The constancy of the speed of light and other basic physical constants is supported by a variety of astronomical observations. For example, the light from distant galaxies is redshifted, which indicates that the speed of light has remained constant over time. Additionally, the cosmic microwave background radiation is consistent with the predictions of the Big Bang theory, which relies on the constancy of the speed of light. Finally, the abundance of elements in the universe is consistent with the predictions of nuclear physics, which also relies on the constancy of the speed of light.

In short, the constancy of the speed of light and other basic physical constants is supported by a variety of astronomical observations, and any deviation from this constancy would have drastic implications for our understanding of the cosmos.