Hubble's constant, critical density, and length contraction thought experiments

[Olivia Grace]

Hi, I'm new to this forum, but saw that everyone was so kind and helpful, so was wondering if anyone could help me with a couple of things..

How does one calculate the age of the universe using Hubble's constant, if the constant is in km/s/Mpc?

Do we know the critical density of the universe? I always thought that experts had a few pretty good estimates, but then someone told me today that this wasn't true..

Does anyone know a thought experiment for length contraction that does not involve a train and a tunnel? For some reaosn this thought experiment always confuses me...I knew one once with a rocket traveling to alpha centauri at 0.8c, but am not sure if this is allowed if it assumes time dilation..

If anyone could help I would be so grateful! I have an exam on all of this tomorrow!

 

[Olivia Grace]

For the age of the universe, I've tried multiplying the constant by 1x10^3, then changing the Mpc into light years..is this correct?

 

[P3X-018]

If H is the Hubble constant, then the age of the universe can be determined as the inverse of the constant, that is 1/H.
EDIT: But this is ofcourse a very crude estimation.

 

[Logarythmic]

The age depends on what model you are using. For example, the age using the Einstein-de Sitter model is given by

$$\frac{2}{3}H^{-1}$$.

The critical density is also dependent on the choice of model so no one "knows" this density.

 

[Dick]

The Hubble constant has the units of 1/sec. An estimate of the age of the universe is given by 1/H. The exact age depends on your exact model of the universes evolution. E.g. assuming it is matter dominated (should be a good approximation) we get 3/(2*H). We know the critical density exactly as well as we know H. They define each other. What we don't know is the real density. A difference between these two would indicate the universe is spatially curved to a significant degree. Current consensus is that it is not.

 

[Dick]

The Hubble constant has the units of 1/sec. An estimate of the age of the universe is given by 1/H. The exact age depends on your exact model of the universes evolution. E.g. assuming it is matter dominated (should be a good approximation) we get 3/(2*H). We know the critical density exactly as well as we know H. They define each other. What we don't know is the real density. A difference between these two would indicate the universe is spatially curved to a significant degree. Current consensus is that it is not.

 

[Olivia Grace]

Thanks for your help so far! My problem is determining the age of the universe from the units I have been given, km/s/Mpc...how does one change these units ino units suitable for the 1/H method?

 

[Dick]

1 Mpc=3*10^19 km. Put this in and cancel the km.

 

[Olivia Grace]

Hey thanks!

 

[Logarythmic]

We know the critical density exactly as well as we know H. They define each other.

We do not know H exactly, but it is estimated to be around 70 km/s/Mpc with an error of ~10%.

 

[Dick]

My point was that the uncertainty in H is "exactly the same" as the uncertainty in the critical density. Not that either was measured exactly. Thanks for the clarification.