Taking Another Look at the Universe

It might be a big claim here, but I suspect that we might be looking at the universe incorrectly.

Generally, we tend to think of the universe a little like this:

I’m not saying that this is entirely wrong (so long as the circle sort of represents a sphere), but this is not how we see the universe.  What we see off at the distance, ~13.787 billion light years away, is the cosmic microwave background that originated no more than 380,000 light years away from us.

It could be more accurate to represent how we view the universe as like this:

That’s not to say that we are outside the universe, per se, but we are certainly not in the universe that we see.  The universe that we see is in the past.  It is merely a trick of perspective that the universe appears to be all around us even though the furthest reaches of what we can see (apparently 13.787 light years away) only arose about 380,000 light years from where we are now.

However, not even this is correct.  There is a relationship between how long it took light from an event to arrive where we are and where it started from and where that location is now.  This relationship is given by the pair of equations: x'=(ct₀-x).x/ct₀, x=ct where t₀ is time since the instanton, t is time since the event, while x and x' is the distance to where the event took place (actual and observed).

This graph illustrates the concept (noting that we are considering a FUGE universe):

Interestingly, the length of that blue curve from intercept to intercept on the x-axis … is ~1.148 times that of the length of the x-axis between intercepts – if laid flat against the x-axis, that would be 15,800 million years, or 15.8Gyr which, when multiplied by the speed of light, is well within the range of 15.7±0.4 Glyr as used by Lineweaver and Egan (see FUGE Entropy).

So, the question must be asked, is the apparent variability of the scale factor merely an artifact of our observation of the universe?  And if so, does it explain what is currently explained by the introduction of dark energy (noting that small values of Δx translate to values of Δx' that start off at about 1.4 times x and decrease towards the top of the curve to equivalence [at 6.9 billion years ago] and then increase again)? 

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Note the section of the graph that relates to the “dark-energy-dominated era” (using the description from Space Telescope Science Institute's HubbleSite page on dark energy* – “About halfway into the universe’s history — several billion years ago — dark energy became dominant and the expansion accelerated”:

Is it possible that what appears to be dark energy could be an artefact of observation?

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* Note that on the Wikipedia page on the scale factor, the section on the dark-energy-dominated era indicates that this era began when the universe was about 9.8 billion years old, but the reference is from a 2006 book whereas the HubbleSite page was updated in late 2022 so, while it has a more vague reference, it should be considerably more current.  There is also a claim by the Department of Energy (which seems to be paraphrased from a 2022 article by post-doctoral cosmology researcher Luz Ángela García at space.com) that “somewhere between 3 and 7 billion years after the Big Bang, something happened: instead of the expansion slowing down, it sped up. Dark energy started to have a bigger influence than gravity. The expansion has been accelerating ever since”.  Ethan Siegel has the dating at “about 6-to-9 billion years ago”.  Other sources of varying levels of authoritativeness give the figure as about 7 billion years ago (for example Eric Lindner from the Supernova Cosmology Project – but there is no date on the page, so it’s difficult to assess whether this is based on recent work or was just a good guess from as long ago as 2010).