Bias on Tensor-to-Scalar Ratio Inference With Estimated Covariance Matrices

Understand

We investigate simulation-based bandpower covariance matrices commonly used in cosmological parameter inferences such as the estimation of the tensor-to-scalar ratio $r$.

• We find that upper limits on $r$ can be biased low by tens of percent.
• The underestimation of the upper limit is most severe when the number of simulation realizations is similar to the number of observables.
• Convergence of the covariance-matrix estimation can require a number of simulations an order of magnitude larger than the number of observables, which could mean $\mathcal{O}(10\ 000)$ simulations.