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tokens: factor. This equation has the solution , where ‘en’ corresponds to the entry time of a perturbation mode into the horizon. Then, at the time at which a dark matter halo becomes non-linear (i.e. δ D ∼ 1), the density contrast of baryonic matter also approaches one. In the non-linear phase of structure formation, assuming a top-hat spherical model, each shell collapses without crossing the other shells and at the turnaround time structures start collapsing and finally virialize (Padmanabhan 1993 ). If we ignore the dissipation of baryonic matter at the first stage of virialization, then baryonic matter particles will have almost the same amount of kinetic and potential energy as dark matter particles and will virialize at the same time as dark matter fluid. Then, in the gravitational potential of dark matter, we expect that baryonic matter extends to the same scale as the dark matter structure. We can now calculate the density of baryonic matter in the dark matter halo from the following relation: where h ν 0 is the energy of CMB photons, m p is the mass of a proton and the ‘zero’ sub/superscript corresponds to the value of parameters at the present time. The important issue concerning the amount of baryonic matter within the gravitational potential of dark matter is the possibility of formation of baryonic structure. Formation of baryonic structure after the virialization of a halo is possible if plasma can cool and fall to the centre of the gravitational potential of the dark matter. The essential criterion is comparing the dynamical time-scale with the cooling time-scale of the baryonic matter. The dynamical time-scale for a test particle in the potential of dark matter is given by and, on the other hand, the cooling time-scale is where σ T is the Thomson cross-section and α is the fine-structure constant. For t cool t grav , we have a sufficient condition for the formation of baryonic structures. Substituting temperature from the virial condition, we get the simple result where baryonic and dark matter are enclosed within the same radius R . Integrating from equation ( 32 ) and equating it with equation ( 35 ), we obtain the following relation between the size of structure and the mass of baryonic matter in terms of η B : where η 10,B is the definition of η B normalized to 10 −10 . For a Galactic halo with mass of order of M D ≃ 10 12 M ⊙ , for η 10,B > 10 −5 , a structure with the mass of a globular cluster can form within this dark halo. Another lower value for the baryonic asymmetry could be η 10,B ≃ 10 −12 , where only one star with M min ∼ 0.1 M ⊙ condenses to form a single star within a 10 12 solar mass halo. We can think about another extreme case, having only one star within the cosmological horizon. In this case, we can write the η B parameter in terms of the minimum mass for a star and the mass of matter within the horizon (i.e. M H ), where m X and m p are the mass of a dark matter particle and the proton mass. Substituting the