Our universe is born of a tunnelling from nothing in quantum cosmology. Nothing here can be interpreted as a state with zero entropy. As a reliable modification of the Hartle-Hawking wave function of the universe, the improved Hartle-Hawking wave function proposed by Firouzjahi, Sarangi and Tye gives many interesting observational consequences which we explore in this paper. Fruitful observations are obtained for chaotic inflation, including a detectable spatial curvature and a negligible tunnelling probability for eternal chaotic inflation. And we find that the tensor-scalar ratio and the spatial curvature for brane inflation type models should be neglected.

12 pages, harvmac; refs. added and minor corrections; version for publication in Nucl.Phys.B