The cosmological redshift is primarily a consequence of the expansion of the universe. It is not directly related to accelerated time or time dilation as described by the theory of relativity.
When light travels through expanding space, its wavelength is stretched, resulting in a redshift. This redshift is commonly observed in the light from distant galaxies and is attributed to the expansion of the universe causing the stretching of the space between the source and the observer.
Accelerated time and time dilation, on the other hand, are concepts from the theory of relativity. Time dilation occurs when there is a difference in the passage of time between two reference frames that are in relative motion or are in a gravitational field. This effect has been experimentally verified and is a well-established aspect of relativity.
While both the cosmological redshift and time dilation are consequences of the underlying principles of general relativity, they are distinct phenomena. The cosmological redshift is a result of the expansion of the universe, while time dilation is related to differences in relative motion or gravitational fields. The two phenomena are not directly connected or inconsistent with each other.