# What is the implication of an expanding universe on a small scale? [duplicate]

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As a layman I am struggling to understand what effects the fact that the universe itself expands has on distance, density etc. If the universe expands by a factor $k$, does that mean that the distances within the universe also expand (in other words, the time light needs to travel a given distance increases), or does distance "scale" with the expansion? More concretely, will an expanding universe mean that stars within a galaxy get further apart over time or that the distance of chemical bonds in atoms increase or even that e.g. the distance of where the strong force acts changes? If everything scales with the expansion, then all the constants of physics will remain the same, but then the density of the universe would also remain constant, because everything in it would scale up according to the expansion. But if this is not the case, would not certain physical constants have to change over time? Sorry if I am missing something trivial or obvious here.

## marked as duplicate by Rob Jeffries, Kyle Kanos, Ryan Unger, Martin, ACuriousMind♦May 28 '15 at 12:25

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• It depends on whether the expansion of the universe is accelerating, but I think we had these questions many times before. Did you search for other questions on this site before asking? – CuriousOne May 26 '15 at 17:16
• Yes, I did search. Also, I do not understand why this should be dependent on whether the expansion is accelerating? What I do not understand is basically if everything scales with the expansion or not: if yes, why was the universe denser in the initial seconds, if not, why/how not? – Johsm May 26 '15 at 18:29
• The universe was extremely dense in the beginning and its matter density is decreasing. The cosmological constant aka dark energy is an energy density term. If it's an actual constant, then it simply adds to the local zero point energy, which is irrelevant for all local physics. If it is increasing itself, then there is a local effect that would act like an internal pressure on objects that are bound (like galaxies, stars, atoms and even nuclei). In some models the increase of dark energy is going to be so fast in the future that it will rip all matter and all of spacetime apart. – CuriousOne May 26 '15 at 18:34
• The question (v2) is essentially a duplicate of physics.stackexchange.com/q/2110/2451 and links therein. – Qmechanic May 26 '15 at 18:57

## 2 Answers

First of all the current expansion rate of the universe is called the Hubble constant and the best current value for the Hubble constant is:

$67.80\pm 0.77\ km/s$ per megaparsec - (from the Plank satellite data).

Notice the units are a speed divided by a distance which means that the units are really $(1/time)$ and in inverse time units the value would be $2.2\times10^{-18}/s$ or $1/(14.4\ billion\ years)$ - note that this is approximately 1/(the age of the universe) since the age of the universe is 13.8 billion years - this is not a coincidence! The Hubble constant is not really a constant - it approximately scales like 1 / the age of the universe (if there were no Dark Energy), so at the time of the Big Bang the expansion rate would have approached infinity.

What the current value of the Hubble constant means is that if there are two galaxies that are 1 megaparsec apart and if these galaxies are not gravitationally bound to each other, then they would look like they are travelling apart at $67.8\ km/s$. To all observers this will look like a real relative velocity, but the cause is really the expansion of the space between the objects. As they get further apart they will appear to be travelling apart from each other at speeds above that value. For example, if you wait approximately 1.4 billion years (at $67.8\ kmn/s$) the distance would have increased to 1.1 megaparsecs and the apparent speed between the objects would have increased to approximately $1.1 \times 67.8 = 74.6\ km/s$

The expansion of space means that it will take light longer to travel between those objects. One megaparsec is 3.26 million light years and in those nominal 3.26 million years that it would take for light to travel from one galaxy to the other, the distances between the galaxies would have increased by about 737 light years - so it will take slightly more than 737 years on top of the 3.26 million years for light to travel from one galaxy to the other. Now this kind of expansion really only applies to very distant galaxies that are not bound in the same cluster or super cluster of galaxies.

Gravitationally bound systems, like our Solar system or the Milky Way will not be affected by this expansion of the universe. Since objects, like a meter stick, are electromagnetically bound together, they will also not be affected by this expansion. So stars within a galaxy will not get further apart and the size of atoms, molecules or meter sticks will not increase.

This expansion rate is very small. For example, if a meter stick was not electromagnetically or gravitationally bound, then at the end of a year the length of the meter stick would increase by about half the diameter of a helium atom - not very fast expansion! However this velocity scales with distance so if the Earth and the Sun were not graviationally bound then at the end of a year the distance between them would have increased by about 10 meters.

The reason the Earth Sun distance does not increase by 10 meters per year is because it takes energy to increase the size of the Earth's orbit. The "force" of the space expansion is simply not strong enough to impart that much energy to the Earth in a year. So even though the "space" between the Earth and Sun does expand by 10 meters in a year, the actual distance between the Earth and Sun does not change because of conservation of energy.

To setup a scenario where something like the Earth Sun distance would change we would need to go far into inter-galactic space - far from any galaxy so there is no significant gravitational field. If we took two masses equivalent to the mass of Deimos (the larger moon of Mars) and place them absolutely at rest relative to each other at a distance of 1 AU (the average Earth Sun distance). If there was no space expansion, then the two moons would start to fall towards each other. But the gravity is so weak that after a year they would only be 2 millimeters closer together (See calculation on Wolfram Alpha). With the current expansion of space they would actually end up 10 meters - 2 mm further apart at the end of a year.

The matter (and Dark Matter) density of the universe does decrease with time as the universe expands but this does not require physical constants to change with time. It is not clear to me why you think decreasing matter density would required physical constants to change with time.

• Thank you! I think my question then is: why and how is being electromagnetically or gravitationally bound relevant? Why is the distance between Sun and Earth NOT increasing by 10 meters? And why does the distance between galaxies increase? Even if they are far apart there is still some gravitational bond, or is there not? My confusion about the density comes from my failure to understand what actually is expanding and thus I do not know if e.g. atom would expand proportionally, thus taking the same proportion of the universe (same density) or not, taking a smaller proportion of the universe. – Johsm May 27 '15 at 12:25
• I updated the answer to explain this better. The density is the mass per unit volume and since the space is expanding, in a constant unit volume, there will be less mass since the mass will move out beyond the edges of the volume as space expands. – FrankH May 27 '15 at 22:33

If the universe expands by a factor k, does that mean that the distances within the universe also expand

It means the distances between the galaxies expands. Check out the raisin-cake analogy.

the time light needs to travel a given distance increases

That depends on the speed of light. See the Wikipedia variable speed of light article. Physicists such as João Magueijo at Imperial have proposed that the speed of light was higher in the early universe. I think it was slower myself, so the time light needs to travel a given distance decreases.

More concretely, will an expanding universe mean that stars within a galaxy get further apart over time

Generally no, because they're gravitationally bound.

or that the distance of chemical bonds in atoms increase

Generally no, because they're electromagnetically bound.

then the density of the universe would also remain constant

Conservation of energy is one of the most important tenets of physics. I do not believe in perpetual motion machines, and I do not know how the spatial energy-density of an expanding universe can remain constant.

But if this is not the case, would not certain physical constants have to change over time?

Yes. See the Relation to other constants section of the Wikipedia article. But note that this article isn't quite right. One section describes Einstein's VSL attempt in 1911. But see Einstein talking about the speed of light varying here. That was in 1920. Also see NIST and note that the fine-structure constant is a running constant:

"Thus α depends upon the energy at which it is measured, increasing with increasing energy, and is considered an effective or running coupling constant. Indeed, due to e+e- and other vacuum polarization processes, at an energy corresponding to the mass of the W boson (approximately 81 GeV, equivalent to a distance of approximately 2 x 10-18 m), α(mW) is approximately 1/128 compared with its zero-energy value of approximately 1/137. Thus the famous number 1/137 is not unique or especially fundamental".

It varies with energy. It isn't constant. Note that you can write it as $\alpha = \frac{e^2}{(4 \pi \varepsilon_0) \hbar c}$ and that whilst the NIST article talks about QED and "screened" charge, another tenet of physics is conservation of charge.