Reddit mentions of Principles of Roman Architecture

> they were not supposed to be seen, they were originally covered by bronze plaques that were melted down by Bernini to build the baldachino at St Peter's if the legend is true.

The coffers were meant to be seen, though could have had bronze ornament such as rosettes. For a really good analysis of the design, check out Principles of Roman Architecture by Mark Wilson Jones. He devotes a chapter each to the interior, and exterior.

The roof itself was originally bronze tile that was stripped off, and eventually replaced with a lead one.

Urban VIII took way the bronze ceiling of the portico.