How did the Sun's brightness change during its first few billion years?
Although its brightness seems pretty constant today, it did change in a very complicated way while it was still forming from infalling gas and dust. It was actually tens to hundreds of times more luminous, but mostly as an infrared 'star'. Then when its nuclear fusion reactions kicked-in, stellar evolution models show that it began to stabilize within a few million years as a star with a power about 70% of its current output. Soon after it formed, the Sun was actually dimmer than it is today. It has grown steadily in power as it has evolved as a star, and will continue to increase in power for the next seven billion years. During most of this time, the power will increase by about 1% every 300 million years. In the distant past, our atmosphere was loaded with greenhouse gases such as carbon dioxide and methane so these gases could have kept water in a liquid form on Earth's surface even when the Sun was 30% dimmer than today. By 500 million years from now, the power of the Sun will be several percent higher. This will cause extensive heating of Earth, the destruction of the biosphere, and by one billion years from now, the evaporation of the oceans into a Venus-like atmosphere.