CERN? Particle Accelerators?
Well, I don't know of any specific studies but they are closely linked to Big Bang theorists as you have implied.
There are a couple unexplained problems and there are many research projects going on. To my amateurish way of thinking it all stems from our measuring speeds at great distances. Comparing Brightness and "Doppler" Red-Shift are the two main methods. I personally can't imagine the proper perspective for distances. Our closest stellar neighbor is Proxima Centauri, 4.22 light years away. The Milky Way is 100,000 light years wide with a thickness of 1000 light years. There are literally billions of galaxies in the known universe.
Okay, how big is a billion???
You were 87,840 seconds old exactly 24 hours after the moment you were born.
When you reached 1 million seconds, you were less than 12 days old.
How old were you when you reached a billion seconds?
It takes a little over 32 Y
EARS to reach a billion.
Big difference between a million (12 days) and a billion (32 years)

.
When we start talking about things that are 100,000 L
IGHT Y
EARS wide and then say there are B
ILLIONS of them and say that the space in between the galaxies is bigger still... well, you get the idea.
Observers wanted to find out if there was enough matter in the universe to reverse the outward motion. All matter is moving away from us at startling speeds and this fact supports the theory known as Big Bang. They wondered if the universe was only getting slower or if there would be a chance of it halting and then contracting and shrinking back.
B
IG S
URPRISE: The outward motion of the universe is accelerating. There is no known scientific reason for it, hence "dark energy". We gotta blame something, right? According to the math and recent studies only 4% of the universe is comprised of baryonic matter. Baryons are the stuff that make up atoms. So 96% of the universe is comprised of 'other stuff'.
CERN and particle accelerators come in because that's how we study quarks and sub-atomic particles (baryonic matter). It is surmised that the collisions and energy that results from these collisions most closely represent the universe at the time of the Bang. Well, maybe 1/10,000 of a second after, that is.
Click to enlarge:
