By means of galaxy evolutionary models , we explore the direct consequences of the \Lambda Cold Dark Matter ( \Lambda CDM ) cosmogony on the size evolution of galactic discs , avoiding intentionally the introduction of intermediate ( uncertain ) astrophysical processes .
Based on the shape of the rotation curves and guided by a simplicity criterion , we adopt an average galaxy mass baryon fraction \mbox { $f _ { gal } $ } = 0.03 .
In order to study general behaviors , only models with the average initial conditions are analyzed .
The stellar and B -band effective radii , R _ { * } and R _ { B } , of individual galaxies grow significantly with time ( inside-out disc formation ) with laws that are weakly dependent on stellar mass , M _ { * } , or luminosity , L _ { B } .
However , the change of R _ { * } with z at a fixed M _ { * } is slow ; for z \leq 2.5 , R _ { * } ( M _ { * } =constant ) \propto ( 1 + z ) ^ { -0.4 } for a large range of masses .
On the other hand , the change of R _ { B } with z at a fixed L _ { B } is strong and it resembles the R _ { B } decreasing law of the individual models ; roughly R _ { B } ( L _ { B } =constant ) \propto ( 1 + z ) ^ { -0.85 } for z { { } _ { < } \atop { { } ^ { \sim } } } 0.75 , and \propto ( 1 + z ) ^ { -1.1 } for higher z ^ { \prime } s. We find also that at z = 0 , \mbox { $R _ { * } $ } \propto \mbox { $M _ { * } $ } ^ { 0.38 } and \mbox { $R _ { B } $ } \propto L _ { B } ^ { 0.40 } , remaining the slopes of these relations practically the same up to z \approx 3 .
Our model predictions are in reasonable agreement with observational inferences on the typical radius change with z of late-type galaxies more luminous ( massive ) than high values imposed by the selection effects .
The models seem also to be consistent , within the large scatter , with the R _ { B } and L _ { B } values obtained from small ( non complete ) samples of sub- L _ { * } late-type galaxies with available rest-frame photometric information at different z ^ { \prime } s. The properties and evolution of the \Lambda CDM haloes seem to be the main drivers of galaxy disk size evolution .
Nevertheless , the models reveal a potential difficulty in explaining the observed steepening of the R _ { B } - L _ { B } relation with respect to the R _ { * } - M _ { * } one , an effect related to the well established color-magnitude relation .