How does time dilation relate to the Big Bang Theory?
Based on the distances in light years of stars the age of the universe has been estimated at 13.8 billion years. The time dilation is not usually considered in the age of the universe as it should be. The estimates of the age of the universe that disregard the time dilation are most likely inaccurate.
Time itself began with the big bang and the expansion of matter creating space. Time is affected by both mass and the speed of motion. At a singularity like thought to have occurred before the big bang and shortly after, time does not exist. Basically the more matter or mass in a location the slower the elapse of time. Not all parts of the universe experience time in the same extent.
Basing the age of the universe on light years fails to take into effect the time dilation of the speed of motion. Photons do not experience time. To a photon there is no difference between 1000 years or one day, or for that matter 1 billion years and 1 second. At the speed of light time itself does not exist.
Figure 4.10 page 110 The elegant Universe Brian Greene "shows the infinite number of paths a single electron must travel from single source. This means that the one electron" ( electron has more mass the photon) actually goes through both silts. This means that the time dilution allows the electron to effectively exceed the speed of light. The electron does not actually at any point in time exceed the speed of light but the time dilation allows it ignore time.
The time dilation should affect the estimates of the age of the Universe and timing of the Big Bang