During the formation of the large scale structure of the Universe , matter accretes onto high density peaks .
Accreting collisionless dark matter ( DM ) forms caustics around them , while accreting collisional baryonic matter ( BM ) forms accretion shocks .
The properties of the accreting matter depend upon the power spectrum of the initial perturbations on a given scale as well as the background expansion in a given cosmological model .
In this paper , we have calculated the accretion of DM particles in one-dimensional spherical geometry under various cosmological models including the Einstein-de Sitter universe , the open universe with \Omega _ { o } < 1 , and the flat universe with \Omega _ { \Lambda } = 1 - \Omega _ { o } .
A density parameter in the range 0.1 \leq \Omega _ { o } \leq 1 has been considered .
The initial perturbation characterized by a point mass at the origin has been considered .
Since the accretion shock of BM is expected to form close to the first caustic of DM , the properties of the accreting BM are common with those of the DM .
Hence , the accretion calculations with DM particles have been used to find the position and velocity of the accretion shock and the cluster mass inside it .
The average temperature of BM has been estimated by adopting simplifying assumptions .
The velocity of the accreting BM around clusters of a given temperature is smaller in a universe with smaller \Omega _ { o } , but only by up to \sim 24 \% in the models with 0.1 \leq \Omega _ { o } \leq 1 .
Thus , it would be difficult to use that quantity to discriminate among the cosmological models .
However , the accretion velocity around clusters of a given mass or a given radius depends more sensitively on the cosmological models .
It is smaller in a universe with smaller \Omega _ { o } by up to \sim 41 \% and \sim 65 \% , respectively .
So , it can provide a better signature of the background expansion for different cosmological models .
Although the existence of the caustics and the accretion shocks may not be confirmed by direct x-ray observations , the infalling warm gas of 10 ^ { 4 } -10 ^ { 5 } K upstream of the shocks may be observed as the absorption systems of quasar emission lines .
According to this study , the suggestion made by Kang , Ryu , & Jones ( 1996 ) that the large scale accretion shocks around clusters of galaxies can serve as possible acceleration sites of ultra high energy cosmic rays above 10 ^ { 18 } eV remains plausible in all viable cosmological models .