What the Hubble constant must be set to if Univ is flat

[robertjford80]

What must the Hubble constant be if the Universe is flat. At the Lamda CDM article on wiki it says 70.4 km/s mpc. I'm not sure if that's what it must be if the universe is flat or if that's what experiments have measured it to be, I'm 99% sure that it's the former but I want to be 100% sure. Also I've read the wiki article on the Hubble constant and all the various experiments that have been done to measure it so you don't need to tell me that.

 

[Chronos]

The Hubble constant is a measured, not theoretical value. We currently cannot derive it from first principles.

 

[robertjford80]

Could you give me some more info. I'm pretty sure what determine if the universe is flat is the density, but I forget what the equation is that determines omega.

 

[Chronos]

Google on critical density of the universe.

 

[robertjford80]

it says a'/a is the Hubble parameter, and the friedman equation is

(8piG rho + lamda c^2)/3 = (a'^2 + kc^2)/a^2

So I would think that

(8piG rho + lamda c^2)/3 - kc^2/a^2 is what the Hubble constant would have to equal if the universe is flat, since I'm pretty sure the friedmann equation must equal 1 for a flat universe.

 

[GeorgeDishman]

it says a'/a is the Hubble parameter, and the friedman equation is

(8piG rho + lamda c^2)/3 = (a'^2 + kc^2)/a^2

So I would think that

(8piG rho + lamda c^2)/3 - kc^2/a^2 is what the Hubble constant would have to equal if the universe is flat, since I'm pretty sure the friedmann equation must equal 1 for a flat universe.

The parameter 'k' measures the curvature. For a flat universe, you only need k=0. The scale factor and hence the Hubble Constant at any epoch then depend on the various densities (matter, radiation, dark energy).

http://en.wikipedia.org/wiki/Friedmann_equations#The_equations

 

[robertjford80]

am I right that a'^2/a^2 is the Hubble parameter? I specifically remember reading in Sussking's the Cosmic Landscape that the Hubble constant must be a certain ratio in order for the universe to be flat. He writes:

Astronomers have been closing in on the value of the Hubble constant for almost eighty years with ever more sophisticated instruments. It now seems very unlikely that it can be small enough to allow the universe to be closed. If this were the end of the story, then we would have to conclude that the cosmic mass density was insufficient to close the universe — but we’re not done yet.

 

[twofish-quant]

What must the Hubble constant be if the Universe is flat. At the Lamda CDM article on wiki it says 70.4 km/s mpc.

It doesn't have to be anything in particular. Once you have dark energy, then if you change hubble's constant, then you can change the dark energy component and still end up with a flat universe.

I'm not sure if that's what it must be if the universe is flat or if that's what experiments have measured it to be, I'm 99% sure that it's the former but I want to be 100% sure.

It's a direct measurement. Also with our other observations we can tell that the universe as is flat within observational limits, but all of that are measurements.

 

[twofish-quant]

I specifically remember reading in Sussking's the Cosmic Landscape that the Hubble constant must be a certain ratio in order for the universe to be flat.

Once you add in dark energy, you have an extra variable that you can tweak.

Also in the 1970's the fact that the universe seems close to flat was considered a "problem" but flat universes pop out naturally from inflation so it's no longer considered weird or unusual that the universe is flat.

The other thing was that there's been a lot of talk about the anthropic principle, but the experience with inflation points out that one shouldn't go "anthropic" too early. In the 1970's, there were a lot of "weird coincidences" that suggested fine tuning, but inflation solved most of them without the need to go anthropic.