Why multitracer surveys beat cosmic variance

Galaxy surveys that map multiple species of tracers of large-scale structure can improve the constraints on some cosmological parameters far beyond the limits imposed by a simplistic interpretation of cosmic variance. This enhancement derives from comparing the relative clustering between different tracers of large-scale structure. We present a simple but generic expression for the Fisher information matrix of surveys with any (discrete) number of tracers, and show that the enhancement of the constraints on bias-sensitive parameters are a straightforward consequence of this multitracer Fisher matrix. In fact, the relative clustering amplitudes between tracers are eigenvectors of this multitracer Fisher matrix. The diagonalized multitracer Fisher matrix clearly shows that while the effective volume is bounded by the physical volume of the survey, the relational information between species is unbounded. As an application, we study the expected enhancements in the constraints of realistic surveys that aim at mapping several different types of tracers of large-scale structure. The gain obtained by combining multiple tracers is highest at low redshifts, and in one particular scenario we analysed that the enhancement can be as large as a factor of greater than or similar to 3 for the accuracy in the determination of the redshift distortion parameter, and a factor of greater than or similar to 5 for the local non-Gaussianity parameter f(NL). Radial and angular distance determinations from the baryonic features in the power spectrum may also benefit from the multitracer approach.