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The Fisher matrix is a widely used tool to forecast the performance of futureexperiments and approximate the likelihood of large data sets. Most of theforecasts for cosmological parameters in galaxy clustering studies rely on theFisher matrix approach for large-scale experiments like DES, Euclid, or SKA.Here we improve upon the standard method by taking into account three effects:the finite window function, the correlation between redshift bins, and theuncertainty on the bin redshift. The first two effects are negligible only inthe limit of infinite surveys. The third effect, on the contrary, is negligiblefor infinitely small bins. Here we show how to take into account these effectsand what the impact on forecasts of a Euclid-type experiment will be. The mainresult of this article is that the windowing and the bin cross-correlationinduce a considerable change in the forecasted errors, of the order of 10-30%for most cosmological parameters, while the redshift bin uncertainty can beneglected for bins smaller than $\Delta z = 0.1$ roughly.

Improving Fisher matrix forecasts for galaxy surveys: window function, bin cross-correlation, and bin redshift uncertainty