# Power Spectra Based Planck Constraints on Compensated Isocurvature, and Forecasts for LiteBIRD and CORE Space Missions

## TL;DR

This paper analyzes Planck data to constrain compensated isocurvature perturbations (CIP), finds evidence for non-zero CIP variance, and forecasts the capabilities of future missions like LiteBIRD and CORE-M5 to improve these constraints and distinguish between models.

## Contribution

It provides the first constraints on CIP from Planck data, demonstrates CIP's potential to resolve lensing anomalies, and offers detailed forecasts for upcoming satellite missions.

## Key findings

- Planck data favors a non-zero CIP variance at 2.3σ.
- CIP improves the fit to Planck data and reduces lensing anomalies.
- CORE-M5 can significantly tighten CIP constraints and distinguish CIP from lensing effects.

## Abstract

Compensated isocurvature perturbations (CIP), where the baryon and cold dark matter perturbations cancel, do not cause total matter isocurvature perturbation. Consequently, at the linear order in the baryon density contrast $\Delta$, CIP is not detectable by the CMB power spectra. At the second order CIP smoothes the power spectra in a similar manner as lensing, causing a degeneracy between the CIP variance $\Delta^2_{rms}=<\Delta^2>$ and lensing parameter $A_L$. We show that the CMB lensing data breaks this degeneracy. Nested sampling of the LCDM+CIP(+$A_L$) model, the Planck 2015 temperature, polarization, and lensing data give $\Delta^2_{rms}=0.0069\pm0.0030$ at 68% CL. A non-zero value is favored at 2.3$\sigma$. CIP with $\Delta^2_{rms}=0.007$ improves the bestfit $\chi^2$ by 3.6 compared to the adiabatic LCDM model. In contrast, although the temperature data favor $A_L=1.22$, allowing $A_L\ne1$ does not improve the joint fit, since the lensing data disfavor $A_L\ne1$. Indeed, CIP provides a rare example of a simple model, which can reduce the Planck lensing anomaly by fitting well simultaneously the high multipole temperature and lensing data, as well as the polarization data. Finally, we derive forecasts for future satellite missions (LiteBIRD proposal to JAXA and Exploring Cosmic Origins with CORE proposal to ESA's M5 call). Due to its coarse angular resolution, LiteBIRD is not able to improve the constraints on CIP or $A_L$, but CORE-M5 approaches the cosmic variance limit and improves the CIP constraint to $\Delta^2_{rms}<0.0006\ (0.0014)$ at 68% (95%) CL, which is 9 times better than the current trispectrum based upper bound and 6 times better than obtained from the simulated Planck data. In addition, CORE-M5 will exquisitely distinguish between CIP and $A_L$. No matter whether CIP is allowed for or not, the uncertainty of the lensing parameter will be $\sigma(A_L)=0.012$.