A new multiprobe analysis of modified gravity and evolving dark energy

TL;DR

This work tests dynamical dark energy by combining a CPL background $w(a)=w_0+w_a(1-a)$ with two perturbation frameworks: a fluid PPF approach and an EFTofDE description for Horndeski-type theories, focusing on the braiding and Planck-mass running parameters $c_B$ and $c_M$. The analysis unifies EFTofLSS full-shape information from BOSS with tomographic angular spectra $C_ell^{gg}$, $C_ell^{κg}$, $C_ell^{Tg}$ and $C_ell^{Tκ}$ from Planck and DESI, using beyond-Limber calculations via Swift$C_ell$. By progressively adding EFTBOSS, ISWL, and DESIcross, the paper demonstrates substantial tightening of the $\{w_0,w_a\}$ constraints (about 50% reduction) and strengthens the evidence for evolving dark energy to around $4\sigma$ when all probes are combined, while constraining EFTofDE parameters to values consistent with General Relativity at roughly $2\sigma$. The results show that cross-correlations between late-time gravity, lensing, and ISW signals are crucial for breaking degeneracies, and they remain robust to choices of BAO and SN data, underscoring the value of a fully multiprobe approach for testing gravity and dark energy. These findings have practical impact for future surveys (DESI, Euclid, LSST) by highlighting the enhanced constraining power from joint LSS and CMB analyses and guiding the modelling of DE perturbations.

Abstract

We study the $(w_0, \, w_a)$ parametrization of the dark energy (DE) equation of state, with and without the effective field theory of dark energy (EFTofDE) framework to describe the DE perturbations, parametrized here by the braiding parameter $α_B$ and the running of the Planck mass $α_M$. We combine the EFTofLSS full-shape analysis of the power spectrum and bispectrum of BOSS data with the tomographic angular power spectra $C_\ell^{gg}$, $C_\ell^{κg}$, $C_\ell^{Tg}$ and $C_\ell^{Tκ}$, where $g$, $κ$ and $T$ stand for the DESI luminous red galaxy map, Planck PR4 lensing map and Planck PR4 temperature map, respectively. To analyze these angular power spectra, we go beyond the Limber approximation, allowing us to include large-scales data in $C_\ell^{gg}$. The combination of all these probes with Planck PR4, DESI DR2 BAO and DES Y5 improves the constraint on the 2D posterior distribution of $\{w_0, \, w_a\}$ by $\sim 50 \%$ and increases the preference for evolving dark energy over $Λ$ from $3.8 σ$ to $4.6 σ$. When we remove BAO and supernovae data, we obtain a hint for evolving dark energy at $2.3 σ$. Regarding the EFTofDE parameters, we improve the constraints on $α_B$ and $α_M$ by $\sim 40 \%$ and $50 \%$ respectively, finding results compatible with general relativity at $\sim 2 σ$. We show that these constraints do not depend on the choice of the BAO and supernovae likelihoods.

Figures (12)

• Figure 1: The response of $\mu$ and $\Sigma$ to variations in $c_M$ and $c_B$ at redshifts $z = 1.0$, $0.5$, and $0.0$. The arrows indicate the gradient direction: $\mu$ is more sensitive to $c_M$ at high redshift and to $c_B$ at low redshift, while $\Sigma$ shows the opposite trend. The cosmology is fixed to the best-fit values of the "All" analysis obtained in Sec. \ref{['sec:res_all']}
• Figure 2: 2D posterior distributions of $\{w_0, \, w_a \}$ and $\{c_B, \, c_M \}$ reconstructed from all data combinations considered in this work, namely Baseline, Baseline + EFTBOSS, Baseline + ISWL, Baseline + DESIcross and the combination of all these datasets. The black dashed lines correspond to the $\Lambda$CDM limits, while the baseline analysis is shown in yellow dotted line.
• Figure 3: Constraints on $\{w_0, \, w_a, \, c_B, \, c_M \}$ for several CMB likelihood combinations, namely Hillipop (H) vs Camspec (C) for the high-$\ell$ TTTEEE likelihood, Lollipop (L) vs Simall (S) for the low-$\ell$ TT likelihood, and Planck PR4 (P) vs ACT DR6 (A) for the lensing likelihood. Note that for all the data combinations, we use the low-$\ell$ TT likelihood from Commander, together with DESI DR2 BAO and DES Y5. In the first two columns, we assume the CPL parametrization without EFTofDE, while in the last two columns we consider our EFTofDE configuration (with a CPL background). The black dashed lines represent the mean values of our baseline analysis.
• Figure 4: Left: Residuals of the monopole and quadrupole of the galaxy power spectrum for the CPL model with and without EFTofDE, normalized to the $\Lambda$CDM model (for the baseline + EFTBOSS analysis). We also show the impact of varying $c_B$ and $c_M$ on this observable, setting the other cosmological parameters to the best-fit. Note that we show here the predictions and the data for the low-$z$ NGC sample of BOSS. Right: Same for the bispectrum monopole for different triangle configurations.
• Figure 5: Residuals (with respect to $\Lambda$CDM) of the linear matter power spectrum, $C_\ell^{gg}$, $C_\ell^{\kappa g}$, $C_\ell^{Tg}$ and $C_\ell^{T \kappa}$ for several values of $c_B$ (left) and $c_M$ (right). The residuals are computed at $z=0.625$, corresponding to the effective redshift of the second redshift range of the DESIcross likelihood. All cosmological parameters are fixed to their best-fit values (reconstructed from the "All" analysis), while the solid green curves correspond to the best-fit values of $c_B$ and $c_M$. For the sake of clarity, we divide the error bars of $C_\ell^{\kappa g}$ and $C_\ell^{Tg}$ by $2$ (see Fig. \ref{['fig:namaster_cltg']} for a real representation of these data points).