How Does Redshift and Lambda-CDM Model Explain the Universe's Expansion?

[Cajun]

I would first like to thank everyone on this website. So much knowledge i haven't been able to leave. I am researching the time line of the universe and have read a lot of great articles about red shift and the Lambda-CDM. I found a Cosmology Calculator where you can find out the distance in space and time by entering the red shift of galaxies. If i understand it corectly, I got to thinking what would it look like if i plotted the co-ordinates on a graph with the age of the universe on the Y axis and the proper distance on the X axis. What i came out with is a tear drop shape as time increases, the line of the tear drop would be our line of sight. Can anyone first tell me if this chart makes any sense or is an accurate representation of the distance of stars through time? If this chart does make sense, then why does the "tear" shape change around 1.75 redshift and what causes it? Is the Lambda-CDM consistent throughout time? Could the Lambda-CDM be wrong, an assumption based on missing evidence? Thanks in advance.

Example Redshift of 1.75 was 3825 Million Years Old and 5741 Million Light Years away from us.

 

[cepheid]

EDIT: Welcome to PF!

I would first like to thank everyone on this website. So much knowledge i haven't been able to leave. I am researching the time line of the universe and have read a lot of great articles about red shift and the Lambda-CDM. I found a Cosmology Calculator where you can find out the distance in space and time by entering the red shift of galaxies.

Which cosmological calculator are you looking at? Is it Ned Wright's?

If i understand it corectly, I got to thinking what would it look like if i plotted the co-ordinates on a graph with the age of the universe on the Y axis and the proper distance on the X axis. What i came out with is a tear drop shape as time increases, the line of the tear drop would be our line of sight. Can anyone first tell me if this chart makes any sense or is an accurate representation of the distance of stars through time?

I could use some more details about what quantity you are plotting on each axis, and how you are making the plots? Are you just taking sample data points for different redshifts from the cosmological calculator? Also, what values did you use for Ω_Λ, Ω_m, and H₀?

By the way, it makes more sense to talk about distant galaxies when talking about things that are moving away from us on cosmological distance scales. Everything that far away is in another galaxy, whereas all of the stars that you can see in the night sky are in our own galaxy, and these are not moving away from us due to the expansion.

If this chart does make sense, then why does the "tear" shape change around 1.75 redshift and what causes it? Is the Lambda-CDM consistent throughout time? Could the Lambda-CDM be wrong, an assumption based on missing evidence? Thanks in advance.

Again, I'd need more information about what exactly you are plotting before I could answer the first part of your question. As for the second part, ΛCDM is a cosmological model, one that happens to fit the observed data very well. It is possible that we're not seeing the whole picture, that we're missing something. But, given the success of the model, I think that most cosmologists would argue in favour of new evidence leading to minor refinements to the model rather than it being thrown out entirely.

 

[Cajun]

I used http://www.einsteins-theory-of-relativity-4engineers.com/cosmocalc.htm with the default values. I entered the Redshift of known galaxies and got the "Age of the universe then" and "Proper distance then" and plotted them out. 13666 Million years for the Y axis and 45908 Million Light Years for the top X Axis. For example Redshift of 1.75 was 3825 Million Years Old and 5741 Million Light Years away from us. If i do that for every redshift from the CMB (1090) to .01, i get a "Tear Drop" shape as our line of sight, does that have to do with expansion? Also thanks about the stars in the sky, ALL of those lights we see are in the milky way galaxy so we can't see stars outside of our galaxy without help?

 

[cepheid]

I understand what you are trying to do. You want to "sample" the distances to objects at various times in the past in order to get a sense of the expansion history of the universe. But this attempt is complicated by the fact that those sample galaxies at different redshifts don't all have the same proper distance from us now. So to select out the effects that are only due to expansion, the thing to do is to take the ratio of the proper distance then to the proper distance now. We call this ratio the scale factor: a(t). It represents by what factor the separation between any two objects will have changed between now and a time 't' in the past. Therefore, the evolution of this scale factor with time is a good representation of the dynamical history of the universe's expansion. So a(t) vs. t is what you want to plot.

Another way to think about it is this: the proper distance to a galaxy at time t is the distance to it that you would measure if you could somehow just "freeze" the expansion at time t and then go out with a measuring tape and figure out the distance between our galaxy and that galaxy. So, although it may be easy to understand conceptually, it is not something that we will ever be able to measure through astronomical observations. Another type of distance we can think of defining is the distance as measured on a grid that moves along with the expansion. This grid is an example of a co-moving coordinate system (since it moves along with the expansion) We call this the co-moving distance. It's handy because the co-moving distance to an object never changes (assuming that its motion relative to us is only due to the expansion of the universe). The reason for that is that the locations of our galaxy and that galaxy ON the expanding grid are fixed, so the number of grid lines between us and the other galaxy is always the same. Furthermore, we usually set the scale factor today (a(t₀) where t₀ is the age of the universe today) equal to 1 so that the co-moving distance to an object is just the proper distance to it now. To figure out the proper distance to an object at time t, we just take its co-moving distance and "scale it back" by the factor a(t). So the scale factor a(t) represents the ratio between the co-moving distance to an object and its proper distance at time t (EDIT: no, the reciprocal of that). Obviously, in the past, a < 1.

The good news is that you don't have to manually compute these ratios of proper distance/co-moving distance for every single redshift that you enter into the calculator. The reason is that there is a very simple relationship between the scale factor of the universe at time t and the redshift of light emitted by an object at time t:

a = 1/(1 + z)

(If you don't believe me, try it for z = 1.75. You should get a ratio of proper distance (then to now) of a = 0.363636, which is equal to 1/2.75). So, really, you just have to plot 1/(1 + z) vs t. The relationship between z and cosmic time implicitly contains the information you are looking for. You won't get a tear drop shape. For a universe with dark energy (Ω_Λ is not zero) you get a universe that will continue to expand forever, and that is accelerating. However, it was not always accelerating in the past (the curve has a weird bend in it, which occurs close to now).

Regarding stars in other galaxies: I think that we can see individual stars in very small, nearby dwarf galaxies that are essentially satellites of the Milky Way (e.g. the Large and Small Magellanic Clouds). But for even the nearest galaxy that is well outside the Milky Way's region of influence (Andromeda) the distance is too far for us to be able to resolve individual stars in that galaxy with the unaided eye.