Time dilation does not directly affect the age of the universe as a whole. The age of the universe is typically measured in terms of its proper time, which is the time experienced by an observer who is at rest with respect to the expansion of the universe on average.
However, time dilation can have indirect effects on the perception of time and the measurement of cosmic events, which in turn can impact our understanding of the age of the universe. For example:
Expansion of the universe: The expansion of the universe can lead to a cosmological time dilation. As the universe expands, the wavelengths of light from distant galaxies get stretched, causing their light to be redshifted. This redshift is an indication of the expansion and can affect the perceived rate at which time is passing in those distant regions. Therefore, when we observe distant objects, we are seeing them at an earlier cosmic time, and this can affect our estimation of the age of the universe.
Gravitational time dilation: The distribution of matter and energy in the universe can create gravitational fields that cause time dilation. In regions of higher gravitational potential, such as near massive objects or in dense clusters of galaxies, time passes more slowly compared to regions of lower gravitational potential. While this gravitational time dilation can affect the local perception of time, it does not directly impact the overall age of the universe.
In summary, time dilation can influence our measurements and observations of cosmic events, but it does not alter the overall age of the universe as determined by its proper time. The age of the universe is estimated based on a variety of cosmological observations, such as the cosmic microwave background radiation and the measurements of the Hubble constant, which provide insights into the history and expansion of the universe.