The best theory that is in the best argument with those two experiments (Hubble law and the background radiations) is the Big Bang Theory. According to the Big Bang theory, the universe was in a compact state of infinite density and zero volume, a sudden blast started everything even time as well. It began some 1-15 billion years ago in a state of extreme temperature and density.
The universe was much much hotter than today. There were no galaxies, stars, planets, and clumped matter as we know today. The stuff of the early universe was the high temperature, radiations, particles, and anti-particles. The density of the radiations and matter is related to the temperature of the universe. As the universe expands, it cools. If we make a rough assumption about the expanding rate of the universe, we can find a relationship between temperature and the time after the formation of the universe.
Where temperature T is in Kelvin and time t is in sec. This is the relation between the temperature of the universe and the time.
Radiations and Particles:
Radiations in the early universe very consisted of photons, particles, and anti-particles. The energy of photons typically is roughly KT where K is the Boltzman constant and T is the temperature in Kelvin. Due to high temperature and radiations, the dominant processes were the annihilation of the particle and anti-particle to photon or photon to particle and anti-particle pairs, this process is called pair production.
Photon to particle + anti-particle .... (1)
Particle + anti-particle to Photons .....(2)
As the universe expanded its temperature dropped and the following processes became unbalanced. At the beginning pair, production and annihilation of particle anti-particle were nearly equal.
At time 0.000001 sec the universe consists of Protons, anti-protons, neutrons, anti-neutrons, leptons, and photons. The rate of pair production and annihilation are roughly equal, so the number of each particle is equal to the number of its anti-particle. The number of photons is equal to the number of protons, which is equal to the number of electrons.
At times 10-2 now the there is no pair productions of nucleons while nucleons and anti-nucleons annihilation continue to occur, due to a slight excess of matter over anti-matter, all the anti-matter(anti-nucleons) disappear leaving the small excess of matter(nucleons) behind. Photons are still hot enough to produce electrons-positrons pairs. At this time universe consists of protons, electrons, neutrons, positrons, neutrinos, and anti-neutrinos.
When t = 1 sec, as the expansion of the universe, continues neutrinos are cooling down with photons and lose their energy. The neutrinos no longer have the energy to change protons to neutrons. At this point, neutrinos began to decouple from the matter and their interaction with the matter become less frequent and those few interactions have little effect on the properties of the neutrinos. From this point, neutrinos continue to fill the universe and continue their cooling as the universe expands. Today their average energy is 0.0005 eV and density is 400 per cm-3.