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Multiprobe constraints on early and late time dark energy

Alexander Reeves, Simone Ferraro, Andrina Nicola, Alexandre Refregier

TL;DR

This work investigates whether ΛCDM needs modification by combining CMB data (Planck PR4 and ACT DR6), DESI DR2 BAO, Pantheon+ SNe, and a novel $5\times2$pt large-scale structure data vector (ACT DR6 lensing, DESI LS galaxies, Planck ISW). It jointly samples ΛCDM and two extensions—early dark energy (EDE) and dynamical dark energy (DDE with CPL w(a))—to address tensions between CMB and BAO, and to study impacts on $S_8$, $H_0$, and neutrino masses $M_\nu$. The analysis finds a mild but notable preference for the extended models when the $5\times2$pt data are included: DDE yields stronger improvements (up to $\Delta\chi^2\approx14$; $\sim3\sigma$) and relaxes neutrino mass bounds to $M_\nu\lesssim0.17$ eV, while EDE raises $H_0$ toward the SH0ES value (up to $H_0\approx70.5$ km s$^{-1}$ Mpc$^{-1}$ with a $\sim1.2$ GeV precision) but does not fully resolve all tensions. Pantheon+ and SH0ES priors shift the balance, reducing the DE deviations in some cases and strengthening EDE’s fit when $H_0$ priors are included. Overall, both DDE and EDE remain viable within current uncertainties, illustrating the power and necessity of multiprobe, high-precision analyses to constrain early- and late-time physics.

Abstract

We perform a multiprobe analysis combining cosmic microwave background (CMB) data from Planck and the Atacama Cosmology Telescope (ACT), ACT CMB lensing, and large-scale structure (LSS) measurements from the Dark Energy Spectroscopic Instrument (DESI), including DESI Legacy Imaging Survey (LS) galaxies and baryon acoustic oscillations (BAOs). We present the first $5\times2$pt analysis of ACT DR6 lensing, DESI LS, and Planck ISW. Within $Λ$CDM, this yields $S_8 = σ_8(Ω_m/0.3)^{0.5} = 0.819 \pm 0.016$, in good agreement with primary CMB inferences and provides a sound-horizon-free Hubble constant constraint of $H_0 = 70.0 \pm 4.4$ km s$^{-1}$ Mpc$^{-1}$. Then, combining with CMB primary and BAO, we reconfirm a CMB-BAO discrepancy in the $Ω_m$-$\frac{D_v}{r_d}$ plane, which is heightened when combining BAO with the $5\times2$pt data vector. We explore two dark-energy extensions that may reconcile this: an early-time modification, early dark energy (EDE), and late-time dynamical dark energy (DDE) parameterized by $w_0w_a$. For CMB primary+BAO+$5\times2$pt, we find a $3.3σ$ preference for DDE over $Λ$CDM, while EDE is modestly favoured at $2.3σ$. The models address different shortcomings of $Λ$CDM: DDE relaxes the neutrino mass bound ($M_ν<0.17$eV vs. $<0.050$eV under $Λ$CDM), making it compatible with neutrino oscillation measurements, while EDE raises the Hubble constant to $H_0=70.5\pm1.2\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, easing the discrepancy with SH0ES. However, neither model resolves both issues simultaneously. Our analysis indicates that both DDE and EDE remain viable extensions of $Λ$CDM within current uncertainties and demonstrates the capacity of combined probes to place increasingly stringent constraints on cosmological parameters.

Multiprobe constraints on early and late time dark energy

TL;DR

This work investigates whether ΛCDM needs modification by combining CMB data (Planck PR4 and ACT DR6), DESI DR2 BAO, Pantheon+ SNe, and a novel pt large-scale structure data vector (ACT DR6 lensing, DESI LS galaxies, Planck ISW). It jointly samples ΛCDM and two extensions—early dark energy (EDE) and dynamical dark energy (DDE with CPL w(a))—to address tensions between CMB and BAO, and to study impacts on , , and neutrino masses . The analysis finds a mild but notable preference for the extended models when the pt data are included: DDE yields stronger improvements (up to ; ) and relaxes neutrino mass bounds to eV, while EDE raises toward the SH0ES value (up to km s Mpc with a GeV precision) but does not fully resolve all tensions. Pantheon+ and SH0ES priors shift the balance, reducing the DE deviations in some cases and strengthening EDE’s fit when priors are included. Overall, both DDE and EDE remain viable within current uncertainties, illustrating the power and necessity of multiprobe, high-precision analyses to constrain early- and late-time physics.

Abstract

We perform a multiprobe analysis combining cosmic microwave background (CMB) data from Planck and the Atacama Cosmology Telescope (ACT), ACT CMB lensing, and large-scale structure (LSS) measurements from the Dark Energy Spectroscopic Instrument (DESI), including DESI Legacy Imaging Survey (LS) galaxies and baryon acoustic oscillations (BAOs). We present the first pt analysis of ACT DR6 lensing, DESI LS, and Planck ISW. Within CDM, this yields , in good agreement with primary CMB inferences and provides a sound-horizon-free Hubble constant constraint of km s Mpc. Then, combining with CMB primary and BAO, we reconfirm a CMB-BAO discrepancy in the - plane, which is heightened when combining BAO with the pt data vector. We explore two dark-energy extensions that may reconcile this: an early-time modification, early dark energy (EDE), and late-time dynamical dark energy (DDE) parameterized by . For CMB primary+BAO+pt, we find a preference for DDE over CDM, while EDE is modestly favoured at . The models address different shortcomings of CDM: DDE relaxes the neutrino mass bound (eV vs. eV under CDM), making it compatible with neutrino oscillation measurements, while EDE raises the Hubble constant to , easing the discrepancy with SH0ES. However, neither model resolves both issues simultaneously. Our analysis indicates that both DDE and EDE remain viable extensions of CDM within current uncertainties and demonstrates the capacity of combined probes to place increasingly stringent constraints on cosmological parameters.

Paper Structure

This paper contains 40 sections, 20 equations, 15 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Datasets
  3. DESI Legacy Imaging Survey
  4. ACT DR6 CMB Primary and Lensing
  5. Planck Primary CMB Anisotropies
  6. DESI DR2 Baryon Acoustic Oscillations
  7. Pantheon + Type Ia Supernovae
  8. Modeling, data vector, covariance, inference pipeline
  9. Modeling
  10. Theoretical predictions
  11. Scale cuts
  12. Neural-network emulators
  13. Data vector
  14. Mask deconvolution
  15. Measuring the data vector
  16. ...and 25 more sections

Figures (15)

  • Figure 1: The measured $5\times2$pt data vector with corresponding simulation-based error bars. We show also the best-fit prediction for these spectra under $\Lambda$CDM.
  • Figure 2: Contours for $\Lambda \mathrm{CDM}$ model with LSS data.Green contours: $5\times2$pt refers to the combination of ACT DR6 lensing, LS LRGs clustering and Planck ISW. Blue contours: same $5\times2$pt combination as before with added DESI DR2 BAO data. Note for the constraints shown here we fix $n_s=0.9649$, and $\omega_b = 0.02236$.
  • Figure 3: Sound horizon free $H_0$ measurements. The $5\times2$pt+SNe contour combines the Pantheon+ SNe dataset with our LSS data combination. A Gaussian prior is placed on the spectral tilt and $\omega_b$ is varied in a flat uniform prior as described in the text.
  • Figure 4: Posterior constraints in extended dark–energy models. Shown are posteriors for DDE and EDE from CMB, BAO, and LSS combinations. Vertical shaded bands show local $H_0$ constraints, the latest from CCHP ($H_0 = 70.4\pm1.9\,{\rm km\,s^{-1}\,Mpc^{-1}}$) Freedman:2024eph and SH0ES ($H_0 = 73.04\pm1.04\,{\rm km\,s^{-1}\,Mpc^{-1}}$) Riess:2021jrx. Dashed lines at $(w_0,w_a)=(-1,0)$ indicate the $\Lambda$CDM cosmological constant limit.
  • Figure 5: Constraints in the $\Omega_m$--$\frac{D_v}{r_d}$ plane for different individual datasets in each of the three models analysed in this work. The ACT DR6 constraints here are without lensing auto-correlation data which is instead included in the $5\times2$ data combination.
  • ...and 10 more figures