Can CMB show that the universe was accelerating at the time the CMB formed thus measuring dark energy early in the universe?

Yes, the Cosmic Microwave Background (CMB) can provide information about the early universe, including whether the universe was accelerating at the time the CMB formed. Let me explain how this works:

The CMB is the faint radiation left over from the Big Bang and is essentially a snapshot of the universe when it was only about 380,000 years old. It can reveal valuable information about the composition and evolution of the universe.

Now, to address your question about the acceleration of the universe and dark energy:

1. CMB Anisotropies: The CMB is not perfectly uniform. It has tiny temperature fluctuations or anisotropies across the sky. These anisotropies can be measured by instruments like the Wilkinson Microwave Anisotropy Probe (WMAP) or the Planck satellite.

2. Primordial Density Fluctuations: The CMB anisotropies are generated by primordial density fluctuations, which are imprinted in the matter distribution of the early universe. These fluctuations originated during an epoch called inflation, which occurred very shortly after the Big Bang.

3. Effects of Dark Energy: If the universe was experiencing acceleration during the time the CMB formed, it would leave subtle imprints on the pattern of these primordial density fluctuations. Dark energy, which is thought to be responsible for the current acceleration of the universe, could have influenced the growth of these fluctuations and left its signature on the CMB.

By studying the statistical properties and patterns of the CMB anisotropies, cosmologists can analyze the information in terms of cosmological parameters, including the presence and nature of dark energy.

However, it is important to note that while the CMB can provide clues about the early universe and dark energy, it alone is not sufficient to measure dark energy directly. Other observations, such as the measurements of distant supernovae or the large-scale distribution of galaxies, are also needed to piece together a more comprehensive picture of the universe's evolution and the role of dark energy.