A non-standard cosmology is any physical cosmological model of the universe that has been, or still is, proposed as an alternative to the Big Bang model of standard physical cosmology.
In the history of cosmology, various scientists and researchers have disputed parts or all of the Big Bang due to a rejection or addition of fundamental assumptions needed to develop a theoretical model of the universe.
From the 1940s to the 1960s, the astrophysical community was equally divided between supporters of the Big Bang theory and supporters of a rival steady state universe.
It was not until advances in observational cosmology in the late 1960s that the Big Bang would eventually become the dominant theory, and today there are few active researchers who dispute it.
The term non-standard is applied to any cosmological theory that does not conform to the scientific consensus, but is not used in describing alternative models where no consensus has been reached, and is also used to describe theories that accept a "big bang" occurred but differ as to the detailed physics of the origin and evolution of the universe.
Because the term depends on the prevailing consensus, the meaning of the term changes over time. For example, hot dark matter would not have been considered non-standard in 1990, but would be in 2010.
Conversely a non-zero cosmological constant resulting in an accelerating universe would have been considered non-standard in 1990, but is part of the standard cosmology in 2010.