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A recent physorg article is titled "The measurements of the expansion of the universe don't add up". The article says

The current analysis of the variable brightness of cepheids with space telescopes such as the Hubble, along with other direct observations of objects in our cosmic environment and more distant supernovae, indicate that the H0 value is approximately 73.9 kilometres per second per megaparsec (an astronomical unit equivalent to about 3.26 million light years).

However, measurements based on the early Universe provide an average H0 value of 67.4 km/s/Mpc. These other records, obtained with data from the European Space Agency's Planck Satellite and other instruments, are obtained indirectly on the basis of the success of the standard cosmological model (Lambda-CDM model) ...

I thought I could learn more about these different methods from wikipedia, but the age of the universe article only talks about the Planck data and WMAP, and an age ~ 13.7B years. The wiki talk page does have a section that refers to the Hubble's Law page, which does talk about different methods and history, but also says

More recent measurements from the Planck mission published in 2018 indicate a lower value of 67.66±0.42% although, even more recently, in March 2019, a higher value of 74.03±1.42% has been determined using an improved procedure involving the Hubble Space Telescope.[60] The two measurements disagree at the 4.4σ level, beyond a plausible level of chance.[61] The resolution to this disagreement is an ongoing area of research.[62]

So why is the Planck/WMAP estimate of the age of the universe preferred over similar alternatives, such as estimates based on Hubble observations?

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You have partly answered your own question. The Planck measurements are more precise. Moreover, it is generally assumed, perhaps wrongly, that the measurements based on the cosmic microwave background are subject to fewer systematic uncertainties than other methods.

You also need to think about how the age is derived. For that you need more than just the value of $H_0$. In particular you need estimates of the energy densities of matter and dark energy. These can come from the cosmic microwave background data alone and give the value of 13.8 billion years.

If $H_0$ from Planck and from other methods do not agree, then there is a problem with the measurements, cosmology, or both. But you can't really just adopt a different value of $H_0$ and then use the other cosmological parameters that are derived from the CMB to derive a new age (though people have).

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  • Hubble observations can only produce a local measurement of Hubble constant $H_0$. The cosmic ladders such as cepheids and supernovae are used to arrive at the Hubble parameter $H(t)$ at low redshift. In other words, Hubble observations only tell you the cosmic behavior of the recent epoch. It's a snapshot of the universe in its adulthood, with beards and what not.
  • Planck Satellite observations determine cosmic parameters (6 of them) based the remnant signals emanating from the universe in its embryonic stage, such as Cosmic Microwave Background (CMB). It's a point-in-time picture of the universe when it's still a cute baby with chubby face.

Two takeaways:

  • Since Planck Satellite observations are interpreted in the context of $\Lambda CMD$ to reproduce the whole evolution history of the universe, one can impute the age of the universe as well as the current value of the Hubble parameter $H_0$. Nevertheless, one should bear in mind that these Planck results are model ($\Lambda CMD$) dependent. Given the tightened error margin in cosmic ladder and CMB measurements, the $H_0$ tension between Hubble and Planck is most likely due to some defect in the standard cosmology model $\Lambda CMD$. Therefore the Planck-based estimation (in conjunction with $\Lambda CMD$) of the age of the universe is questionable.
  • Hubble observations CAN be used to directly calculate the Hubble constant $H_0$ without resorting to any cosmological model such as the concordance model $\Lambda CMD$. However, without enlisting the aid from $\Lambda CMD$ (and the questionable $\Lambda CMD$ parameters sourced from Planck), Hubble observations alone are INCAPABLE of inferring the age of the Universe.

Is there any direct way of observing the age of the universe? Well, the estimation of the age of the old globular clusters might put a lower bound on the age of the universe, since the universe must be older than these globular clusters. As of yet, the observations of the age of the oldest globular clusters are inconclusive, with some of them MIGHT exceed the Planck-based estimation of age of the universe.

And this is where things stand with the wonderfully "accurate" standard cosmology.


Added note on 2023/8/2:

I composed the original answer in 2019. In 2023, James Webb Space Telescope (JWST) discovered galaxy candidates which would have emerged only ∼230 million years after the big bang in the context of $\Lambda CMD$. The so-called ‘impossibly early galaxy’ problem would therefore be inconsistent with the age-redshift relation predicted by $\Lambda CMD$. This dramatic development would put the wonderfully "accurate" estimate of the age of the universe on even more shaky ground.

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  • $\begingroup$ I'm not rich on cosmology, but from what I understood - the uncertainy's driven by a combination of (1) incomplete cosmological model; (2) insufficient data - correct? Also, can the estimate be extrapolated beyond the observable universe, or only within? $\endgroup$ Commented Dec 12, 2019 at 15:00
  • $\begingroup$ @OverLordGoldDragon, when Planck data was released in 2013, cosmologist were pretty confident that we have a complete cosmological model, only to be contradicted by the more recent local measurements of the Hubble constant $H_0$, which indicates that our former confidence on the 'concordance model' is misplaced. The whole cosmology community is currently scrambling to mitigate the embarrassing discordance: either denying the accuracy of the measurements or fashioning more fudging factors to salvage the concordance model. $\endgroup$
    – MadMax
    Commented Dec 12, 2019 at 15:12
  • $\begingroup$ accurate is not a synonym for precise in astrophysics experiments. $\endgroup$
    – ProfRob
    Commented Aug 2, 2023 at 22:47
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How exactly do you measure the age of the universe? I want to emphasize this because it cuts to the heart of the question.

Right now the only way I'm aware of is to calculate it using measured values of the Hubble constant + the density of matter/dark energy/radiation, and assuming the Lambda-CDM model (which in turn assumes General Relativity, homogeneity, and isotropy). You need all these things to calculate the age of the universe - it is not directly measurable.

Now let's dissect these ingredients:

  1. The Hubble constant can be measured in several ways. More on this later.
  2. There are a variety of ways to measure the density of matter. See Wikipedia on dark matter. (In cosmology, matter and dark matter are nearly the same, since they both scale as $a^{-3}$).
  3. Same goes for how to measure the density of dark energy.

The article you're reading says there is a discrepancy in measuring the Hubble constant. Different tools are giving different results. Planck/WMAP measures the Hubble constant using early-universe physics, while the Hubble Space Telescope (and several other experiments) measure it using local-universe physics. The first gives a value of about 67 km/s/Mpc, while the latter gives a value of about 73 km/s/Mpc. This discrepancy is known as the Hubble tension. Because the Hubble constant is one of the ingredients that go into the age of the universe, it shouldn't be surprising that you get different values for the age of the universe, depending on which value of the Hubble constant you use.

Finally, let's get to the question of why we prefer the Planck/WMAP estimate of the age of the universe. The answer is we don't. I'm not sure what gave you that impression. At present, it's clear that something is wrong, but any of several possibilities are possible:

  • We need to change some of the physics in the early universe (this would be equivalent to saying that the Planck/WMAP values are wrong)
  • We need to change some of the physics in the late universe (this goes the other way, suggesting there is something wrong with HST measurements)
  • We need to change some of the physics in both the early and late universe
  • There is an unaccounted-for effect based on known physics that removes the discrepancy
  • There is an undiscovered systematic error in either instrument

At present, any of these are possible, and they're all active areas of research. We don't "prefer" the Planck/WMAP estimates - there are people seriously investigating whether the Planck/WMAP estimates are wrong.

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