Expansion of the Universe: Distinguishing No.1 & No.2

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The discussion centers on two types of cosmic expansion: Expansion No.1, linked to the Big Bang and characterized by initial rapid inflation followed by deceleration, and Expansion No.2, associated with the current acceleration of the universe due to dark energy. Observations of cosmological redshifts provide evidence for Expansion No.1, indicating a younger universe as we look deeper into space. However, the conversation critiques the conflation of these expansions, arguing that examples of redshift are often misinterpreted as evidence of ongoing acceleration rather than reflecting the initial deceleration post-Big Bang. The need for clear evidence supporting the acceleration of the universe at around 7 billion years is also emphasized, with references to external sources for further validation.
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Expansion of the universe: Aren't there 2 distinct expansions we are talking about?

Expansion No.1: This is caused due to Big Bang. Singularity expanded with huge acceleration. Also called inflation. With time, this expansion decelerated. It is observed in the cosmological redshifts. The deeper we look in space, the deeper into past we are looking. So, as we look deeper, we witness a younger universe. A universe as was sooner after big bang. Here, we see matter with large cosmological redshifts,up to 1089 in case of the Cosmic Microwave Background, which happened around 378000 years after Big Bang. The cosmological redshifts in case of very distant galaxies(currently received light from these has traveled 13.1 billion years) are 8, and this happened 652 million years after Big Bang. Closer galaxies(currently received light from these has traveled 11.5 billion years) show cosmological redshift of 3.

Expansion No.2: This is the reason why we are talking about increasingly expanding universe. And that leads to dark energy.

However, we are often given explanations of presently expanding universe due to Expansion No. 2 with the irrelevant examples of cosmological redshifts which are observed to be increasing as we look deeper, while these examples actually indicate only the fact that there was a big bang and inflation, and this expansion no.1 decelerated with time. Right?(read the first paragraph again if you didn't grasp the point I'm trying to make about expansion no.1 and cosmological redshifts)

Also, what are the relevant examples and evidences for expansion no.2 then?
 
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1) go to http://www.wolframalpha.com/
2) Enter “redshift”
3) You will see an entry with a note saying “Assuming Doppler redshift ”...Next to it there is a more drop-down. It gives 4 options. Select the cosmological redshift from the more drop-down.

4) Now you will get, by default, a redshift of 0.001 and results about it.
Change this value to 1089, 8, 4 and see the results every time. Especially Observe the big bang “timeline” and “time since big bang” row.

Getting what I mean to say about cosmological redshift and expansion no.1 now?
 


Umm, no, there is only one expansion... It makes sense to separate it into distinct epochs, perhaps, but I don't understand your question.

Here's the brief expansion history:
t=10^-43s: Planck era. Start here, take as initial conditions some matter densities, curvatures, and initial expansion rate.
t=10^-35s: GUT eta. Inflation happens. Period of very rapid expansion. Change in scale factor by about 10^30.
t=10^-28s (roughly): Expansion stops. Universe resumes its normal expansion. That is to say, there was the introduction at t=10^-35s of some scalar field which produced an extremely large negative pressure, thus acting as a cosmological constant to create accelerated expansion. But by 10^-28s, the particle decayed and the constituents of the universe are the normal matter, radiation, and dark energy (dominated completely, during this epoch, by radiation).
t~10000yr: Energy density of matter/radiation equal. Universe is decelerating at this point (but still expanding!)
t~7Gyr: Matter/Dark energy equal. At this point, universe begins accelerating.
t=14Gyr: Now!
(Note, numbers are only order of magnitude, don't mean to look them up right now)

One can label a redshift at any point along this timeline, by knowing how the scale factor was evolving as a function of time. So I don't understand why you think your "two expansions" (which don't even make sense to me) are meaningful.

Hopefully I've cleared up the question?
 


I still have doubts:
1)The red shift has been decreasing as we observe more recent universe. So this indicates deceleration of expansion rate as time has progressed. (as already illustrated in my question: "we see matter with large cosmological redshifts,up to 1089 in case of the Cosmic Microwave Background, which happened around 378000 years after Big Bang. The cosmological redshifts in case of very distant galaxies(currently received light from these has traveled 13.1 billion years) are 8, and this happened 652 million years after Big Bang. Closer galaxies(currently received light from these has traveled 11.5 billion years) show cosmological redshift of 3. " In fact, the cosmological red shift around 7Gyr is 0.76 and around 9Gyr is 0.45. So, its decreasing all the time! The cosmological redshift evidence only tells that universal expansion is decreasing!

So, what evidence do we have that universal expansion accelerated at 7Gyr as you stated?
 


Thanks! :)
 
https://en.wikipedia.org/wiki/Recombination_(cosmology) Was a matter density right after the decoupling low enough to consider the vacuum as the actual vacuum, and not the medium through which the light propagates with the speed lower than ##({\epsilon_0\mu_0})^{-1/2}##? I'm asking this in context of the calculation of the observable universe radius, where the time integral of the inverse of the scale factor is multiplied by the constant speed of light ##c##.
Why was the Hubble constant assumed to be decreasing and slowing down (decelerating) the expansion rate of the Universe, while at the same time Dark Energy is presumably accelerating the expansion? And to thicken the plot. recent news from NASA indicates that the Hubble constant is now increasing. Can you clarify this enigma? Also., if the Hubble constant eventually decreases, why is there a lower limit to its value?
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