Bayesian Reconstruction of the Local Universe from 2MRS: Testing the Gravitational Flow with Cosmicflows-4

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Abstract We present a Bayesian reconstruction of the local density and velocity fields traced by the 2MASS Redshift Survey (2MRS) and test the inferred gravitational flow against independent Cosmicflows-4 (CF4) galaxy-group peculiar velocities. The fiducial reconstruction is the maximum a posteriori (MAP) solution of a Zel’dovich-approximation forward model, constrained by the 2MRS redshift-space distribution through an unbinned Poisson point-process likelihood. The model assumes Gaussian initial conditions and includes the 2MRS selection function, the Zone of Avoidance, redshift-space distortions, and a distance-dependent galaxy-bias prescription. The MAP field is obtained by optimization of the posterior, while Hamiltonian Monte Carlo is used to draw posterior samples and constrained realizations within the same framework. The reconstructed velocity field agrees well with CF4 in object-by-object, density–velocity correlation, and shell-by-shell reflex-dipole tests. These comparisons are made at the CF4 redshift-space positions and do not require smoothing the observed CF4 velocities to the MAP resolution. We also evolve constrained initial conditions with Gadget-4 . The real-space density retains the large-scale Zel’dovich structure while developing additional nonlinear small-scale structure, and the redshift-space distribution develops nonlinear Fingers of God. The results show that the 2MRS field-level reconstruction captures the large-scale gravitational flow of the nearby Universe and provides initial conditions suitable for constrained simulations.

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