Cosmic Background Radiation. All matter radiates heat, regardless of its temperature. Everywhere astronomers look, they can detect an extremely uniform radiation, called the cosmic background radiation. It appears to come from perfectly radiating matter whose temperature is 2.73 K, near absolute zero. The cosmic Background radiation was initially thought to be left over from the big bang. Many incorrectly believe that the big bang theory predicted this radiation.
Since the CBR (cosmic background radiation) is so uniform, the matter from which it originated must have been spread uniformly throughout the universe. But if matter was uniformly distributed, it would hardly gravitate in any direction; even after tens of billions of years, galaxies would not evolve. Since matter in the universe is highly concentrated into galaxies, galaxy clusters, and superclusters, the CBR does not appear to be a remnant of a big bang.
Helium. The amount of helium in the universe is not explained by the big bang theory; the theory was adjusted to fit the amount of helium. Ironically, the lack of helium in certain types of stars (B type stars0 and the presence of beryllium in other stars contradicts the theory.
Redshift. The redshift of distant starlight is usually interpreted as a Doppler effect; namely, stlars and galaxies are moving away from the earth, stretching out (or reddening) the wave lengths of light we see. While this may be true, other possible explanations do not involve an expanding universe. Besides, many objects with high redshifts seem connected, or associated, with other objects of low redshifts. They could not be traveling at such different velocities and be connected for long. For example, many quasars appear to be connected to galaxies by threads of gas. Finally, redshifted light from galaxies has some strange features that are inconsistent with the Doppler effect. If redshifts are from objects moving away from the earth, one would expect the amount of redshifting to take on continuous values. Much remains to be learned about redshifts.
Secondly, a big bang should neighter produce highly concentrated nor rotating bodies. Galaxies are examples of both. A large volume of the universe should not be, but apparently is, moving sideways, almost perpendicular to the direction of expansion.
Thirdly, big bang would, for all practical purposes, only produce hydrogen, and helium. Therefore, the first generation of stars to somehow form after a big bang should consist of only hydrogen and helium. Some of these stars should still exist, but none can be found. These observations make it doubtful that a big bang occurred.
If a big bang occurred, what caused the bang? Stars with enough mass become black holes, so not even light can escape their enormous gravity. How then could anything escape the trillions upon trillions of times greater gravity caused by concentrating all the mass in the universe in a "cosmic egg" that existed before the bang?
If the big bang theory is correct, one can calculate the age of the universe. The age turns out to be younger than objects in the universe whose ages were based on other evolutionary theories. Since this is logically impossible, one or both sets of theories must be incorrect?