Constraints on Phenomenological Amplitudes of CMB Anisotropy with Multi-Datasets

TL;DR

This study constrains phenomenological amplitude parameters related to CMB anisotropies using multiple datasets, finding that only the lensing amplitude $A_{L}$ shows significant deviation from the standard model, with implications for future observations.

Contribution

It introduces constraints on six phenomenological parameters of CMB anisotropies using combined datasets, highlighting the significance of high-$ ext{ell}$ ground-based data for cosmological analysis.

Findings

Only $A_{L}$ is favored with deviations from $ ext{Lambda CDM}$.

High-$ ext{ell}$ ACT data strengthens $A_{L}$ preference and reduces $A_{Pol}$ uncertainty.

No significant improvement on Hubble and $ ext{sigma}_8$ tensions in extended models.

Abstract

Cosmic microwave background anisotropies encode crucial information about the early Universe and fundamental cosmological physics. Although the standard $\Lambda$CDM model provides a successful description of cosmic evolution, persistent cosmological tensions and subtle small-scale anomalies still challenge its internal consistency. In this paper, we investigate six phenomenological amplitude parameters $A_{\rm{new}}$ (new=L, SW, Dop, eISW, lISW, Pol) corresponding to the key effects related to CMB anisotropy: the Lensing, Sachs-Wolfe, Doppler, early Integrated Sachs-Wolfe, late Integrated Sachs-Wolfe, and Polarization effects, respectively. Using modified CAMB and Cobaya packages, we constrain the $\Lambda$CDM$+A_{\rm{new}}$ models with two data combinations: Planck+DESI+PantheonPlus (PDP) and Planck+ACT+DESI+PantheonPlus (PADP). Only the $\Lambda$CDM+$A_{\rm{L}}$ is favored by AIC, with $A_{\rm{L}}=1.0656_{-0.0303}^{+0.0304}$ from PDP and $A_{\rm{L}}=1.0795_{-0.0289}^{+0.0260}$ from PADP, which implies 2.16$\sigma$ and 3.06$\sigma$ deviation from the $\Lambda$CDM model; values of $A_{\rm{SW}}$ show 1.21$\sigma$ and 1.96$\sigma$ deviations to 1; $A_{\rm{lISW}}$ is poorly constrained because the lISW effect has negligible influence at $\ell \geq 30$; and others are consistent with the $\Lambda$CDM model. Moreover, no noticeable improvement on the Hubble and $\sigma_8$ tensions is found within these one-parameter extended scenarios. ACT DR6 high-$\ell$ data strengthens the $\Lambda$CDM$+A_{\rm{L}}$ preference over the $\Lambda$CDM model, and reduces $A_{\rm Pol}$ uncertainty by more than one order of magnitude, highlighting the importance of ground-based high-$\ell$ observations for future CMB analyses.