Constraints on the decay of dark matter to dark energy from weak lensing bispectrum tomography

TL;DR

This paper tackles the question of whether dark matter decaying into dark energy, parameterized by a constant rate $\Gamma$, can be constrained by weak-lensing bispectrum tomography. It develops a framework combining hyper-extended perturbation theory for nonlinear structure with tomographic weak-lensing projections, and performs a Fisher-matrix forecast for the DUNE (formerly DUNE) survey, incorporating Planck priors. The results show that weak-lensing bispectrum tomography can bound $\Gamma$ at the level $\Delta\Gamma \sim 0.13$, translating to a CDM lifetime $t_\Gamma > 7.7/H_0 \approx 75.3/h$ Gyr, with strong degeneracies against the DE EOS parameters $w_0$ and $w_a$. This approach highlights the potential of future lensing surveys to test interacting dark-fluid models and address the coincidence problem by linking growth, geometry, and background evolution in a single observable.

Abstract

We consider a phenomenological model for a coupling between the dark matter and dark energy fluids and investigate the sensitivity of a weak lensing measurement for constraining the size of this coupling term. Physically, the functional form of the coupling term in our model describes the decay of dark matter into dark energy. We present forecasts for tomographic measurements of the weak shear bispectrum for the DUNE experiment in a Fisher-matrix formalism, where we describe the nonlinearities in structure formation by hyper-extended perturbation theory. Physically, CDM decay tends to increase the growth rate of density perturbations due to higher values for the CDM density at early times, and amplifies the lensing signal because of stronger fluctuations in the gravitational potential. We focus on degeneracies between the dark energy equation of state properties and the CDM decay constant relevant for structure formation and weak lensing. A typical lower bound on the CDM decay time ~7.7/H_0 = 75.3 Gyr/h$ which could be provided by DUNE would imply that it would not possible to produce the dark energy content of the universe by CDM decay within the age of the Universe for a constant equation of state parameter of w close to -1.

Figures (12)

• Figure 1: The scaled Hubble function $\tilde{H}_0(a)=a^{3/2}H(a)/H_0$ (thick lines) and the derivative $\tilde{H}_1(a)=a^{5/2}\mathrm{d} H(a)/\mathrm{d} a/H_0$ (thin lines) in models with decaying CDM, in comparison to models with stable dark matter: $\Lambda$CDM (solid line), $\Lambda_\Gamma$CDM with $\Gamma=\frac{1}{3}$ (dashed line), $\phi$CDM (dash-dotted line), and $\phi_\Gamma$CDM with $\Gamma=\frac{1}{3}$ (dotted line).
• Figure 2: Growth function $D_+(a)$ for four dark energy models: $\Lambda$CDM (solid line), $\Lambda_\Gamma$CDM with $\Gamma=\frac{1}{3}$ (dashed line), $\phi$CDM (dash-dotted line), and $\phi_\Gamma$CDM with $\Gamma=\frac{1}{3}$ (dotted line). Additionally, the growth function $D_+(a)=a$ for SCDM is plotted (solid straight line).
• Figure 3: Lensing efficiency functions $W(\chi)/\chi$ for the four dark energy models: $\Lambda$CDM (solid line), $\Lambda_\Gamma$CDM with $\Gamma=\frac{1}{3}$ (dashed line), $\phi$CDM (dash-dotted line), and $\phi_\Gamma$CDM with $\Gamma=\frac{1}{3}$ (dotted line), without subdivision into tomography bins.
• Figure 4: Linear convergence power spectra $C_\kappa(\ell)$ for the four specified dark energy models: $\Lambda$CDM (solid line), $\Lambda_\Gamma$CDM with $\Gamma=\frac{1}{3}$ (dashed line), $\phi$CDM (dash-dotted line), and $\phi_\Gamma$CDM with $\Gamma=\frac{1}{3}$ (dotted line), without subdivision into tomography bins.
• Figure 5: Equilateral convergence bispectra $B_\kappa(\ell)$: $\Lambda$CDM (solid line), $\Lambda_\Gamma$CDM with $\Gamma=\frac{1}{3}$ (dashed line), $\phi$CDM (dash-dotted line), and $\phi_\Gamma$CDM with $\Gamma=\frac{1}{3}$ (dotted line), for the entire galaxy sample.