Forecasts for interacting dark energy with time-dependent momentum exchange

TL;DR

This work investigates pure momentum-exchange interactions between dark energy and dark matter, parameterized by a time-dependent coupling $ξ(z)$, as a route to addressing the $S_8$ tension. It employs Fisher forecasting and MCMC analyses to forecast how well DESI-like, Stage IV surveys can constrain the coupling across redshift bins for both a constant equation of state $w=-0.9$ and a thawing $w(z)$ model, using five redshift bins and multiple tracers. The results show that, for a constant $w$, $ξ(z)$ can be well constrained in all bins, while thawing $w(z)$ reduces sensitivity at high redshift due to smaller $(1+w(z))$ values; leveraging the derived quantity $A(z)=ξ(z)(1+w(z))$ helps mitigate degeneracies with the equation of state. The findings highlight the potential of next-generation surveys to test momentum-exchange dark-sector models, offering a pathway to refining our understanding of structure growth and cosmological tensions, with the caveat that high-redshift constraints degrade under thawing dynamics. Overall, the work emphasizes the importance of time-dependent couplings and robust parameterizations (like $A(z)$) in disentangling dark-sector interactions from background expansion effects.

Abstract

Models of interacting dark energy and dark matter offer a possible solution to cosmological tensions. In this work, we examine a pure momentum-exchange model with a time-dependent coupling strength $ξ(z)$ that could help to alleviate the $S_8$ tension. We perform Fisher forecasting and MCMC analysis to constrain the coupling strength of this interaction for different redshift bins $0.0<z<2.1$, using the specifications of upcoming DESI-like surveys. For this analysis, we examine both a model with a constant equation of state $w=-0.9$, as well as a thawing dark energy model with an evolving $w(z)$. We show that, for a constant equation of state, $ξ(z)$ can be well constrained in all redshift bins. However, due to a weaker effect at early times, the constraints are significantly reduced at high redshifts in the case of a thawing $w(z)$ model.

Figures (9)

• Figure 1: The impact on $f\sigma_{8}$ from changing the coupling in each redshift bin. The error bars are derived from a DESI-like survey, and we show the impact when using the calculated $\xi_{\mathrm{low}}$ and $\xi_i$$3\sigma$ error values derived below. (See Table \ref{['tab:iii']}.) These figures used a constant equation of state $w = -0.9$.
• Figure 2: The dark energy equation of state, $w(z)$. We examine the interaction constraints for constant $w_0 = -0.9$ (blue dotted) and the CMP parametrisation motivated by thawing quintessence models (orange, dot-dashed). For comparison, we also plot the best fit $w_0$-$w_a$ model found by DESI using DESI+CMB+DESY5 SNe Ia data DESI:2025zgx ($w_0=-0.752\pm0.057$ and $w_a=-0.86^{+0.23}_{-0.20}$). This exhibits phantom behaviour at high redshift.
• Figure 3: Forecasted $1\sigma$ and $2\sigma$ contours of the $\xi_i$ parameters, when modelled with a constant $w_0=-0.9$. We include the marginalised Fisher matrix results (dashed) as well as the constrained Fisher (blue) and MontePython (purple) results when computed with a $\xi \ge 0$ prior. The constrained Fisher and the MontePython results are very similar.
• Figure 4: A PCA, where each mode is a linear combination of different parameters with different weighting. Here we show the eigenfunctions when $w_0=-0.9$ and is constant.
• Figure 5: Forecasted constraints on the $\xi_{\mathrm{low}}$, $\xi_{\mathrm{high}}$ and $w_0$ parameters, where the fiducial model has $w_0=-0.9$. We include the marginalised Fisher matrix results as well as the Fisher results when constrained with $\xi \ge 0$ and $w_0>-0.999$ priors. We see that $w_0 = -1$ is allowed within $1\sigma$; in this limit, the $\xi$ parameterisation is not adequate, and it is better to constrain $A = \xi(1+w_0)$.