On approximations of the redshift-space bispectrum and power spectrum multipoles covariance matrix

Understand

We investigate, in dark matter and galaxy mocks, the effects of approximating the galaxy power spectrum-bispectrum estimated covariance as a diagonal matrix, for an analysis that aligns with the specifications of recent and upcoming galaxy surveys.

• We find that, for a joint power spectrum and bispectrum data-vector, with corresponding $k$-ranges of $0.02<k\,[h{\rm Mpc}^{-1}]<0.15$ and $0.02<k\,[h{\rm Mpc}^{-1}]<0.12$ each, the diagonal covariance approximation recovers $\sim 10\%$ larger error-bars on the parameters $\{\sigma_8,f,\alpha_\parallel,\alpha_\bot\}$ with respect to the full covariance case, while still underestimating the corresponding true errors on the recovered parameters by $\sim 10\%$.
• This is caused by the diagonal approximations weighting the elements of the data-vector in a sub-optimal way, resulting in a less efficient estimator, with poor coverage properties, than the maximum likelihood estimator featuring the full covariance matrix.
• We further investigate intermediate approximations to the full covariance matrix, with up to $\sim 80\%$ of the matrix elements being zero, which could be advantageous for theoretical and hybrid approaches.