Hartle James B, Hawking S W, Hertog Thomas
Department of Physics, University of California, Santa Barbara, CA 93106, USA.
Phys Rev Lett. 2008 May 23;100(20):201301. doi: 10.1103/PhysRevLett.100.201301.
We consider the no-boundary proposal for homogeneous isotropic closed universes with a cosmological constant and a scalar field with a quadratic potential. In the semiclassical limit, it predicts classical behavior at late times if the scalar field is large enough. The classical histories may be singular in the past or bounce at a finite radius. This probability measure selects inflationary histories but is biased towards small numbers of e-foldings N. However, to obtain the probability of our observations in our past light cone these probabilities should be multiplied by exp(3N). This volume weighting is similar to that in eternal inflation. In a landscape potential, it would predict that the Universe underwent a large amount of inflation and could have always been semiclassical.
我们考虑具有宇宙学常数和二次势标量场的均匀各向同性封闭宇宙的无边界提议。在半经典极限下，如果标量场足够大，它预测晚期的经典行为。经典历史在过去可能是奇异的，或者在有限半径处反弹。这种概率测度选择暴胀历史，但偏向于少量的暴胀倍数N。然而，为了获得我们过去光锥中观测的概率，这些概率应该乘以exp(3N)。这种体积加权类似于永恒暴胀中的情况。在一个景观势中，它将预测宇宙经历了大量的暴胀，并且可能一直是半经典的。
