The Information Content of Projected Galaxy Fields

Understand

The power spectrum of the nonlinearly evolved large-scale mass distribution recovers only a minority of the information available on the mass fluctuation amplitude.

• We investigate the recovery of this information in 2D "slabs" of the mass distribution averaged over $\approx100$~$h^{-1}$Mpc along the line of sight, as might be obtained from photometric redshift surveys.
• We demonstrate a Hamiltonian Monte Carlo (HMC) method to reconstruct the non-Gaussian mass distribution in slabs, under the assumption that the projected field is a point-transformed Gaussian random field, Poisson-sampled by galaxies.
• When applied to the \textit{Quijote} $N$-body suite at $z=0.5$ and at a transverse resolution of 2~$h^{-1}$Mpc, the method recovers $\sim 30$ times more information than the 2D power spectrum in the well-sampled limit, recovering the Gaussian limit on information.