Jun 11 2024

Light and Distance in an Expanding Universe

Published by under Astronomy
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Commenter Lal asks in the topic suggestions:

“Media reports that light has been travelling from that distant galaxy for 13 and a half billion years, which I assume is true, but this neither represents the original nor the current distance to that galaxy in terms of light years. I would be interested to know where we lie in the expanding universe compared to these distant galaxies.”

This is a good question, and is challenging to grasp. We need experts who have been thinking about this for decades and who actually understand what’s happening and who can explain it well. Here, I think, is an excellent discussion of this very question. I’ll give a quick summary, but for those interested, you may want to read the full article.

The basic background is that, according to modern cosmological theory, which includes the Big Bang, the universe was a singularity – one point that contained all of spacetime and all matter and energy – about 13.7 billion years ago. This point underwent rapid expansion, at first very rapid, called the inflationary period. Then it continued to rapidly expand, although at a much slower pace, although this rate of expansion has been increasing over time due to dark energy. What happens to the universe when it expands? It’s important to note first that the universe is not expanding into space – space-time itself is expanding.

Matter in the universe gets less dense and hot as the universe expands. At first matter was too hot for particles to exist. Once it cooled enough for protons and neutrons to exist, they mostly formed into hydrogen, but that was still too hot to hold onto electrons so the matter was all plasma. That eventually cooled enough for hydrogen (and some helium and a tiny bit of lithium) atoms to exist – at about 380,000 years after the Big Bang. Since then the matter in the universe has continued to cool and become less dense. However, it was also able to form stars, galaxies, heavier elements, and then lots of interesting things like people.

Radiation, including light, in the universe also became less dense as the universe expanded. However, something else interesting happens to radiation when spacetime itself expands – it’s wavelength also expands. In terms of light, this means it becomes red shifted. This further means that distant objects become fainter than they would purely because of distance. According to the inverse square law, when something is twice as far away any light or waves emanating from it will be 2 squared or one fourth as intense. Sound will be one quarter the volume and light will be one quarter the brightness. But in the universe distant object are more dim than can be accounted for by mere distance, because of light’s redshift.

Energy density in the universe, however, remains constant even when the universe expands. This is because the universe is not expanding into empty space – space itself is expanding. In a sense more space is being created, keeping the energy density of space constant.

This brings us to the core question above – how do we account for all this when measuring the distance to a distant object. If we think about two galaxies in the early universe, about 500 million years after the Big Bang – as the universe expanded these two galaxies would become farther and farther apart. Light leaving one galaxy would have to catch up with the other galaxy as it moves away with the expansion of space. So it takes longer than the original distance of the galaxies, the distance apart at the moment that light leaves one headed for the other, would indicate. The farther apart the galaxies were initially, the longer it will take to catch up.

The time the light has been traveling to get from one galaxy to the other is called the “lookback time”. This is not the same as the actual current distance, which is much greater. For a lookback time of about 13 billion years, that would correspond to a current distance of about 40 billion light years. This also means that if there has not been enough time yet in the age of the universe for light from an object to catch up to an observer, that object is outside the visible universe for that observer. Our visible universe, therefore, corresponds to the age of the universe, 13.78 billion years, which equals a current distance of 41.6 billion light years. Actually I think it’s a bit less than this, the age at which it became transparent to light.

Beyond 41 billion light years, or a look back time of 13.7 billion years, there is more universe but it is outside our visible universe. Interestingly, as the universe expands the percentage of the total universe that is within the visible range of any observer will decrease. Eventually future astronomers will only be able to see our local group of galaxies and that’s it. This will happen in about 100 billion years. What is the percentage of the total universe that is currently visible? We have to make some cosmological assumptions to give a precise answer, but according to some estimates only about 1.5%.

There is a lot more complexity to this question, but this is a quick summary to at least give a basic idea of the structure of the universe over time. The currently view is also evolving as we gather more information. It was only relatively recently that astronomers realized the expansion of the universe is accelerating, for example. So the precise numbers are likely to change, but these basics are fairly reliable.


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