which evidence supports the idea that cosmic microwave background radiation is a remnant of the big bang.

There are several lines of evidence that support the idea that cosmic microwave background radiation (CMB) is a remnant of the Big Bang:

1. Its temperature: The CMB has a nearly uniform temperature of about 2.7 Kelvin (-270.45 degrees Celsius), which is very consistent across the sky. This uniformity supports the idea that CMB is the "afterglow" of the highly energetic and incredibly hot Big Bang event.

2. Its spectrum: The CMB has a blackbody spectrum, which means that its energy distribution follows a specific pattern that can be explained by the Planck's law of black body radiation. This type of spectrum is highly indicative of a remnant radiation from an initial hot, dense and uniform state, such as the Big Bang.

3. Its isotropy: The CMB is extremely isotropic, meaning it appears the same in all directions of the sky. This isotropy is consistent with the idea that the CMB originated from the early universe, as any other source nearby would not have the same level of isotropy. This uniformity strongly suggests that the CMB is a remnant of the thermal radiation left behind by the Big Bang.

4. Its predicted abundance: The Big Bang theory predicts the existence of CMB radiation as a natural consequence of the early universe's expansion and cooling. The observations of CMB match the predicted abundance and properties, providing further evidence for the Big Bang model.

5. Its spatial variations: Although the CMB is isotropic on large scales, it does contain small fluctuations or anisotropies. These fluctuations are believed to be the imprints left behind by the early universe's density fluctuations, which later gave rise to the formation of galaxies and large-scale structures we observe today. The observations of these fluctuations are consistent with the predictions of the inflationary Big Bang model.

Overall, the combination of its temperature, spectrum, isotropy, predicted abundance, and spatial variations strongly supports the idea that cosmic microwave background radiation is a remnant of the Big Bang.