The universe is calculated to have begun 8-20 billion years ago. However the math and physics we have can only account to as far back as 10^-43 seconds (plank time) after the bang. Only up to then can we do calculations using the present laws of gravity and quantum physics that exist. This is because the time from the zeroth to the 10^-43rd second requires a quantum law of gravity that is yet to be devised.
At 10^-43s the laws of the universe as we know it became valid. The universe then only 10^-33 of a centimeter wide (plank scale) was 10^32 degrees hot! Okay. Let me put this straight. Take a second; get a quadrillionth of that, then get a quadrillionth of that, then get a thousandth of that. That’s how young the universe was at the moment. If you were put inside molten iron for that amount of time, you’d never notice! Now how big? Imagine a slice of bread divided to a quadrillion pieces, then one of those pieces to a trillion more pieces. That’s how big, I mean, how small, it was. That is as small as a quark. A quark is a very small subatomic particle that if dropped on your head, would go through your body without touching anything! Now, about the temperature. It was about a billion, billion, and billion, hundred times hotter than molten steel. I may not tell you how they got to these numbers because if I was to summarize it in 10 pages you’d need an unusual love for numbers and the Greek alphabet to get through the first page.
At 10-43 seconds, the universe was filled with radiation and all the four fundamental forces of nature gravity, strong and weak forces and electromagnetic forces- were still one. At 10-34 s the universe expanded 1030 times and cooled to 1027 K. The expansion and cooling continued throughout the life of the universe. In its early stages where it happened by large factors it gave the impression of an explosion. A bang. At this temperature it was cool enough for radiation that filled the universe to form matter. The energy of the photons turned into mass with respect to Einstein’s equation e=mc2. This happened by collision of photons forming quarks, antiquarks and leptons.
After 10-4 seconds, quarks combined to form protons, neutrons, antiprotons and antineutrons. As the universe expanded and cooled, creation of mater ceased. By principle, matter formed and their antiparticles annihilated on collision. However by a biased mechanism not fully understood, some particles (one in every million) remained to matter of the universe that we see today. Otherwise all the matter would have disappeared leaving a universe filled with only a remnant of the radiation.
One second later, temperature dropped to 109K. The grand unified force split to the four forces of nature that exist today. After one minute it was cool enough for colliding protons and neutrons to combine and form helium nuclei and 7Lithium. About ¼ of the total nuclei that fused formed Helium.
Nothing much happened until 300,000 years later when temperature dropped 3000K. It was then cool enough for electrons to fuse and form neutral atoms. Thus the universe became transparent to radiation with no more free electrons to scatter photons.
Over 10 billion years since the Big Bang, the universe has expanded by a factor of a thousand causing the temperature of radiation to fall by the same amount. Now the radiation is resting at 3K with a corresponding radiation wavelength in the microwave part of the electromagnetic spectrum. This is one of the greatest strengths of the Big bang theory: because the observed temperature agrees with calculations made 2 decades earlier by the Gamow team and confirmed by Princeton University Physicists.
Another backing of the BBT is the abundance of helium observed in the universe, consistent with the theory. Helium has been observed to make 27% of the matter around us. This is true according to predictions by the BBT which allowed for fusion of ¼ of the protons of the early universe in the first few minutes of the Big Bang.
In the 1960’s scientists observed that more quasars and radio galaxies are found in distant galaxies than in nearby ones. Watching the distant is like watching the past. Since most galaxies arte billions of light years away light from them takes billions of years to reach us. And the present images are pictures of billions of years back. Since distant galaxies appear to be more active, it means that the universe has been changing with time.
These support coupled with he observations of receding galaxies , that led to theory itself have made us so confident of the BBT that we can now brag of having the ultimate creation theory.
Moreover, Stephen Hawking has shown that a universe can only be described by the theory of General Relativity if and only if it started as a singularity. Since General Relativity applies for our universe it must have started as a singularity. Thus the Big Bang.