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My question is a bit abstract, but I'm wondering if it makes sense to expect/hope that one day we will be able to measure the age of the universe (in Earth's frame of reference) much more precisely, down to sub-year precision? Is that a well defined question and is it physically possible to figure out?

I'm thinking that maybe the expansion of the universe or something to do with relativity could make this impossible to answer or a nonsensical question to ask.

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Even assuming we have the correct cosmological model, the precision to which we can measure cosmological parameters is fundamentally limited by our vantage point. Our location in the universe is random, but every experiment we do is from the same random location. We can reduce instrumental error in measuring the cosmic microwave background, but we are always measuring the same inherently noisy pattern. This problem is called "cosmic variance".

In principle, we could discover a theory of everything that forces a certain value for certain cosmological parameters (perhaps the cosmological constant), allowing us to better fit the other parameters, or we could find maps of the microwave background from millions of years ago in the ruins of Atlantis and combine it with the current map to reduce the noise. Failing that, I think that future astronomical observations can only slightly improve the precision of the fit.

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Within our present model of the universe, the age of the universe is deduced from observational data :

Ancient light from the Big Bang has revealed a precise new estimate for the universe's age: 13.77 billion years, give or take 40 million years.

13.770.000.000 earth years +/- 40.000.000 earth years.

If we accept the claim that it is the best precision, (ignoring maybe larger errors due to models used),the error given is too far removed for your "sub year precision" for it to be attainable, imo.

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    $\begingroup$ Did you forget the famous Hubble Tension? The number you quote does not come directly from observational data, but from fitting it to the Friedmann cosmology, which is in an existential crisis as the worst theory of the mankind mismatching by whooping 95% the actually observed matter content in the universe. $\endgroup$ – safesphere Feb 27 at 6:59
  • $\begingroup$ @safesphere the error is the important thing, which is experimental, no matter what the theory predicts. Take the ratio: you cannot get great improvement no matter what the theory predicts in billions of years. $\endgroup$ – anna v Feb 27 at 7:03
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    $\begingroup$ The Hubble Tension is the difference between relatively direct measurements (which are still not geometry independent) and fitting indirect observations to the Friedmann model. This difference is much larger that the error you quoted. The actual uncertainty is in the range of a billion years. $\endgroup$ – safesphere Feb 27 at 7:08
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    $\begingroup$ The Hubble tension is 67 to 74. With simple math this translates to about a 1.3-billion-year difference. $\endgroup$ – safesphere Feb 27 at 8:08
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    $\begingroup$ We should stick to the present calendar(s) until the accuracy is improved. $\endgroup$ – my2cts Feb 27 at 9:29
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The key concept in the question is. "Is it theoretically possible...?" This a distinctly different question than whether it is practically possible. As astronomical instruments get bigger, their precision will also get better. The biggest current instrument in recent times is the Hubble with a diameter of 2.4m, which has produced an error of about 40,000,000 years. One can imagine theoretically creating a telescope the size of the solar system with a diameter of about 22,000,000,000,000m. If such an instrument were to someday be created, it would not be too surprising to me that the precision of the age of the universe will very possibly become less than a year.

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