c=-0.005$ (black line) and the best model for the baseline dataset with $c=-0.025$ fixed ($c$- optimized, orange line). The other curves show the effect of varying the EDS parameters $c$, ${\theta }_i$, and $z_c$ from the former to the latter in the direction indicated by the $+$ and $-$ with the remaining parameters fixed to the global best-fit model.

Figure 5

Density growth of EDS best-fit model as $c$ varied, with fixed $H_0$ and all other parameters (except ${\theta }_s$) fixed to their values in Eqs. (17) and (18). The vertical line indicates the location of $z_c$. Here $k=0.2h{\mathrm{Mpc}}^{-1}$.

Figure 6

$S_8$ value as function of $c$, with fixed $H_0$ and all other parameters (except ${\theta }_s$) fixed to their values in Eqs. (17) and (18). The red dot indicates the best-fit model.

Figure 7

Matter power spectra of EDS best-fit model as $c$ varied, with fixed $H_0$ and all other parameters (except ${\theta }_s$) fixed to their values in Eqs. (17) and (18). The results are compared to the best-fit $\mathrm{\Lambda }\mathrm{CDM}$ model.

Figure 8

Interplay of the $H_0$ and $S_8$ tensions in the EDS, EDE, and $\mathrm{\Lambda }\mathrm{CDM}$ models (as labeled). The plot shows posterior distributions for the fit to the baseline dataset (CMB, CMB lensing, BAO, SNIa, and SH0ES). Shaded gray and pink bands denote the SH0ES measurement and the DES-Y3 $S_8$ constraint, respectively.

Figure 9

Enlarged set of posterior distributions for the fit to the baseline dataset (CMB, CMB lensing, BAO, SNIa, and SH0ES) for $\mathrm{\Lambda }\mathrm{CDM}$, EDE, and EDS.

Figure 10

The impact of $S_8$ data. The plot shows posterior distributions for the fit to the baseline dataset (CMB, CMB lensing, BAO, SNIa, and SH0ES) supplemented with DES-Y3 data, approximated by a prior on $S_8$, for $\mathrm{\Lambda }\mathrm{CDM}$, EDE, and EDS. Shaded gray and pink bands denote the 2019 SH0ES measurement and the DES-Y3 $S_8$ constraint, respectively.

Figure 11

Constraints including ACT data. The plot shows posterior distributions for the fit of the EDS model to the baseline dataset (CMB, CMB lensing BAO, SNIa, and SH0ES) with and without the addition of ACT primary CMB data. Shaded gray and pink bands denote the SH0ES measurement and the DES-Y3 $S_8$ constraint, respectively.

Figure 12

Early dark energy and the swampland conjectures. We show the posterior distributions of the field excursion, axion decay constant, and dark matter mass dependence, along with their correlation with $H_0$, in the fit to varying datasets. The swampland distance conjecture would suggest that $c=\mathcal{O}(1)>0$, while the data constrain $c<0.068$, 0.035, and 0.042 at 95% confidence, for the baseline dataset, the $\text{baseline}+\mathrm{DES}-\mathrm{Y}3$, and $\text{baseline}+\mathrm{ACT}$, respectively, and slightly prefer $c<0$.

Figure 13

Scalar field $\varphi$ evolution for $c=-0.025$ with fixed $H_0$ and all other parameters (except ${\theta }_s$) fixed to their values in Eqs. (17) and (18). The quasistatic estimation (b10) is also shown for comparison.

Figure 14

Enlarged set of posterior distributions for the fit to the baseline dataset (CMB, CMB lensing, BAO, SNIa, and SH0ES) supplemented with DES-Y3 data, approximated by a prior on $S_8$ for $\mathrm{\Lambda }\mathrm{CDM}$ and EDS.

Figure 15

Enlarged set of posterior distributions for the fit of the EDS to the baseline dataset (Planck CMB, CMB lensing, BAO, SN, and SH0ES) with and without the addition of ACT data. Shaded gray and pink bands denote the SH0ES measurement and the DES-Y3 $S_8$ constraint, respectively.