Studying the critical scalar theory in four dimensional Euclidean

space with the potential term $-g\phi^4$ we show that the theory

can not be analytically continued through $g=0$ from $g<0$ region to $g>0$

region. For $g>0$ although energy is not bounded from below but there exist a

classical trajectory with an $\mbox{AdS}_5$ moduli space,

corresponding to a metastable local minima of the action.

The fluctuation around this solution is governed by a minimally coupled scalar theory

on four dimensional de~Sitter background with a reversed Mexican hat potential.

Since in the weak coupling limit, the partition function

picks up contribution only around classical solutions, one can assume

that our de~Sitter universe corresponds to that local minima which lifetime increases

exponentially as the coupling constant tends to zero. Similar results is obtained in

the case of critical scalar theory coupled to U(1) gauge field which is essential

for people living on flat Euclidean space to observe a de Sitter background by optical

instruments.