Why Higher Space or Time Dimensions?
Measurable relics of the Big Bang include the observed background radiation at 2.7 Kelvin, the inhomogeneities in the energy distribution, the relative abundance of the chemical elements in our universe, and more. The Big Bang theory provides a quantitative explanation of what we see today, by relying on our theoretical understanding of the rest of the universe. The great success is that the prediction matches the experimental observation in quantitative detail. This is what gives us the confidence that the Big Bang and inflation theories are more or less correct.