Calibration errors unleashed: effects on cosmological parameters and requirements for large-scale structure surveys

Imperfect photometric calibration of galaxy surveys due to either astrophysical or instrumental effects leads to biases in measuring galaxy clustering and in the resulting cosmological parameter measurements. More interestingly (and disturbingly), the spatially varying calibration also generically leads to violations of statistical isotropy of the galaxy clustering signal. Here we develop, for the first time, a formalism to propagate the effects of photometric calibration variations with arbitrary spatial dependence across the sky to the observed power spectra and to the cosmological parameter constraints. We develop an end-to-end pipeline to study the effects of calibration, and illustrate our results using specific examples including Galactic dust extinction and survey-dependent magnitude limits as a function of zenith angle of the telescope. We establish requirements on the control of calibration so that it does not significantly bias constraints on dark energy and primordial non-Gaussianity. Two principal findings are (1) largest-angle photometric calibration variations (dipole, quadrupole and a few more modes, though not the monopole) are the most damaging and (2) calibration will need to be understood at the similar to 0.1 per cent-1 per cent level (i.e. rms variations mapped out to accuracy between 0.001 and 0.01 mag), though the precise requirement strongly depends on the faint-end slope of the luminosity function and the redshift distribution of galaxies in the survey.