Redshift caused by the Doppler effect and cosmological redshift are two distinct phenomena, though they both result in the stretching of light wavelengths. The Doppler redshift occurs due to the relative motion between the light source (e.g., a star or galaxy) and the observer. When the source moves away from the observer, the light's wavelength stretches, leading to a redshift. This is analogous to the change in pitch heard from a receding siren. On the other hand, cosmological redshift is a result of the expansion of the universe itself. As the universe expands, the space between objects, including galaxies and the Earth, increases. Light travelling through this expanding space stretches in wavelength. This type of redshift is not due to the movement of the galaxy through space, but rather the expansion of space itself. It's a key observation supporting the Big Bang theory, indicating that the universe has been expanding since its inception. Cosmological redshift is fundamental to our understanding of the large-scale structure of the universe and its evolution.

Redshift can indeed be used as a tool to estimate the age of the universe, although the process involves complex calculations and assumptions. The key lies in understanding the relationship between redshift and the expansion rate of the universe. By measuring the redshift of distant galaxies, astronomers can determine how fast these galaxies are moving away from us. Using Hubble's Law, which states that the velocity of a galaxy moving away from us is proportional to its distance, astronomers can calculate the rate of expansion of the universe. By extrapolating this rate backwards, it's possible to estimate how long it would have taken for the universe to expand from a singular point to its current size. This calculation gives an estimate of the age of the universe. However, this method is not without complexities. It requires precise measurements of distances and velocities, and the value of Hubble's constant (the proportionality factor in Hubble's Law) has been subject to revision as measurement techniques improve. Additionally, understanding the dynamics of the universe's expansion, including the role of dark energy, is crucial for accurate calculations.

Observing a high redshift in a distant galaxy carries significant implications in cosmology. High redshift values indicate that the galaxy is moving away from us at a very high speed. This is a direct consequence of the expansion of the universe: the further a galaxy is, the faster it appears to be receding from us. High redshifts also imply that we are observing the galaxy as it was in the distant past. Due to the finite speed of light, observing distant galaxies is essentially looking back in time. Thus, a galaxy with a high redshift is seen in a state it was in billions of years ago. This provides astronomers with a unique opportunity to study the early universe and understand how galaxies formed and evolved over time. High redshift observations are crucial for testing theories about the origins and evolution of the universe, including the Big Bang theory, the formation of galaxies, and the role of dark matter and dark energy in shaping the cosmos.

Redshift provides compelling evidence for the Big Bang theory through its demonstration of the universe's expansion. The Big Bang theory posits that the universe started from an extremely hot, dense state and has been expanding ever since. The observation of redshift in the light from distant galaxies is a key piece of evidence for this expansion. According to Hubble's Law, the degree of redshift in a galaxy's light correlates with its distance from us; the further away a galaxy is, the faster it appears to be moving away. This is consistent with a model of the universe that started from a singular point and has been expanding in all directions. The cosmological principle, which suggests that the universe is homogeneous and isotropic on a large scale, is supported by the observation of redshift in every direction in the sky. This uniformity of redshift across the universe supports the notion of a singular, explosive event like the Big Bang as the origin of the universe. Moreover, the study of redshift helps astronomers understand the rate of expansion of the universe, which is crucial for models of cosmic evolution and the fate of the universe.

The concept of redshift in astronomy is closely related to the Doppler effect observed in sound. The Doppler effect explains how the frequency (and thus the pitch) of a sound changes relative to an observer when the source of the sound is moving. For sound, if the source is moving towards the observer, the waves are compressed, leading to a higher frequency or pitch (blueshift), and if moving away, the waves are stretched, leading to a lower frequency or pitch (redshift). When applied to light, a similar principle holds. If a celestial body, like a galaxy, is moving away from the observer (us on Earth), the light waves it emits are stretched, increasing their wavelength and shifting them towards the red part of the spectrum. This is observed as redshift. Conversely, if a galaxy were moving towards us, its light would blueshift. This astronomical redshift provides crucial information about the movement and speed of celestial objects and supports the theory of the expanding universe.