We used high resolution dark matter only cosmological simulations to investigate the structural properties of Lambda Cold Dark Matter ( \Lambda CDM ) haloes over cosmic time .
The haloes in our study range in mass from \sim 10 ^ { 10 } to \sim 10 ^ { 12 } M _ { \odot } , and are resolved with 10 ^ { 5 } to 10 ^ { 7 } particles .
We fit the spherically averaged density profiles of DM haloes with the three parameter Einasto function .
For our sample of haloes , the Einasto shape parameter , \alpha , is uncorrelated with the concentration , c , at fixed halo mass , and at all redshifts .
Previous reports of an anti-correlation are traced to fitting degeneracies , which our fits are less sensitive to due to our higher spatial resolution .
However , for individual haloes the evolution in \alpha and c is anti-correlated : at redshift z = 7 , \alpha \simeq 0.4 and decreases with time , while c \simeq 3 and increases with time .
The evolution in structure is primarily due to accretion of mass at larger radii .
We suggest that \alpha traces the evolutionary state of the halo , with dynamically young haloes having high \alpha ( closer to a top-hat : \alpha ^ { -1 } = 0 ) , and dynamically relaxed haloes having low \alpha ( closer to isothermal : \alpha = 0 ) .
Such an evolutionary dependence reconciles the increase of \alpha vs peak height , \nu , with the dependence on the slope of the power spectrum of initial density fluctuations found by previous studies .