Final answer:
Since the Big Bang, the size of the universe has increased while the temperature has decreased, in accordance to the predictions of the Big Bang model and supported by Wien's law.
Step-by-step explanation:
To answer the question of what has happened to the size and the temperature of the universe since the Big Bang, we look to the evidence provided by physical cosmology and the observations inferred from cosmic background radiation. Since the Big Bang, the size of the universe has increased, and correspondingly, the temperature of the universe has decreased. This relationship between size and temperature is due to the expansion cooling the universe, as represented by cosmic background radiation that stretches and cools as the universe grows.
Immediately after the Big Bang, the universe was extremely hot, but as it expanded over billions of years, its temperature has continuously dropped. According to the Big Bang model, in the first 0.01 second, the temperature was about 100 billion K, and after about 3 minutes, it decreased to 1 billion K. Since then, the universe kept expanding and cooling down, reaching temperatures much lower.
Wien's law supports these observations by relating the increase in wavelength of cosmic background radiation to a decrease in temperature. Therefore, as the universe expands, wavelength increases while temperature decreases.