Scientists can't just agree to disagree. It's not because we are stubborn or ornery (OK, maybe we are). It's because the whole point of science is to establish "public knowledge" — an understanding of the cosmos on which we can all agree. That is why there is trouble brewing at the beginning of the Universe.
There is a number, the Hubble Constant, that's fundamental to the study of the cosmos. The problem is, different folks are finding different values for that number and no one yet knows what that means.
Two weeks ago the scientific team running the Planck satellite announced the most comprehensive analysis of their data to date. The Planck mission was designed to study radiation left over from just a few-hundred-thousand years after the Big Bang. This is the famous cosmic microwave background radiation (or CMB) and it's a kind of fossil light, imprinted with all kinds of details about how the Universe evolved. These details include parameters describing the proportions of material in the Universe, like dark matter and dark energy.
One of the parameters that fall out of their analysis is the Hubble Constant (written as Ho) that describes the rate of the Universe's expansion in the current epoch of cosmic history. The Hubble constant is directly tied to finding the Universe's age (though other parameters are needed as well). The Planck analysis yielded a value of Ho = 67.11 kilometers per second per Megaparsec (km/s/Mpc: yes those units are weird but don't worry about them for now). Put it all together and the Planck team finds the Universe to be 13.89 billion years old give or take a few hundred million years. You gotta admit, that kind of precision is pretty impressive.
So what's the problem?
Other teams using a very different set of methods get a very different answer for the Hubble Constant. When Edwin Hubble (you know, that guy with the constant named for him) first discovered the Universe was expanding back in 1928, he did it by measuring how fast galaxies were flying away from us versus their distance from us. The CMB wasn't even a gleam in scientist's eye back then. This direct method — measure the distance and recession velocity of lots of galaxies, then plot up the result — has been getting more refined ever since. These days the best values for the Hubble Constant that come from this approach find something around Ho = 74 km/s/Mpc.
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