In this paper, we will obtain the basic parameters of primordial inflation such as power spectrum, scalar spectral index, and tensor-to-scalar ratio as a function of Hankel index [Formula: see text] for asymptotic-de Sitter inflation and then, based on the observational constraints on these parameters from Planck data, we obtain the allowable range for index [Formula: see text]. We will show that only the non-phantom phase is acceptable for quasi-de Sitter inflation at early universe. As a significant result, both of the primordial and late accelerating expansion are always in a quasi-vacuum phase (with [Formula: see text]) and it has never been in a pure-vacuum phase (with [Formula: see text]), i.e. cosmological constant. Therefore, based on our recent finding [E. Yusofi, M. Khanpour, B. Khanpour, M. A. Ramzanpour and M. Mohsenzadeh, Surface tension of cosmic voids as a possible source for dark energy, Mon. Not. R. Astron. Soc. 511 (2022) L82], we offer the surface tension of cosmic voids as a suitable alternative to the cosmological constant [Formula: see text], for accelerating universe.