Power Suppression and Lensing Anomaly -- A phenomenological investigation

TL;DR

This work tests whether a suppressed primordial power at long wavelengths can mitigate the CMB lensing anomaly by using phenomenological extensions to the nearly scale-invariant spectrum, analyzed via Bayesian methods on Planck data (PR3 and PR4) with various likelihoods. It finds that data often prefer parameters that reduce power at low multipoles, and that stronger suppression correlates with a more consistent lensing amplitude $A_L$ with unity, though model selection via information criteria yields mixed preferences. The analysis shows suppression is most pronounced in the SA+α+β template, and that future missions like ECHO could decisively constrain or detect such suppression. Overall, simple low-$\ell$ power suppression templates provide a flexible framework to probe early-universe physics and its imprint on CMB lensing.

Abstract

Primordial power spectra with low power at long wavelengths can alleviate lensing anomaly. However the extent to which data favours such a primordial spectra is not clear. In this work, we investigate power suppression and related mitigation of lensing anomaly with the help of phenomenological models which are valid over scales of interest. We consider simple extensions to nearly scale invariant power spectra such as those which includes running and running of running of spectral index. We perform Bayesian analysis of these models, which are agnostic about power suppression, with Planck legacy data and show that data tend to choose parameters which leads to power suppression at low multipoles. We then investigate the connection between power suppression and alleviation of lensing anomaly and show that lensing anomaly is mitigated the most in models with maximum suppression of power at low multipoles. We also analyse the significance of these findings using information criteria. These results are further analyzed in the light of Planck Release 4 data using CamSpec, HiLLiPoP and LoLLiPoP likelihoods in which departure of lensing parameter from one is significantly reduced. Furthermore, we investigate the ability of near-ultimate future CMB missions such as ECHO to put tighter constraints on these models and to settle the issue. We conclude that we can make stronger conclusions about the presence of power suppression in the future by studying such simple phenomenological models.

Figures (10)

• Figure 1: The plots of $D_\ell^{TT}$ (left) and $C^{TT}(\theta)$ (right) corresponding to the standard model (solid lines) together with data obtained from Planck (black dots) Planck:2018nkj. To compute $D_\ell^{TT}$ generated in $\Lambda$CDM model, we worked with marginalised mean values of parameters obtained using Bayesian parameter estimation with PR3 data of temperature, polarisation and lensing obtained by Planck. Power spectrum in angular space $C^{TT}(\theta)$ is computed from $C_\ell^{TT}$ using equation (\ref{['eqn:Ctheta']}). The data for $C^{TT}(\theta)$ is derived from appropriately masked Planck temperature map (COM_CMB_IQU-smica_2048_R3.00_full.fits together with the common mask COM_Mask_CMB-common-Mask-Int_2048_R3.00.fits) using healpyGorski:2004byZonca:2019vzt. In particular, we downgrade the masked map to NSIDE$\,=\, 64$, construct $C_\ell^{TT}$ for $\ell \in [2,\,128]$ and then compute $C^{TT}(\theta)$ using Eqn. (\ref{['eqn:Ctheta']}).
• Figure 2: Plots on the left illustrates the effect of lensing on $D_\ell^{TT}$. From the plots, especially from the lower subplot, we see that the effect of lensing is more prominent at higher multipoles. In the lower subplot, $\Delta\,D^{TT}_{\ell}$ refers to ratio of difference between lensed and unlensed $D^{TT}_{\ell}$ divided by lensed $D^{TT}_{\ell}$. The right panel was obtained by Bayesian estimation of $A_L$ along with the usual six parameters with different combinations of Planck data. We find that value of $A_L$ is closer to one only when lensing data is included.
• Figure 3: Illustration of power spectra generated in the models that we consider for two different sets of values of model parameters. One set of parameter values lead to power suppression (solid lines) and the other leads to enhancement in power at small wavenumbers (dashed lines). To plot solid lines, we have worked with the marginalised mean values of $\alpha$ and $\beta$ given in table \ref{['T:A1']}. The dashed lines are obtained by working with the same values of $\alpha$ and $\beta$ but with an opposite sign. This plot illustrates that the templates that we consider are agnostic to a suppression in power, ı.e., it can lead to both suppression or enhancement of power at small wavenumbers.
• Figure 4: Plots of $D_\ell^{TT}$ as a function of multipoles (left) and of $C^{TT}(\theta)$ (right) corresponding to different models are given. We have worked with marginalised mean values of parameters given in table \ref{['T:A1']} which were obtained by comparing models with TT + lowl + lowE data. Figure illustrates that data prefers parameter values that lead to suppression in power at low multipoles or at large angles.
• Figure 5: Plot of marginalised probability distribution of $A_L$ for all four models obtained by following Method I (left) and Method II (right). We have worked with TT + lowl + lowE data. In Method I, all model parameters including $\alpha$ and $\beta$ are varied, whereas in Method II, we have fixed the values of $\alpha$ and $\beta$ to their respective mean values given in table \ref{['T:A1']}. We find from Method I that the probability distribution for $A_L$ becomes broader for models $SA\, +\, \beta$ and $SA + \alpha + \beta$ and hence $A_L\,=1$ becomes more probable. From Method II, we find that the probability distribution indeed shifts closer to one for models $SA\, +\, \beta$ and $SA + \alpha + \beta$ which leads to suppression of power at low multipoles.