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Semi-analytical Study on the Generic Degeneracy for Galaxy Clustering Measurements

From the galaxy power spectrum in redshift space, we derive semi-analytical results on the generic degeneracy of galaxy clustering measurements. Defining the observables $\bar{A}= Gbσ_8$ and $\bar{R} = Gfσ_8$, (being $G$ the growth function, $b$ the bias, $f$ the growth rate, and $σ_8$ the amplitude of the power spectrum), we perform a Fisher matrix formalism to forecast the expected precision of these quantities for a Euclid-like survey. Among the results we found that galaxy surveys have generically a slightly negative correlation between $\bar{A}$ and $\bar{R}$, and they can always measure $\bar{R}$ about 3.7 to 4.7 times better than $\bar{A}$.