Hubble extracted Hubble's law from what we now call a Hubble diagram as aforesaid in subsection Edwin Hubble and the Expansion of the Universe.

See the example Hubble diagrams in the figure below (local link / general link: hubble_diagram.html).

Hubble's law shows that there is a general growth of distances between extragalactic objects when the redshift of remote objects is correctly interpreted as the cosmological redshift.

As mentioned above, this general growth is called the expansion of the universe.

Question: In the Hubble diagram above, there is a scatter about the straight line.
1. This is caused by observational error.

2. The gravitationally bound systems are NOT internally expanding and their components have rather random peculiar velocities which add Doppler shifts to the cosmological redshift (due to the expansion of the universe) to create net redshifts. The redshift velocities thus have deviations from the straight line.

3. The gravitationally bound systems as wholes have their own rather random peculiar velocities which add Doppler shifts to the cosmological redshift (due to the expansion of the universe) to create net redshifts. The peculiar velocities thus have deviations from the straight line.

4. The recession velocity is NOT exactly linear as a function of distance (i.e., true physical distance that can be measured with a ruler at one instant in cosmic time). There are deviations from linearity.













The first 3 answers are all partially right. Together they constitute what we believe to be the right answer.

Distances measured at one instant in cosmic time are called cosmological physical distances or, just physical distances for short.

They are just what one ordinarily means by distance.

But cosmological physical distances are NOT direct observables, except asymptotically as cosmological redshift z becomes small.

In the multiverse paradigm, these models only apply in the deep interior of our pocket universe.

We discuss cosmological models below: see section Einstein, General Relativity, and the Einstein Universe and subsequent sections.

But we CANNOT verify Hubble's law for large physical distances by direct observations.

This is because the at-one-instant-in-cosmic-time recession velocities and physical distances are NOT direct observables beyond about the z ≤ 0.5 local universe. They are dependent on the cosmological model adopted, and so have that model's uncertainty.

We CANNOT observe galaxies and other remote objects (e.g., quasars, supernovae, and gamma ray bursts) at the current cosmic time, but only as they were in the past.

Cosmic time is the time in which the expanding universe stays homogeneous and isotropic.

Also all clocks participating in the mean expansion of the universe stay synchronized with cosmic time.

How the universe evolves with cosmic time is, of course, dependent on the cosmological model adopted.

Well the universe evolves in only one way with cosmic time, but how understanding of how it evolves is model-dependent---but you knew this already.

Cosmic time does NOT flow very differently from local universe times (including Earth-based times) since the deviations of local universe motions from the mean expansion of the universe are rather small.
If it's 10 am here, it's 10 am at cosmological redshift z = 10 evolved to the current cosmic time give or take 10 Myr or so.

So we think we can measure cosmic time accurately locally, but we don't know what the cosmic time is for cosmologically distant objects AT THE TIME light was emitted from them independent of the cosmological model adopted.

Question: Hubble's law implies that:
1. the Milky Way is the center of cosmic expansion.
2. the expansion is a general scaling up of distances between non-gravitationally bound systems in the observable universe. All observers participating in the mean expansion of the universe located in bound systems see the same expansion behavior on average. Such ideal observers are approximated by those in the gravitationally bound systems.












Well either answer could be right logically speaking.

But answer 2 is so overwhelmingly more acceptable that we must accept it as right.

There may be a center of expansion and something to expand into in some sense if we live in a pocket universe, but we have NO where that center is and where the outside is if they exist.

We discuss this point again in subsection Is There a Center of Expansion and Something to Expand Into?

We have no observational evidence or broadly accepted theoretical reason for thinking it is false. In fact, as far as we can tell it seems true.

File: Cosmology file: expanding_universe_further_explication.html.