On the validity of the continuity equation in a modified gravity framework with CMB, DES 3x2pt and tomographic ISW data

TL;DR

This work probes the conservation of the continuity equation at the perturbation level by introducing a phenomenological parameter $A_{ m c}$ in a modified gravity framework and jointly constraining it with $\\mu$ and $\\eta$ using a suite of cosmological probes. The authors consider constant and time-varying parametrizations for $A_{ m c}$ and perform Bayesian analyses with CMB (Planck) plus ISW and DES 3×2pt data, as well as DES-only combinations, implemented in MGCLASS II with MontePython. They find DES+ISW data alone are consistent with standard continuity, but Planck data induce a non-zero preference for $A_{ m c}$ (especially for the constant case, around $A_{ m c} \sim 0.15$ at >2$\\sigma$), with stronger tensions in the time-dependent scenario; correlations between $A_{ m c}$ and MG parameters $\\mu$, $\\eta$ are evident and affect interpretation. The results emphasize that violations of the continuity equation can mimic or compensate MG effects, so conclusions about GR deviations drawn from growth and lensing probes must account for possible non-conservation of the continuity equation.

Abstract

In this work we propose a phenomenological modification to the continuity equation at the linear perturbation level and test it using combinations of the CMB temperature, polarization and lensing potential angular spectrum, the ISW-galaxy cross power spectrum and the 3$\times$2pt lensing and galaxy clustering from DES survey. We investigate two parametrisations of this modification, both proportional to a new parameter $A_c$, which is assumed to be either constant in time, or proportional to the scale factor $a$, in order to be more relevant at late times. We find DES and ISW data to be consistent with the standard continuity equation when $A_c$ is constant, but 2--3$σ$ hints of a non-zero modification appear when Planck data is included. The model $A_c \propto a$ results in stronger tensions. We also test the effects of including the common extra parameters $μ$ and $η$ that modify the Poisson equation and Weyl potential. Although $A_c$, $μ$ and $η$ are correlated, we still find non-zero $A_c$ when Planck data is included or without Planck if $A_c \propto a$ and only either $η$ or $μ$ are allowed to vary. We conclude that violations of the continuity equation should be considered with care when testing additional deviations from general relativity.

Figures (5)

• Figure 1: 68% and 95% confidence contours for $\Omega_{\rm m}$, $h$, $A_{\rm ISW}$, $\sigma_8$, and $A_{\rm c}$ inferred using ISW cross correlation with galaxy surveys distributions, and 3$\times$2pt photometric lensing and galaxy correlations, and cross correlations from DES survey, with and without CMB constraints. We note that the inclusion of CMB $TTTEEE$+lensing results in non-zero constraints for $A_c$ above the 2$\sigma$ confidence-level. The prior ranges for the different parameters follow Table \ref{['tab:params']}.
• Figure 2: Same as Figure \ref{['fig:ANCalone']} but adding also the $\mu$ and $\eta$ modified gravity parameters and assuming $A_c$, $\mu$ and $\eta$ to be constant in time.
• Figure 3: Same as Figure \ref{['fig:cteprio']} but now allowing time-variations of $A_c$, $\mu$ and $\eta$.
• Figure 4: Same as Figure \ref{['fig:cteprio']} but now adding different combinations of CMB $C_{\ell}^{TT,TE,EE}$ and its lensing potential from Plk18.
• Figure 5: Same as Figure \ref{['fig:varprio']} but now adding different combinations of CMB $C_{\ell}^{TT,TE,EE}$ and its lensing potential from Plk18.