Constraints on phenomenological amplitudes of CMB anisotropy from multiple datasets
- 1Shandong Normal University
Abstract
CMB anisotropies encode crucial information about the early Universe and fundamental cosmology. Although the standard Λ Λ CDM model provides a successful description of cosmic evolution, persistent cosmological tensions and subtle small-scale anomalies still challenge its consistency. In this paper, we investigate six phenomenological amplitude parameters Anew A 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 Λ Λ CDM +Anew + A new models with two data combinations – Planck PR3 low- ℓ ℓ +Planck PR4 high- ℓ ℓ +Planck PR4 lensing+DESI+PantheonPlus (PDP) and Planck PR3 low- ℓ ℓ +Planck-cut PR3 high- ℓ ℓ +ACT-cut+P-ACTLenslike+DESI+PantheonPlus (PADP). In the Λ Λ CDM+ AL A L model, we get AL=1.0498−0.0281+0.0278 A L = 1 . 0498 - 0.0281 + 0.0278 from PDP and AL=1.0740± 0.0273 A L = 1.0740 ± 0.0273 from PADP, which implies 1.77 σ σ and 2.71 σ σ deviation from the Λ Λ CDM model; values of ASW A SW show 1.13 σ σ and 0.59 σ σ deviations to 1; AlISW A lISW is poorly constrained because the lISW effect has negligible influence at ℓ ≥ ℓ ≥ 30; others are consistent with the Λ Λ CDM model. The deviation of AL A L is to a large extent driven by DESI DR2 which reduces the error-bars significantly and moving its mean value higher. The lensing anomaly decreases when including CMB lensing. ACT DR6 high- ℓ ℓ data strengthens the APol A Pol uncertainty by approximately 35 % % , highlighting the importance of ground-based high- ℓ ℓ observations for future CMB analyses. Moreover, no noticeable improvement on the Hubble tension is found within these one-parameter extended scenarios. For the σ 8 σ 8 tension, the Λ CDM+AL Λ CDM + A L model provides only a mild degree of alleviation, though our posterior results become statistically compatible with DES-Y6.
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BibTeX
@article{han2026constraints,
title = {{Constraints on phenomenological amplitudes of CMB anisotropy from multiple datasets}},
author = {Yang Han and Lu Chen and Guo-Hao Li and Pei-Yuan Xu},
journal = {The European Physical Journal C},
year = {2026},
month = oct,
doi = {10.1140/epjc/s10052-026-16506-1},
url = {https://link.springer.com/article/10.1140/epjc/s10052-026-16506-1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Constraints on phenomenological amplitudes of CMB anisotropy from multiple datasets
AU - Yang Han
AU - Lu Chen
AU - Guo-Hao Li
AU - Pei-Yuan Xu
PY - 2026
DA - 2026/10/27
JO - The European Physical Journal C
DO - 10.1140/epjc/s10052-026-16506-1
UR - https://link.springer.com/article/10.1140/epjc/s10052-026-16506-1
AB - CMB anisotropies encode crucial information about the early Universe and fundamental cosmology. Although the standard Λ Λ CDM model provides a successful description of cosmic evolution, persistent cosmological tensions and subtle small-scale anomalies still challenge its consistency. In this paper, we investigate six phenomenological amplitude parameters A_new A 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 Λ Λ CDM +A_new + A new models with two data combinations – Planck PR3 low- ℓ ℓ +Planck PR4 high- ℓ ℓ +Planck PR4 lensing+DESI+PantheonPlus (PDP) and Planck PR3 low- ℓ ℓ +Planck-cut PR3 high- ℓ ℓ +ACT-cut+P-ACTLenslike+DESI+PantheonPlus (PADP). In the Λ Λ CDM+ A_L A L model, we get A_L=1.0498_−0.0281^+0.0278 A L = 1 . 0498 - 0.0281 + 0.0278 from PDP and A_L=1.0740± 0.0273 A L = 1.0740 ± 0.0273 from PADP, which implies 1.77 σ σ and 2.71 σ σ deviation from the Λ Λ CDM model; values of A_SW A SW show 1.13 σ σ and 0.59 σ σ deviations to 1; A_lISW A lISW is poorly constrained because the lISW effect has negligible influence at ℓ ≥ ℓ ≥ 30; others are consistent with the Λ Λ CDM model. The deviation of A_L A L is to a large extent driven by DESI DR2 which reduces the error-bars significantly and moving its mean value higher. The lensing anomaly decreases when including CMB lensing. ACT DR6 high- ℓ ℓ data strengthens the A_Pol A Pol uncertainty by approximately 35 % % , highlighting the importance of ground-based high- ℓ ℓ observations for future CMB analyses. Moreover, no noticeable improvement on the Hubble tension is found within these one-parameter extended scenarios. For the σ _8 σ 8 tension, the Λ CDM+A_L Λ CDM + A L model provides only a mild degree of alleviation, though our posterior results become statistically compatible with DES-Y6.
SN - 1434-6052
SN - 1434-6044
ER -