Departure to pure de Sitter geometry based on Planck data

Abstract

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.