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In this paper, we will show that a power law asymptotic de Sitter inflation will be established for all values of Hankel indices Î½ that relate to the different background spacetimes of the universe in their evolution. First, we calculate the relations for the Hubble, deceleration, slow roll and the equation of state parameters in terms of the Hankel function index Î½. We then show that the obtained relations and figures correspond to the conventional limit conditions for pure de Sitter inflation. As an important result, power law quasi-de Sitter inflation is more likely to occur after exponential pure de Sitter inflation. Also, in the proposed model, the universe can always be in the accelerating expansion phase for all values of index Î½
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