Cosmological Principle allows the belief that laws of physics can be applied anywhere and they would all lead to the same conclusions. The principle describes;
The universe is homogeneous and isotropic on a large scale.
The universe does not have an observable edge.
Rotational velocity from Newtonian gravitation
The stars rotate around their common center of mass and the rotational velocity can be measured using the following equation.
Rotational Curve (red line) - The rotational speed of the stars in a galaxy can be measured from the Doppler shift measurement and rotational dynamics with rotational speed can be used to measure the density of the galaxy.
The Dark matter fills 85% of the total mass in the universe and is used to explain the missing matter in space. However, it is not detectable due to it not emitting nor absorbing any radiation and thus theories have been formed:
1. Weakly Interacting Massive Particles (WIMPs); are undiscovered particles formed during the Big Bang, not made from baryons which are composed of quarks and only interact by the weak nuclear force and thus are difficult to detect.
2. Massive Compact Halo Objects (MACHOs); are baryonic matter in galaxy halos such as undetected neutron and dwarf stars as well as small black holes. Ever-Expanding Universe
The "Critical density", ρc, of the universe is the average density of matter which in turn results in a flat universe. Observations of the size of fluctuations in the cosmic microwave background radiation have proven that we live in a flat universe. 1. Flat Universe (ρ = ρc), meaning expansion rate eventually reduces to zero after an infinite time.
2. Closed Universe (ρ > ρc), meaning eventually the universe will stop expanding and start contracting instead. 3. Open Universe (ρ < ρc), meaning the universe will continue expanding forever.
4. Accelerating Universe, meaning forever expanding at an increased rate which has supportive evidence from observations using type Ia supernovae and dark energy.
It is believed to account for 68% of the mass-energy in the universe and exists everywhere in space with only gravitational interactions.
The universe cools as it expands
As the universe expands, the overall temperature of the universe decreases due to the matter within scattering farther from one another. As space expands λmax ∝R, cosmic scale factor and since according to Wien's law λmax=1/T, the average temperature of the universe becomes the following equation:
Fluctuations in the CMB
Evidence of the Big Bang theory is the discovery of the same microwave background radiation coming from all directions, but fluctuations have been discovered observed as anisotropies.
Physics Book - John Allum and Christopher Talbot - Second Edition - Hodder 2017