Abstract
We propose that de-Sitter space-time originates from Gaussian distribution in a quantum harmonic oscillator system. This equation associates with a massless Klein-Gordon equation. We discover that every excited states of quantum oscillator also contributes for the de-Sitter space-time. The observable part of metric is related to energy scale and excited quantum number . As for off-diagonal elements, it comes from the superposition of quantum mechanics. These elements can cause in-homogeneous at the very beginning of universe.
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