Ship & Wormhole: Exploring Physics Homework

[charlie05]

Hello everybody,

I am sorry, but I need your help with my physics homework. I will be very happy if somebody could help me.

1. Homework Statement
Task: The ship passed through the wormhole. The “new” temperature of cosmic microwave background is T = 0,3 K. The curvature of the universe is, same as before, negligible and the "old" Hubble’s parameter was H₀ = (67,7±0,5) km · s⁻¹· Mpc⁻¹. The "new" value of Hubble’s parameter is H = (57 ± 4) km · s⁻¹ · Mpc⁻¹. We suppose that the ship is still in our universe.

Hint: ρ_crit = 3H² / 8πG; e^Ht

Homework Equations

a) Does the ship move to the past or to the future?
b) Does the ship move also in place? And for how far?
c) Specify the ratio of space distance (against the present).
d) Verify by calculation that the ship is really still in our universe.
e) For how many years the ship "travel"?

The Attempt at a Solution

a) I think that ship moved to the future, because “new” temperature of cosmic microwave background is T = 0,3 K while now this temperature is about 2,7 K. The whole universe is getting colder so for that reason I think that ship moved to the future.

In other tasks I don’t know how to solve. I think that in one task I will compare the critical density which I calculate by formula in hint.

I want to thank you in advance for your help and willingness!

 

[Orodruin]

What are your thoughts on the remaining questions?

b) How would you tell if you have moved in space?
c) How do some observables scale with the scale factor?
d) What would the universe look like if evolved to this temperature?
e) How does time relate to the expansion?

 

[charlie05]

At first, I would like to thank you for your interest. My English is poor, so I hope that I understand your questions well.

b) I think that measurement of position is very difficult because we can’t measure the distance between the ship and some object because of expanding the universe. Maybe we can calculate the distance which the universe expands for the time the ship travel. Or we can use some constant – for example speed of light which is constant in both time-spaces.

c) I think we can also use the distance which the universe expands for the time the ship travel. The “old” space-time distances will be “1” and “new” distances will be “1+distance”. Scale factor will be bigger than 1. Or it can be a ratio of Hubble’s parameters.

d) The universe will be much bigger because its temperature will be smaller, and it will be closer to its end.

e) Time is dilated by special theory of relativity, so on the edges of universe should be same time as was during the Big Bang.

At the end I want to thank you for your help and mainly for your patience – and sorry for my maybe absurd answers.

 

[Orodruin]

b) I think that measurement of position is very difficult because we can’t measure the distance between the ship and some object because of expanding the universe. Maybe we can calculate the distance which the universe expands for the time the ship travel. Or we can use some constant – for example speed of light which is constant in both time-spaces

What are the basic assumptions behind the FLRW universe?

c) I think we can also use the distance which the universe expands for the time the ship travel. The “old” space-time distances will be “1” and “new” distances will be “1+distance”. Scale factor will be bigger than 1. Or it can be a ratio of Hubble’s parameters.

There is no such thing as a "distance which the universe expands". How is the scale factor related to redshift?

d) The universe will be much bigger because its temperature will be smaller, and it will be closer to its end.

What will the universe being much bigger mean for the different energy components of the universe? How should they evolve to the new time and did they do so?

e) Time is dilated by special theory of relativity, so on the edges of universe should be same time as was during the Big Bang.

There are no edges of a FLRW universe. This answer is unfortunately completely unrelated to the question. The question is how the scale factor should behave as a function of time. If you know that you should be able to find out the time taken to arrive at the new state of the universe.

 

[charlie05]

What are the basic assumptions behind the FLRW universe?

The universe is homogeneous and isotropic, the velocity of objects measured in a particular location will grow linearly with distance.

There is no such thing as a "distance which the universe expands". How is the scale factor related to redshift?

The distance can be measured with a red shift, when moving to the future, it should be less than 1.

What will the universe being much bigger mean for the different energy components of the universe? How should they evolve to the new time and did they do so?

There will be less matter in the universe, the mass density will be lower.

There are no edges of a FLRW universe. This answer is unfortunately completely unrelated to the question. The question is how the scale factor should behave as a function of time. If you know that you should be able to find out the time taken to arrive at the new state of the universe.

Dependence of the length scale on time - Fridman equations?

 

[charlie05]

Temperature dependence of CMB on time: Tr=2,7(1+z)...0,3=2,7(1+z)...z= -0,88...red shift afrter wormhole?

 

[Orodruin]

The universe is homogeneous

So what does ”homogeneous” mean?

The distance can be measured with a red shift, when moving to the future, it should be less than 1.

What shouldbe less than one?

There will be less matter in the universe, the mass density will be lower.

How much lower? How would it impact the cosmological densities and, in turn, the Hubble parameter?

Dependence of the length scale on time - Fridman equations?

Yes. So solve them.

 

[charlie05]

So what does ”homogeneous” mean?

The universe is the same everywhere. It is the same in all directions, it has the same average density everywhere, the same Hubble constant, the same chemical composition, the same temperature CMB, is the same old.

What shouldbe less than one?

I think z...red shift, z will be for the future less than 1.

How much lower? How would it impact the cosmological densities and, in turn, the Hubble parameter?

Will the mass be less in the ratio of Hubble constants? H/H0 ?

Yes. So solve them.

The universe with predominant energy...a(t) = e expHt
a(t0)=e exp H0t0 ...a(t) = e exp Ht...contribution a(t)/a(t0) = e exp Ht/e exp H0t0 ?

 

[Orodruin]

The universe is the same everywhere.

So what does this imply for the possibilities of telling where you are?

I think z...red shift, z will be for the future less than 1.

What is z today?

Will the mass be less in the ratio of Hubble constants? H/H0 ?

You need to scale each energy component separately. I.e., you need to look at the current energy densities and evolve each appropriately. The universe today does not contain matter only.

The universe with predominant energy...a(t) = e expHt
a(t0)=e exp H0t0 ...a(t) = e exp Ht...contribution a(t)/a(t0) = e exp Ht/e exp H0t0 ?

It also has a significant amount of matter that will affect this.

 

[charlie05]

What is z today?

Today is z=0

 

[charlie05]

So what does this imply for the possibilities of telling where you are?

Can I change the position to determine by changing the density of the universe - the density reduction is proportional to the third magnification of the distance enlargement?
densityof matter(t) = density of matter(t0)/a³(t)

 

[Orodruin]

Can I change the position to determine by changing the density of the universe - the density reduction is proportional to the third magnification of the distance enlargement?
densityof matter(t) = density of matter(t0)/a3(t)

I am sorry, but I do not see how this would be relevant to determine where in the universe you are.

Today is z=0

Which means that when the universe has grown, the redshift will be ...

 

[charlie05]

I am sorry, but I do not see how this would be relevant to determine where in the universe you are.

I can only specify the location in relation to other objects...
I can use the expansion of universe as scale factor...a=1/1+z

Which means that when the universe has grown, the redshift will be ...

Redshift will be less than 0...
Temperature dependence of CMB on time: Tr=2,7(1+z)...0,3=2,7(1+z)...z= -0,89...red shift after wormhole?
scale factor a= 1/(1-0,89) = 9,1...
the distance of two points at time t is relative to the distance at time t0: d(t)=a(t)d0...
- after the ship´s passing through the wormhole, the distance increased 9,1times?

 

[charlie05]

Please, is there at least a part of this reasoning right?