About Hubble Radius (Radius of the Hubble sphere)

[Ricky2357]

I found the following definition for the Hubble Radius:

The radius of the Hubble sphere (Hubble radius) is defined to be the distance from a fixed point O (center of coordinate system) of an object moving with the cosmological expansion at the speed of light (with respect to O).

Mathematically, R=c(a/da) , c=speed of light , a=a(t) is the scale factor ,t is time.

How's this definition valid since the Hubble radius as defined depends on the moving object?

 

[Wallace]

It means that each observer (each origin O you choose to define) has a different 'Hubble sphere'.

 

[Chronos]

True, but, they are time limited. The Hubble bubble looks smaller to distant observers [speed of light thing].

 

[Wallace]

I'm not sure what you mean Chronos, the 'Hubble Bubble' doesn't 'look' like anything since it's just a theoretical construct, a useful term in distance measures, rather than a physical structure. I'm not sure what you are saying looks different to distant observers (or who they are distant from?) ?

 

[Ricky2357]

I found out that the Hubble sphere can also be defined as the sphere of center 0 (observer) and radius the distance that light can travel within the characteristic expansion time, that is the Hubble time : τ=1/H(t).
So R=c*τ. From the moment we entered the dust era, the Hubble sphere is the same as the particle horizon.

 

[Wallace]

But what is your question?

 

[Ricky2357]

Nothing, I believe it is clear now. Thanks for the help!

 

[Chronos]

Looks like everyone skipped out Wallace! My intent was merely to point out the Hubble Bubble looks the same to all observers. It looks 'smaller' to distant observers because the universe was younger when 'they' sent us the picture we just received.

 

[hellfire]

From the moment we entered the dust era, the Hubble sphere is the same as the particle horizon.

The Hubble sphere is much closer than the particle horizon. The Hubble sphere has a radius of about 13,700 Mly and the particle horizon is located at about 45,000 Mly. Both distances measured on the hypersurface of current time.