Cosmic inflation & the proof of its existence, The Derben I am too thick & lazy to pick up a book edition.
(shortened for the interweb)

The oldest fossil in existence.

In 1964 two astronomers Arno Penzias and Robert Wilson were listening to radio signals from space, they were hounded by a hum in the back ground, Thinking this was just interference & deciding it was the bird droppings left on the telescope they went about clearing the mess & triumphantly went back to work thinking they had solved the problem, it didnt.
What they had in fact stumbled upon was the afterglow of creation also known as Cosmic Microwave background.
These stretched radio waves being just 2.7 degrees above absolute zero come from a time just 380,000 years after the universe came into being & was referred to as the find of the century by Stephen Hawking.
Right now these radio waves are all around us passing through our bodies through the earth & off back out into space, There is an easy way to observe these radio signals and that is static, turn on a TV and tune from channel from one to the next & you'll see static 1% of the static you see on that screen is the remnants of the big bang fireball.

Congratulations you've just done some science.

The discovery of this fossil which sits up there with the discovery of DNA in how much of a big deal this is forms the foundations for us to be able to go back to a Trillionth of a Trillionth of a second after the big bang.

Surfing

Edward Hubble discovered that Galaxies were moving away from us, although this also seemed to break the laws of physics as it appeared to show galaxies moving faster than the speed of light which we know is impossible (thanks Einstein) What we have discovered is its not the galaxies moving away from us at speed but the the space in between the galaxies that is expanding.
A really good way of demonstrating this is to cut out a load of paper galaxies & stick them to a balloon now blow the balloon up and you'll see how the space around the galaxies expands.

The theory of expansion was first suggested by Alan Guth in the 70's.

Einstein's theory of relativity had predicted the existence of Gravitational waves back in 1916 long before we had any means of detecting them, A classic example of how maths is the language of the universe.

The Bicep telescope at the south pole has recently detected gravitational waves take a look at this video for evidence that inflation is a thing

[Link]

Its narrated far better than I could ever manage.

This is effectively the smoking gun that scientists were looking for, Inflation is now the most accurate model for how the universe came into being, a singular point 100 billion billion times smaller than a proton containing a finite amount of energy inflating outwards at incredible speed.

Also a bit of a tid bit of things we have learned since the discoveries above.
The temperature just a fraction of a second after the big bang event was 100,000,000,000,000,000,000,000,000,000,000 degrees.
Absolutely nothing can exist at this temperature yet amazingly just one second after the big bang it had already cooled to 10 billion degrees & our new universe was already about 1000x the size of our solar system this is literally just 1 second into the big bang (mind blown)
After 3 minutes the Universe was 1 Billion degrees & was already creating atomic nuclei & this is the beauty of e=mc2 is Energy (E) can be turned into matter (M) & vice versa it doesnt need god to explain how matter came to be in a universe made of energy, simply given enough time & the correct amount of cooling Energy will turn into matter.

Edited by Ouzo Dan (13 Jun 2015 2.06pm)

He's barking up the wrong tree....Ancient Aliens has all the answers one needs!

If Dawkins is a hero then Giorgio A. Tsoukalos is the Messiah...not a naughty boy!

Edited by Lyons550 (13 Jun 2015 11.18am)

Yes, I like the ancient aliens ideas. Would explain the curious mix of animal and intelligence in man, and the physical design flaws.

So does evolution, without having to include aliens.

Because scientifically we can only demonstrate it as a theory, based on existing understanding, to within fractions of a second after the event (this is one of the principle reasons for particle accelerators to replicate).

Its one of a number of theories, that are in competition, the evidence accumilated points towards this being the most probable event, based on what is known.