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# Cosmology & Proof Of The Big Bang Theory

Redshift (z)

Line spectra from distant galaxies compared to the same elements emitted on Earth have slightly different wavelengths and frequencies. Lines in the top spectrum are shifted towards longer wavelengths and in the lower spectrum towards shorter wavelengths. In most cases the change in wavelength is an increase, indicating a redshift with the following equation making λ0 initial wavelength and λ the observed wavelength. The redshift is proof that distant galaxies and Earth are moving apart, which is evidence for the expansion of the universe. As galaxies recede from Earth the following equation is applied.

Fast-moving galaxies have redshifts greater than one but the speed is an approximation and thus cannot be used to determine the recession speed of such galaxies. Some stars and galaxies have a blueshift due to their rotational speed within their galaxy or cluster of galaxies being greater than the recession speed of the whole system.

Big Bang Connections

Cepheid variables can be used to determine distances of galaxies and the recession speed can then be compared with since the recession speed of a galaxy is proportional to its distance from Earth. Thus if we imagine turning the clock back, then the galaxies must have been together at first indicating the existence of a hot Big Bang model of the universe. Before,

the Newtonian model described the universe

as uniform, infinite, and static.

Hubble’s law

The straight in the following graph is Hubble's law and the constant is not assumed to be the same forever, thus the subscript 0 is used to indicate the value being of the present. Hubble's law is used to estimate the distance to galaxies from the redshifts in the radiation received from them. The law can also be used to estimate the age of the universe, but it is only an assumption due to the belief that the universe has been expanding at a constant rate.

H = 73 km s^–1 Mpc^–1 gives the age of T=4.3×1017 s (or 1.4×1010 years).

The Isotropic CMB radiation confirms the same average temperature of the universe as the Big Bang Theory following Wien's Law, 2.76 K which is yet another proof that the universe expanding. (λmax T = 2.9 × 10–3 m K) gives the λ = 1.1 × 10–3 m, which is in the microwave in the electromagnetic spectrum. The expansion stretches the shorter wavelengths that were emitted billions of years ago due to the Big Bang.

The cosmic scale factor (R)

The cosmic scale factor represents the expansion of the universe. Following the R graph, time represents the expansion of the universe. As kinetic energy is transferred into the gravitational potential energy of galaxies, there are multiple possibilities of the universe evolution. The orange line indicates the universe reaching a maximum line and then contracting. Greenline is an ever-expanding universe but at a rate that reduces to zero after infinite time. Blueline indicates an expansion to infinity but at a decreasing rate.

Redline indicates an accelerating universe of which expands at an increasing rate.

The accelerating universe

Scientists have found evidence has been found to prove an accelerating universe by using type Ia supernovae also known as "Standard candles" due to their unified luminosity. Their distances to Earth can be measured using their apparent brightness. But, once Hubble's law is used a smaller distance is predicted, indicating a universe that is expanding at a quicker rate.

Around the same time, the idea of "Dark energy" came to be, existing at a low concentration throughout space to explain the cause of the expansion.

Reference

Physics - Book - John Allum and Christopher Talbot - Second Edition - Hodder 2017

Cover Image Credit: https://gfycat.com/gifs/search/cosmology+redshift

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