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Since the cosmological constant is not required to explain that the universe seem to be expanding, why do we have it?

What other factors cause us to have that constant?

Background: Without the cosmological constant, distant stars should be affected by a great redshift. The amount of redshift is a function of their distance from us. This is due to gravitational time dilation. We are looking 13 billion years into the past, where the universe was very dense. Those stars should be experiencing extreme gravity, causing Einstein shift.

Since we DO have the cosmological constant, we are now looking for other explanations for the redshift.

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The cosmological constant is absolutely needed to explain the precise nature of the expansion of the universe (accelerating expansion). See Nobel Prize in Physics for 2011 (nobelprize.org/nobel_prizes/physics/laureates/2011/press.html). –  astromax Jan 10 at 15:25
If you were travelling into a black hole at close to the speed of light, you would probably not be able to observe it coming until you were close to the event horizon. The radius of the event horizon depends on your velocity, from your perspective. If a bright object in front of you were also moving into the hole at 1/10th the speed of light, it would still have an accelerating redshift relative to you, but in fact you could crash into it before it reaching the center of the black hole. Is that plausible? If so, couldn't a collapsing universe display those effects? –  frodeborli Jan 10 at 15:56
If the universe were collapsing you would see blueshifting of galaxies not redshifting. –  astromax Jan 10 at 16:09
@astromax Due to Doppler, perhaps. But I believe that collapse would not behave as a cookie dough deflating. Central regions of space would experience outward pull, more than making up for the inward pull the outer shell should be experiencing. This I believe would contribute to additional redshift, because outer regions will become denser, on top of the initial red shift due to distance. Basically, I think the dynamics would make us see redshift. –  frodeborli Jan 10 at 17:16
This is incorrect thinking. If the universe collapses, the coordinates of space would necessarily decrease over time. All but the closest galaxies would be blueshifted, not redshifted. –  astromax Jan 10 at 17:41
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1 Answer

  • Reason 1:

Let's look at the Friedmann equations without the cosmological constant.

$$ \frac{\dot{a}^2 }{a^2} = \frac{8 \pi G \rho}{3}-\frac{kc^2}{a^2}$$

The term on the LHS is just the Hubble constant squared $H^2$ which can be measured the direct measurement of recession velocity of galaxies

The density term can be said to be a combination of $\rho_{matter}+\rho_{dark- matter}$ both of which can be measured directly;$p_{matter}$ by observation of matter in our galaxy and other galaxies while $\rho_{dark- matter}$ by rotation curves of galaxies.

The curvature constant $k$ can be estimated today by the anisotropy measurements in the CMBR.

As it turns out the parameters don't fit and we need more mass-energy in the universe(almost 2-3 times of that we had estimated).

So comes along Dark energy or basically the cosmological constant. Cosmological constant or the dark energy are just two ways of looking at the equation,either as just a constant or a form of mass-energy(though we have solid reasons to believe the latter).

And this is our picture of the universe today:enter image description here

  • Reason 2:

Now historically the cosmological constant was necessary for an altogether different reason.

The second Friedmann equation without the cosmological constant looks:

$$ \frac{\ddot{a}}{a} = -\frac{4 \pi G}{3}\left(\rho+\frac{3p}{c^2}\right) $$

Now this predicts for normal type of matter,the universe must decelerate.($\ddot{a}<0$)

Now,people measured the redshift of the type-1a supernovae and found out the quite paradoxical result that the universe was being accelerated in its expansion.

enter image description here

Since normal matter can't explain this type or behaviour,we again have to look at Dark Energy(or the cosmological constant).And so with the cosmological constant the equation becomes:

$$ \frac{\ddot{a}}{a} = -\frac{4 \pi G}{3}\left(\rho+\frac{3p}{c^2}\right) + \frac{\Lambda c^2}{3} $$

Thus $\ddot{a}>0$ is possible.

Therefore the cosmological constant is necessary to both explain the current rate of expansion and the accelerated expansion.

So finally the accelerated expansion can be explained and today we have the $ΛCDM$ model of the universe.





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I believe that the universe can be decelerating, or even collapse at this moment, but that collapse would in make it appear visually as if it is expanding at an accelerating rate - due to the quadratic rate of the gravitational shift. As a hollow universe in a dense shell. This is due to our own region becoming less dense relative to the most distant regions. Does those equations contradict that assertion, when removing the cosmological constant? –  frodeborli Jan 10 at 7:21
Regarding the rotation curves of galaxies; how can we know the temperature of the empty space as a function of distance to us? Can we be sure that the universe is was not brighter in the past (in other words distant to us)? More photons in travel in a region should contribute to the rotation curves in that region. –  frodeborli Jan 10 at 7:45
What do you mean by this "I believe that the universe can be decelerating, or even collapse at this moment, but that collapse would in make it appear visually as if it is expanding at an accelerating rate - due to the quadratic rate of the gravitational shift?" –  Sandesh Kalantre Jan 10 at 7:59
The rotation curves are obtained either using the velocities of actual stars or the lines in atomic hydrogen,basically the 21cm line.There are other ways of detecting dark matter,for example dark matter can also cause gravitational lensing.E.g.:en.wikipedia.org/wiki/Bullet_Cluster –  Sandesh Kalantre Jan 10 at 8:03
Since the universe appears to be expanding, it should mean that distant stars affect us with gravity less as a function of time. Distant stars, on the other hand should appear to be more affected by gravity as a function of time (due to distance). I then assume time dilation shift. If, on top of that effect, the universe is collapsing - and gravity propagates at c - distant regions should be more affected by gravity than close, experiencing a similar effect to the sound barrier - but for gravity. The sum of this should amount what we call the cosmological constant, I believe. –  frodeborli Jan 10 at 9:46
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