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Cosmology is the scientific study of the large scale properties of the universe as a whole. It endeavors to understand the history, structure, and future of the cosmos, looking into aspects such as space, time, matter, and energy. At the heart of this field is the model of an expanding universe, which was formulated based on observations that galaxies appear to be moving away from each other. This expansion is a key concept, indicating that the universe has been growing ever since the Big Bang, a massive expansion event that is considered as the birth of the universe.
Cosmologists use a variety of methods to study the universe, such as analyzing light from distant celestial objects, studying cosmic microwave background radiation, and using theoretical models to predict and understand observations. It's a discipline that not only requires a grasp of physics and mathematics but also a broad understanding of astronomical phenomena to piece together the history and large-scale structure of the cosmos.

The redshift phenomenon is an essential tool in astrophysics, serving as a cosmic yardstick for measuring the universe's expansion. Analogous to the change in pitch of a passing siren, redshift occurs when the wavelength of light stretched as it travels across the expanding fabric of space, causing it to appear redder than it would be if the source were stationary. This change in wavelength is directly related to the velocity at which an object is moving away from the observer.
In practice, astronomers observe the spectral lines of elements within a galaxy. These lines serve as fingerprints for those elements, and their shift towards the red end of the spectrum indicates that the galaxy is receding. The rate of this redshift increases with distance, which provides compelling evidence that the universe is not static but expanding. Additionally, this phenomenon helps in determining the approximate speed at which a galaxy is moving away, which when put together with other galaxies' data, helps to map the expansion of the universe. Einstein's theory of general relativity also predicted this redshift, further underlining its significance in cosmology.

Empirical evidence in astronomy consists of data collected through observations and measurements that can confirm or challenge theoretical models. The expanding universe theory, bolstered by redshift observations, is one of the field's most potent examples of empirical evidence. Astronomers collect data from telescopes and other instruments, assessing the light from distant celestial bodies to understand their movements, composition, and the forces acting upon them.
Hubble's law is a primary example of empirical evidence that supports the expansion of the universe. It states that the velocity at which a galaxy is moving away from us is proportional to its distance. The law emerged from the observation that galaxies display a redshift that corresponds with their distance from us. Other forms of empirical evidence, such as the cosmic microwave background radiation, the distribution of galaxies, and the observation of supernovae, each serve different roles in testing and supporting the cosmological model of an expanding universe. These pieces of evidence also allow astronomers to estimate the rate of expansion, which has led to the understanding that the expansion is actually accelerating, pointing to the mysterious presence of dark energy.