Question

In a universe with dark energy, the rate of expansion of the universe immediately after the formation of the universe is decelerating but changes to accelerating in the more recent past. Why might this change occur?(Recall how the density of the universe changes with time)

Answer 1

In 10-32 of a second after the big bang, the volume of universe suddenly increased by a factor of 1078 . After that it continued to decelerate till 9.8 billion years because the gravitational force was dominating at that time and since gravitational force attacts celestial bodies, it slowers the expansion But before aproximately 4 billion years from now universe entered its dark-energy-dominated era. And as we know that it acts against gravity. It started to accelerate the exapansion. It can be accounted for by the positive value of cosmological constant(dark energy is said to be cosmological constant) which repersents the presence of dark energy.

We can explain it with the help of density.

We know know that the dark enegy has negative pressure which is

P=wc2

Where is the energy density

C is speed of light

And

w has different values in different theories.

When w is less than -0.33 for cosmic acceleration

Which yealds a positive value of acceleration.

When w=-1

Expenssion can be explained by lambda CDM MODEL(standered model of cosmology).

This model says that the universe contains three different major components which are

• Cosmological constant(dark energy)
• Cold dark matter(CDM)
• Normal matter

Further mathematics is in sheet attached below:-