Julio Friedmann is chief scientist at New York City-based Carbon Direct, a carbon management company.

胡里奥·弗里德曼是总部位于纽约的碳管理公司Carbon Direct的首席科学家。

Friedmann predicted exactly what Hubble found!

弗里德曼准确地预测了哈勃的发现！

From these two ideas alone, Friedmann showed that we should not expect the universe to be static.

仅从这两个想法，弗里德曼就表明我们不应该期望宇宙是静止的。

This, as we have seen, was Friedmann's second assumption.

正如我们所见，这是弗里德曼的第二个假设。

For a long time, this was sufficient justification for Friedmann's assumption—as a rough approximation to the real universe.

很长一段时间，这足以证明弗里德曼的假设——作为对真实宇宙的粗略近似。

In Friedmann's model, all the galaxies are moving directly away from each other.

在弗里德曼的模型中，所有的星系都在直接远离彼此。

But which Friedmann model describes our universe?

但是哪个弗里德曼模型描述了我们的宇宙？

Although Friedmann found only one, there are in fact three different kinds of models that obey Friedmann's two fundamental assumptions.

尽管弗里德曼只发现了一个，但实际上存在三种不同类型的模型都遵循弗里德曼的两个基本假设。

But more recently a lucky accident uncovered the fact that Friedmann's assumption is in fact a remarkably accurate description of our universe.

但最近一次幸运的事故揭示了这样一个事实，即弗里德曼的假设实际上是对我们宇宙的非常准确的描述。

Similarly, in Friedmann's model the speed at which any two galaxies are moving apart is proportional to the distance between them.

同样，在弗里德曼的模型中，任何两个星系移动的速度都与它们之间的距离成正比。

In the first kind (which Friedmann found) the universe is expanding sufficiently slowly that the gravitational attraction between the different galaxies causes the expansion to slow down and eventually to stop.

在第一种（弗里德曼发现的）中，宇宙膨胀得足够慢，以至于不同星系之间的引力导致膨胀减慢并最终停止。

In Friedmann's models, the galaxies are all moving directly away from each other—so it is not surprising that at some time in the past they were all at the same place.

在弗里德曼的模型中，星系都直接远离彼此 - 所以在过去的某个时候它们都在同一个地方也就不足为奇了。

All of the Friedmann solutions have the feature that at some time in the past (between ten and twenty thousand million years ago) the distance between neighboring galaxies must have been zero.

所有的弗里德曼解都有一个特点，即在过去的某个时间（10 到 20 亿年前）相邻星系之间的距离必须为零。

What Lifshitz and Khalatnikov did was to study models of the universe that were roughly like Friedmann's models but took account of the irregularities and random velocities of galaxies in the real universe.

Lifshitz 和 Khalatnikov 所做的是研究宇宙模型，这些模型与弗里德曼的模型大致相似，但考虑了真实宇宙中星系的不规则性和随机速度。

So I could in fact use it to prove that there should be a singularity only if the universe was expanding fast enough to avoid collapsing again (since only those Friedmann models were infinite in space).

所以我实际上可以用它来证明只有当宇宙膨胀得足够快以避免再次坍缩时才应该有一个奇点（因为只有那些弗里德曼模型在空间中是无限的）。