Hi Helena and Welcome!
Right, inflation in a nutshell attempt
The comic microwave background (CMB) of our universe is a remnant from when the universe became "see-through" about 300,000 after the big bang. The problem with it is that it displays a symmetry that cannot be accounted for - i.e. if you look in one direction it's displays symmetry with itself in completely the other direction.....
This is fine, except that we can "see" 13 billion light years, so the CMB we are looking at the 13 billion years old. In the big bang model, the universe itself is about 13 billions years old. But, the CMB is one direction is separated from the CMB in the other direction by 26 billion light years.
What that means is that the two cannot have come into 'causal' contact within the life span of our universe, so how can the symmetry have formed?
This is when inflation comes in. A few milliseconds after the big bang, the model states that the universe started a rapid expansion - an expansion much faster than light - that 'blew up' the universe like a bubble.
Since the universe is 13 billions years old, we can only see 13 billion light years, but if there is symmetry in the CMB, this implies that there is plenty more universe beyond our sight - we just can't see it as when we look great distances, we are looking back in time, so we cannot see anything further than ~13 billion light years.
I hope that makes a little sense.
Basically, in order to account for an observation of the CMB, cosmologists had to include this rapid inflation period into the big bang in order to explain the observation.
Now of course, they are linking that to dark matter as welll......
