We investigate the dependence of ellipticities of clusters of galaxies on cosmological parameters using large-scale cosmological simulations .
We determine cluster ellipticities out to redshift unity for LCDM models with different mean densities \Omega _ { m } and amplitudes of mass fluctuation \sigma _ { 8 , 0 } .
The mean ellipticity increases monotonically with redshift for all models .
Larger values of \sigma _ { 8 , 0 } , i.e. , earlier cluster formation time , produce lower ellipticities .
The dependence of ellipticity on \Omega _ { m } is relatively weak in the range 0.2 \leq \Omega _ { m } \leq 0.5 for high mass clusters .
The mean ellipticity \bar { e } ( z ) decreases linearly with the amplitude of fluctuations at the cluster redshift z , nearly independent of \Omega _ { m } ; on average , older clusters are more relaxed and are thus less elliptical .
The distribution of ellipticities about the mean is approximated by a Gaussian , allowing a simple characterization of the evolution of ellipticity with redshift as a function of cosmological parameters .
At z = 0 , the mean ellipticity of high mass clusters is approximated by \bar { e } ( z = 0 ) = 0.248 - 0.069 \sigma _ { 8 , 0 } +0.013 \Omega _ { m, 0 } .
This relation opens up the possibility that , when compared with future observations of large cluster samples , the mean cluster ellipticity and its evolution could be used as a new , independent tool to constrain cosmological parameters , especially the amplitude of mass fluctuations , \sigma _ { 8 , 0 } .