# Principal component analysis of the primordial tensor power spectrum

## TL;DR

This paper investigates how future CMB B-mode polarization experiments can constrain the primordial gravitational wave spectrum shape using PCA, accounting for foreground residuals and lensing effects, and assesses the impact on parameter uncertainties.

## Contribution

It introduces a PCA-based method for constraining the primordial tensor spectrum shape, incorporating foreground residuals and lensing effects, and evaluates its limitations with MCMC analysis.

## Key findings

- Foreground residuals significantly affect PCA constraints.
- Adding foregrounds can increase uncertainties by up to a factor of 4.
- Methodology limitations are quantified via MCMC analysis.

## Abstract

We study how the shape of the spectrum of primordial gravitational waves can be constrained by future experiments looking at the B-mode of the Cosmic Microwave Background (CMB) polarization. We implement a Principal Component Analysis (PCA) including the effects of diffuse foreground residuals, following component separation, in the uncertainty of CMB angular power spectra, and taking into account the gravitational lensing by Large Scale Structure. We perform our study by considering the capabilities of future B-mode CMB experiments such as LiteBIRD, the Simons Observatory (SO) and Stage-IV (CMB-S4), in particular in detecting deviations of the primordial tensor spectrum from the scale-invariant behavior. We find that diffuse foreground residuals impact substantially both the derivation of the PCA basis and the corresponding constraining power, in all cases. In particular, depending on which experimental specifications and which value $r$ of tensor-to-scalar ratio for cosmological perturbations are considered, adding foregrounds residuals can determine an increase as large as a factor $\sim 4$ both on the uncertainty on $r$ and on the recovery of the PCA modes. We study the limitations of the methodology, including the effect of physicality priors on the PCA, which we quantify via a Monte Carlo Markov chain (MCMC) analysis of the combined cosmological and PCA power spectrum parameter space.