Constraints on phenomenological amplitudes of CMB anisotropy from multiple datasets

Abstract

CMB anisotropies encode crucial information about the early Universe and fundamental cosmology. Although the standard

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

$$A_\textrm{new}$$ 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

$$\Lambda $$ Λ

CDM

$$+A_\textrm{new}$$ + A new

models with two data combinations – Planck PR3 low-

$$\ell $$ ℓ

+Planck PR4 high-

$$\ell $$ ℓ

+Planck PR4 lensing+DESI+PantheonPlus (PDP) and Planck PR3 low-

$$\ell $$ ℓ

+Planck-cut PR3 high-

$$\ell $$ ℓ

+ACT-cut+P-ACTLenslike+DESI+PantheonPlus (PADP). In the

$$\Lambda $$ Λ

CDM+

$$A_\mathrm{{L}}$$ A L

model, we get

$$A_\mathrm{{L}}=1.0498_{-0.0281}^{+0.0278}$$ A L = 1 . 0498 - 0.0281 + 0.0278

from PDP and

$$A_\mathrm{{L}}=1.0740\pm 0.0273$$ A L = 1.0740 ± 0.0273

from PADP, which implies 1.77

$$\sigma $$ σ

and 2.71

$$\sigma $$ σ

deviation from the

$$\Lambda $$ Λ

CDM model; values of

$$A_\mathrm{{SW}}$$ A SW

show 1.13

$$\sigma $$ σ

and 0.59

$$\sigma $$ σ

deviations to 1;

$$A_\mathrm{{lISW}}$$ A lISW

is poorly constrained because the lISW effect has negligible influence at

$$\ell \ge $$ ℓ ≥

30; others are consistent with the

$$\Lambda $$ Λ

CDM model. The deviation of

$$A_\mathrm{{L}}$$ 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-

$$\ell $$ ℓ

data strengthens the

$$A_\textrm{Pol}$$ A Pol

uncertainty by approximately 35

$$\%$$ %

, highlighting the importance of ground-based high-

$$\ell $$ ℓ

observations for future CMB analyses. Moreover, no noticeable improvement on the Hubble tension is found within these one-parameter extended scenarios. For the

$$\sigma _8$$ σ 8

tension, the

$$\Lambda \text {CDM}+A_\mathrm{{L}}$$ Λ CDM + A L

model provides only a mild degree of alleviation, though our posterior results become statistically compatible with DES-Y6.