We review theoretical approaches to the study of galaxy formation , with emphasis on the role of hydrodynamic cosmological simulations in modeling the high redshift galaxy population .
We present new predictions for the abundance of star-forming galaxies in the LCDM model ( inflation + cold dark matter , with \Omega _ { m } = 0.4 , \Omega _ { \Lambda } = 0.6 ) , combining results from several simulations to probe a wide range of redshift .
At a threshold density of one object per arcmin ^ { 2 } per unit redshift , these simulations predict galaxies with star formation rates of 2 M _ { \odot } / yr ( z = 10 ) , 5 M _ { \odot } /yr ( z = 8 ) , 20 M _ { \odot } /yr ( z = 6 ) , 70 - 100 M _ { \odot } /yr ( z = 4 - 2 ) , and 30 M _ { \odot } /yr ( z = 0.5 ) .
For galaxies selected at a fixed comoving space density n = 0.003 h ^ { 3 } { Mpc } ^ { -3 } , a simulation of a 50 { h ^ { -1 } { Mpc } } cube predicts a galaxy correlation function ( r / 5 { h ^ { -1 } { Mpc } } ) ^ { -1.8 } in comoving coordinates , essentially independent of redshift from z = 4 to z = 0.5 .
Different cosmological models predict global histories of star formation that reflect their overall histories of mass clustering , but robust numerical predictions of the comoving space density of star formation are difficult because the simulations miss the contribution from galaxies below their resolution limit .
The LCDM model appears to predict a star formation history with roughly the shape inferred from observations , but it produces too many stars at low redshift , predicting \Omega _ { \star } \approx 0.015 at z = 0 .
We conclude with a brief discussion of this discrepancy and three others that suggest gaps in our current theory of galaxy formation : small disks , steep central halo profiles , and an excess of low mass dark halos .
While these problems could fade as the simulations or observations improve , they could also guide us towards a new understanding of galactic scale star formation , the spectrum of primordial fluctuations , or the nature of dark matter .