Why do we have the cosmological constant? 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.
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:


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.($\ddot{a}&lt;0$)

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.



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 $\ddot{a}&gt;0$ 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. 

References:

1:http://en.wikipedia.org/wiki/Friedmann_equations

2:http://hyperphysics.phy-astr.gsu.edu/hbase/astro/univacc.html

3:http://en.wikipedia.org/wiki/Lambda-CDM_model