A clever observation of some very dim stars confirms that the ratio of some key physical constants (the ratio of the proton mass to the electron mass) was the same 7.5 billion years ago as it is today. A similar result using essentially the same methodology carried out by a heavily overlapping set of investigators was obtained two years ago. The universe is about 13.7-13.8 billion years old.
Now, neither of these constants are actually constant. Both are functions of energy scale (as we know from the extreme conditions of colliders), but those energy scales were present in the universe only in the early parts of the first half-billion years of the universe. But, some theories have supposed that there might be some other source of variation in these constants, a hypothesis that so far has no held up.
See also http://arxiv.org/abs/1501.00560
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