# How did time behave while the universe expanded so rapidly?

• noxic
In summary, astronomers use two concepts: universe time and proper distance. Universe time is the time kept by the synchronized clocks of stationary observers... or the universe at the moment it was frozen in its expansion. Proper distance is the distance at a given instant which you'd measure by any conventional means (e.g. radar but also tape measure if you had one long enough and could stretch it out that far) if you could freeze the process at that instant. Relative motion messes up distance comparisons so they also have an idea of observer at CMB rest.

#### noxic

Didnt know where else to put it..

How did time behave while the universe expanded so rapidly in the beginning?

Was time fixed from then on out?

How fast did the universe expand? And does the theory of time going slower at super-high speeds apply to the speed of which the universe expanded in any for-physics favorable way?

sry bad english lol xD I am also much better in conversational talks like this. mostly.

Thanks

What do you mean with "behave" and "fixed"? How does time "behave" now?
How fast did the universe expand?
Very fast, I guess publications about that have numbers.
And does the theory of time going slower at super-high speeds apply to the speed of which the universe expanded in any for-physics favorable way?
No. The expansion was not something moving through space, it was space itself expanding.

can space expand faster than c? after all it is the thing that imposes the limit c in the first place.

For every reasonable definition of an expansion speed in terms of a velocity: yes it can. In particular, the distance between two distant objects can increase faster than c.

Superposed_Cat said:
can space expand faster than c? ...

Yup. Most of the galaxies we can see are far enough away that the distances to them are growing faster than c.

Since space isn't a material substance, the practical meaning of "space expanding" is distances increasing. (There are some technical details about how you define distances in expanding geometry. Ask about details if you're curious. Think of the distance at a given moment between two galaxies or two observers as what you would measure if you could freeze the expansion process at that moment to give yourself time to measure, e.g. to send a light flash or radar signal etc.)

If you want to get an idea of the speeds of distance growth click on this
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html

Vnow and Vthen are speeds of distance growth given as multiples of the speed of light.

So look in the S column and go down to S=3.2, for example. That refers to a galaxy whose light is coming into us, today, with its waves stretched out 3.2 times longer than when they started on their way to us (back in year...)

Look along the S=3.2 row and you will see what the distance to it is NOW and what the distance was THEN. And you can see that the now distance is growing at 1.27c and the distance it was back then was growing at 1.30c when the light was emitted.

An S=3.2 galaxy is fairly representative of what we can see. Most galaxies we can are farther way than that and have a larger wave stretch factor, i.e. S > 3.2, so would be higher up in the table and have faster distance growth speeds. You can add rows to the table by increasing the number of steps from 10 to 20, say, and pressing "calculate" again.

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1 person
marcus said:

Superposed_Cat said:
Good.
So click on http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html

This implements the standard model of the cosmos that people use, with the latest parameters that were announced by Planck Mission in March 2013.

The great bulk of the galaxies we can see, their light is coming to us stretched by a factor between 3 and 10. So look at the two rows of the table S=10.3 and S=3.2.

You can see that S=10.3 corresponds to the light being emitted back in year 522 million. Galaxies were only just FORMING back then. We don't see so many stars or galaxies back earlier than that.
That's why we can take S=10 as a practical cutoff when we are talking about distances to observable galaxies and the speeds they are increasing.
==============

Astronomers have a concept of "universe time" that the cosmic model runs on.
And they use a type of distance called "proper distance" which I referred to earlier where you imagine freezing expansion process at a given moment, so you can measure.
The proper distance at a given instant is what you'd measure by any conventional means (e.g. radar but also tape measure if you had one long enough and could stretch it out that far) if you could freeze the process at that instant.

Relative motion messes up distance comparisons so they also have an idea of observer at CMB rest. You know the ancient light of the CMB (cosmic microwave background). For an observer at rest it is the same temperature (within a thousandth of a percent) in all directions. No doppler hotspot. The solar system is moving relative to CMB at speed of 370 km/s so we see a doppler hotspot and our observations have to be corrected for that motion if we want them to be from the standpoint of a stationary observer. Universe time is the time kept by the synchronized clocks of stationary observers out in the empty intergalactic wherever. The equation model cosmologists use is designed to run on that time. Hope that's not too abstract. When you are modeling the cosmos it's good to have a concept of time that is not influenced by any peculiar local circumstances.

Did you have any trouble with the cosmic history table at
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html ?

The S = 1090 row refers to the CMB. It is light from hot gas that comes to us with wavelengths stretched by factor of 1090. It was emitted around year 380,000 which the table rounds off to year 0.0004 billion.
You can see from the table how far that matter (which was hot gas at the time and emitted the CMB ancient light that we are seeing) WAS at the time it emitted the light. And you can see how far that matter IS NOW. Presumably that matter has long since cooled and condensed into the usual stuff, stars, dust clouds, galaxies etc. And the people there are seeing the CMB ancient light made by OUR matter back in year 380,000, if they look in our direction with the appropriate instruments.

And you can see how fast the distance to the CMB matter is growing, as a multiple of c. Is growing now and was growing when it emitted the light.

If you wish, look at the table and see if you have any questions about the S=1090 row---the top row---or about the two rows S=3.2 and S=10.3.

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How did time behave while the universe expanded so rapidly in the beginning?

As far as is known, from the moment of the big bang, time proceeds at a fixed steady pace, same as today. That same rate of the passage of time is the one used to describe the rate of change of distance then and now...the expansion velocity, the expansion distance per unit time.

And does the theory of time going slower at super-high speeds apply to the speed of which the universe expanded in any for-physics favorable way?

No, 'slower time' at super high speeds is an aspect of special relativity where two observers at different relative speeds may experience differences in elapsed times when they stop and make comparisons. Individually, each local clock ticks at it usual rate. It's only when they stop and make a comparison that a difference may be observed. One example of this is the 'twin paradox'.

It is not directly related to early cosmological expansion; Today distances are still increasing over vast cosmological distances faster than light...as Marcus explains above. And today our time still ticks at the same steady pace as far as we know.

Keep in mind that, under GR, time is not well defined globally, only locally. In other words, there is no universal clock. Some would argue that suggests time is not even a fundamental property of the universe, but, an emergent one.

Or that there are many times, and Nature has no single favorite. I think that's right.

Cosmologists do find a particular one (Friedmann time aka Universe time) especially convenient, but that hardly means we should be using it for every application.

So when we say there has been 13.8 bio years since the big bang what are we really saying? 13.8 bio years from our perspective but not universally?

It's convenient to remember two things affect the relative passage of time: speed and gravity. In special relativity, the relative speed between observers can lead to differences in elapsed time. This is because spacetime is a dynamic entity, observations change according to relative velocity. [You can think of this as analogous to the components of an electromagnetic wave: relative velocity affects how much E and how much M one observes.] In general relativity, the passage of time is also affected by differences in gravitational potential.

So in Newtonian physics time was fixed, in SR it varies, in GR the idea is 'weakened' further. So how do we measure cosmological time, how do we set some standard for the whole universe?

So when we say there has been 13.8 bio years since the big bang what are we really saying? 13.8 bio years from our perspective but not universally?

roughly yes, but that's not quite correct. Marcus already posted the correct answer above:

Astronomers have a concept of "universe time" that the cosmic model runs on...
The solar system is moving relative to CMB at speed of 370 km/s so we see a doppler hotspot and our observations have to be corrected for that motion if we want them to be from the standpoint of a stationary observer. Universe time is the time kept by the synchronized clocks of stationary observers out in the empty intergalactic wherever. .

So the 13.8 B years as an age of the universe uses as a reference standard being at rest with respect to our local background radiation, the 'CMBR', no 'hotspots' in different directions; that's not dramatically different than direct observations from Earth because we move so slow relative to the CMBR.

Why such a 'crazy' standard?...because the CMBR is everywhere, it's universal, so provides a type of reference you can go anywhere in the universe to use. Even really distant galaxies while moving very fast relative to us, have the same standard locally...they can take measures and correct them to be at rest with respect to their local CMBR, just like we do.

As Marcus post explains if you think about it: before two very distant observers in the universe can establish a common measurement scheme for time, they have to agree on relative gravitational potential [open empty space] and some notion of relative speed [being at rest with respect to the universal CMBR].

I saved a couple of descriptions from experts in these forums:
[Same ideas, different words]

Age of the universe

Donis:
It's the proper time that would elapse since the Big Bang {say,for example an observer whose current spatial location is Earth} but who has always seen the universe as homogeneous and isotropic. Such observers are called "comoving" observers. We don't see the universe as isotropic on Earth: we see a dipole anisotropy in the CMBR, for example, indicating that we are not "comoving" observers, even when the effects of the Earth's rotation and orbit about the Sun are corrected for.

Crowell:
There is not just one such frame for the whole cosmos. There is one such frame for every point in the cosmos. Global frames of reference don’t exist in GR.
But In cosmology, we use the relic radiation as a convenient reference.

Solar system speed is on the order of 1/1000 of speed of light.

The special relativistic effect on clocks, for a platform moving 1/1000 c is what?
1/(1 - 1e-6)^.5 = 1.0000005.

I don't think we have to worry about gravitational effect. It would not be any more significant.

skydivephil said:
So when we say there has been 13.8 bio years since the big bang what are we really saying? 13.8 bio years from our perspective but not universally?

Naty already answered. But I just want to mention that you are asking about a difference that might arise in the sixth or seventh decimal place. We don't measure cosmic model parameters with such fine precision, so our figure of 13.8 billion years is only at best 3-figure accurate.

13.8 billion years is calculated from the Friedman model, so you could say it is universe time. But you could just as well say that 13.8 is also the age "from our perspective".

Or from the perspective of any other platform which (like us) is only moving on the order of 1/1000 c relative to CMB and is not significantly deep down in some gravity well.

13.8 billion hears is something that observers in other parts of the universe (little green men etc) could measure parameters and derive and get essentially the same answer (except for units conversion).

I'm assuming they are our contemporaries, that is if they used the same Kelvin temperature scale or knew how to convert units, they could measure the same temperature of the CMB. My idea of contemporaneous little green men is that they see the CMB same as us and would measure the same temperature (except for units conversion). Earlier LGMs would see a warmer CMB and later LGMs would see a cooler. There has to be some operational meaning of contemporaneity. If you can think of a better, let me know

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Looking at the table, taking for example the row S = 33, the V then velocity (8+)c would seem to require some new expansion process with some new physics - as would all the theoretical hi rates of expansion following the de coupling era -

We have exponential acceleration for the time after 5 or so billion years following the decoupling era and we have inflation as a theory for exponential expansion in the extreme of the early universe, what accounts for the large velocities following inflation?

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yogi said:
Looking at the table, taking for example the row S = 33, the V then velocity (8+)c would seem to require some new expansion process with some new physics - as would all the theoretical hi rates of expansion following the de coupling era -

I'm not sure I understand why you think "new physics" is needed. The expansion speeds come out of 1922 physics of Friedman equation which was derived from 1915 GR equation. IOW the expansion speeds come out of vintage 1915 physics.

When you say "looking at the table" I think you mean the default table you get when you open Jorrie's calculator. You could try playing around with the range of the table (upper and lower S limits) and the number of rows. It makes lots of different tables. But anyway I think what you are looking at is this:
$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 0.001&1090.000&0.000373&0.0006&45.332&0.042&0.057&3.15&66.18\\ \hline 0.003&339.773&0.002496&0.0040&44.184&0.130&0.179&3.07&32.87\\ \hline 0.009&105.913&0.015309&0.0235&42.012&0.397&0.552&2.92&16.90\\ \hline 0.030&33.015&0.090158&0.1363&38.052&1.153&1.652&2.64&8.45\\ \hline 0.097&10.291&0.522342&0.7851&30.918&3.004&4.606&2.15&3.83\\ \hline 0.312&3.208&2.977691&4.3736&18.248&5.688&10.827&1.27&1.30\\ \hline 1.000&1.000&13.787206&14.3999&0.000&0.000&16.472&0.00&0.00\\ \hline 3.208&0.312&32.884943&17.1849&11.118&35.666&17.225&0.77&2.08\\ \hline 7.580&0.132&47.725063&17.2911&14.219&107.786&17.291&0.99&6.23\\ \hline 17.911&0.056&62.598053&17.2993&15.536&278.256&17.299&1.08&16.08\\ \hline 42.321&0.024&77.473722&17.2998&16.093&681.061&17.300&1.12&39.37\\ \hline 100.000&0.010&92.349407&17.2999&16.328&1632.838&17.300&1.13&94.38\\ \hline \end{array}}$$

Just to get some practice reading the different columns of the table. It starts in year 373,000. And something which was then 42 million LY from here, from the matter that eventually became the solar system and us, would have been receding at 66 times c. Do you see that information in the top row of the table? Let us know if you anything needs clarification, about what the columns represent etc. Distance growth is not subject to the 1905 special rel speed limit----which applies to relative motion in a local frame. Distances can grow superluminally without anybody getting anywhere, and without anybody catching up to or passing a photon of light Distance growth is geometry change and you can have everything just getting farther apart without anything approaching a destination.

So there can be superluminal increase in distances without "exponential expansion". It doesn't need to be explained. For instance in 1922 Alex Friedman found solutions of Einstein GR equation that had superluminal expansion WITHOUT ACCELERATION. Friedman solutions did not have inflation and did not have a cosmo constant (aka "dark energy") to cause late-time acceleration.

Superluminal distance growth is very normal and usual without anything fancy. It is a feature of the cosmic models that prevailed for most of the 20th century.

We have exponential acceleration for the time after 5 or so billion years following the decoupling era and we have inflation as a theory for exponential expansion in the extreme of the early universe, what accounts for the large velocities following inflation?
Ordinary GR accounts for them. I don't understand what you think is remarkable or puzzling.

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So there can be superluminal increase in distances without "exponential expansion".

yes, and superluminal expansion continues right now...as far as if understood, always has and always will...

Thanks Marcus. it follows that the early velocity must be large if the density is large and q is not zero. I recall going through the exercise with the Friedmann equation years ago, but forgot how large the early velocities turn out to be. And yes, I was looking at the default table and reading across the s = 33.015 row.

yogi said:
... I recall going through the exercise with the Friedmann equation years ago,... And yes, I was looking at the default table and reading across the s = 33.015 row.

Glad to meet you. Since you were trying out the calculator on your own initiative (as well as having a long-standing interest) you might like another feature.

The calculator let's you select which columns appear in the table, from a "column selection" menu.
And one option tracks the recession speed of a particular sample galaxy as it changes over time.
Imagine a galaxy which is now at a distance of 14.4 Gly, which is the present Hubble radius R0. By definition, its recession speed is exactly c. We can tabulate its recession speeds at past and future times by selecting the R0da/dt column. Here the timederivative of the scale factor a(t), namely da/dt, is denoted a'. So the recession speed history column is labeled "a' R0" Speeds are given in c units, as multiples of the speed of light, so the present value will be 1.

I'll select that column and deselect the event horizon distance Dhor (which is another topic you might want to ask about another time) so the table won't be too wide. I'll also narrow the S range so we are not looking so far back in past and so far into future. Let's set Supper = 10, and Slower = 0.5. So the table will start around the time the first galaxies formed and distances were 1/10 what they are today, and it will go into future only to when distances will be twice their present size. (S is the reciprocal of the scale factor).

$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&a'R_{0} (c)&V_{now} (c)&V_{then} (c) \\ \hline 0.100&10.000&0.5454&0.8196&30.684&3.068&1.76&2.13&3.74\\ \hline 0.133&7.499&0.8403&1.2607&28.148&3.754&1.52&1.95&2.98\\ \hline 0.178&5.623&1.2934&1.9349&25.226&4.486&1.32&1.75&2.32\\ \hline 0.237&4.217&1.9871&2.9549&21.870&5.186&1.16&1.52&1.76\\ \hline 0.316&3.162&3.0412&4.4626&18.045&5.706&1.02&1.25&1.28\\ \hline 0.422&2.371&4.6149&6.5792&13.761&5.803&0.92&0.96&0.88\\ \hline 0.562&1.778&6.8835&9.2557&9.124&5.131&0.87&0.63&0.55\\ \hline 0.750&1.334&9.9580&12.0787&4.404&3.302&0.89&0.31&0.27\\ \hline 1.000&1.000&13.7872&14.3999&0.000&0.000&1.00&0.00&0.00\\ \hline 1.334&0.750&18.1647&15.8793&3.810&5.080&1.21&0.26&0.32\\ \hline 1.633&0.612&21.4488&16.4816&6.037&9.860&1.43&0.42&0.60\\ \hline 2.000&0.500&24.8287&16.8396&7.910&15.820&1.71&0.55&0.94\\ \hline \end{array}}$$

You can see that the recession speed (of our sample galaxy that is now at distance 14.4 billion LY from us) starts out DECLINING and hits a low point of about 0.87 c (in the row of the table corresponding to year 6.88 billion) and then begins to increase.
Sometime around year 7 billion is when ACCELERATION kicked in.
You can add more rows to the table to increase the resolution and narrow it down more precisely.
All the other cosmic scale distances behave proportionally (in synch with the scale factor a(t) ) so they all start accelerating at the same time. If you increase the number of steps (ie. the number of rows of the table) you can get a more accurate estimate of when it was that slowing recession gave way to speeding up.

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