The cosmological principle
In layman terms, the cosmological principle is the study of the several different aspects of the universe: how big is it, when was it formed, when/how will it end, etc. Any model of the universe must explain what we observe. For example, regarding Isaac Newton's studies relating to the universe, his time related observations showed that the universe was static and he set about how to explain it. You may have heard of the term 'flat" with respect to the universe before. This is a synonym for static, and it means that the universe isn't expanding or contracting. However, obviously, this theory is obsolete as it is now widely known that the universe is expanding due to the Big Bang. Whether it happened billions of years ago (as currently proposed) or much more relatively recently, is a topic under discussion.
Newton's Law of Gravitation, that attempted to describe how celestial masses interact, has a major flaw. The problem is that it states all particles in the universe exert a force on every other particle, meaning one particle on one side of the universe exerts a force, however small, on one on the other side. Thus, one would assume that over time these particles would attract and the universe would therefore begin to grow smaller. This isn't true, so the law assumed that the universe is infinitely large. If it were true, then there an infinite number of stars and so every light from every star should've reached earth, rendering the night sky completely bright. This is Olbers' paradox, explained more in my post here.
So, a model that accurately describes the universe must assume that the universe looks the same from every place. This is known as an isotropic universe or a homogenous universe. This isn't true on a relatively small case of course as we have different planets in our Solar System, but on a larger scale it is. It is also assumed that the laws that describe our world hold true for every place in the universe. If not, it would be quite the discovery (perhaps a simulation?). These conditions are what is known as the cosmological principle.
The expanding universe
As Einstein and several other scientists such as Edwin Hubble and Vesto Slipher were developing theories, Slipher was working on line spectra from distant galaxies and Hubble measured how far away they were. Slither noticed that all the lines from all the galaxies were shifted towards the red end of the spectrum (redshift.) Given the change in wavelength, Hubble calculated the velocity of the galaxies using the Doppler formula:
Newton's Law of Gravitation, that attempted to describe how celestial masses interact, has a major flaw. The problem is that it states all particles in the universe exert a force on every other particle, meaning one particle on one side of the universe exerts a force, however small, on one on the other side. Thus, one would assume that over time these particles would attract and the universe would therefore begin to grow smaller. This isn't true, so the law assumed that the universe is infinitely large. If it were true, then there an infinite number of stars and so every light from every star should've reached earth, rendering the night sky completely bright. This is Olbers' paradox, explained more in my post here.
So, a model that accurately describes the universe must assume that the universe looks the same from every place. This is known as an isotropic universe or a homogenous universe. This isn't true on a relatively small case of course as we have different planets in our Solar System, but on a larger scale it is. It is also assumed that the laws that describe our world hold true for every place in the universe. If not, it would be quite the discovery (perhaps a simulation?). These conditions are what is known as the cosmological principle.
The expanding universe
As Einstein and several other scientists such as Edwin Hubble and Vesto Slipher were developing theories, Slipher was working on line spectra from distant galaxies and Hubble measured how far away they were. Slither noticed that all the lines from all the galaxies were shifted towards the red end of the spectrum (redshift.) Given the change in wavelength, Hubble calculated the velocity of the galaxies using the Doppler formula:
Where
v = recessional velocity (how fast the galaxies recede from us)
c = the speed of light
∆wavelength = change in wavelength
wavelength(em) = the original wavelength
z = the fraction increase (redshift)
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