Slow-roll Inflation and Horizon Problem

[AHSAN MUJTABA]

TL;DR

We are currently studying the inflation model in cosmology. This implies the universe accelerated expansion in the initial era.

I am a bit confused regarding the concept of the horizon problem. I have studied that the background radiation data implies that the radiations were not in causal contact at the beginning of the universe as from the big bang model. I want to know that how inflation is solving that problem?
To create a causal contact, the universe initially should expand greater than the speed of light, shouldn't it?
Also, I want to know, in simple words, what exactly is slow-roll inflation? Currently, I am following Andrew Liddle's book, but Sean Caroll's would also work.
Thanks.

 

[Orodruin]

Inflation solves the problem by expanding causally connected regions to become larger than the observable universe.

To create a causal contact, the universe initially should expand greater than the speed of light, shouldn't it?

There is no such thing as "expand greater than the speed of light". The expansion of the universe is an expansion rate, not a speed.

Regarding slow roll inflation, it is difficult to gauge what you would accept as "in simple words". In short, it is an inflation driven by a scalar field that is heavily dominated by its potential energy, thus creating an equation of state that is similar to that of a cosmological constant as long as this holds. You exit the slow roll regime when this is no longer true.