If I'm going to write about "The Consensus Model of Cosmology" should I include Big Bang Model or should I go with just the $\Lambda$-CDM Model?
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The Big Bang Theory is a much more general and less specific description of our theory about the origin of the Universe than the $\Lambda{\rm CDM}$ model (by the way, I don't think that the hyphen is written in that acronym).
The Big Bang Theory says that the Universe was expanding and the distances between two places where galaxies sit today used to be tiny, microscopic, at some distant past which may be said to be the beginning of time. The whole expansion may be described as a curved spacetime manifold obeying the laws of Einstein's general theory of relativity.
On the other hand, $\Lambda{\rm CDM}$ model is a particular state-of-the-art version of The Big Bang Theory that includes the "beginning from the explosion" but also describes the presence of the visible baryonic matter (mostly stars and galaxies) as well as the invisible dark matter, DM.
Dark matter seems to exist because galaxies rotate in a certain way that differs from the rotation that would be sustainable if the visible stars were the only matter in these galaxies. Dark matter should better "sit near the cores" of galaxies because that's where we observe its effect. To do so, it shouldn't move too much relatively to the speed of light. Matter moving by low velocities relatively to the speed of light is said to be "cold". Cold dark matter, ${\rm CDM}$, seems to be the preferred character of most of the dark matter as we observe it and which cosmologists need to explain the data.
The letter $\Lambda$ (Lambda) adds the cosmological constant, the constant omnipresent positive vacuum energy with negative pressure (also called "dark energy" if we want to include some slightly different descriptions than the simplest cosmological constant), and this term is needed to explain the observed acceleration of the expansion rate of the Universe. The Big Bang Theory generally needs neither dark matter (DM let alone CDM) nor the cosmological constant $\Lambda$ but there's a lot of evidence that the $\Lambda{\rm CDM}$ model, and not just the general Big Bang Theory, is the right description of the Universe at the long distance scales and time scales (and its origin).
There are lots of additional details that cosmologists want to determine – and may have partly determined. One of them is whether the Big Bang power-law expansion was preceded by the era of cosmic (exponential) inflation. If one is interested in "votes", and it is not really the right question or type of evidence one should be interested in, I think that a safe majority of cosmologists would still answer Yes, there has been inflation. There would be no majority if a "more specific type of inflation" would have to be picked by the researchers at the same moment. One may also ask what the dark matter is composed of. WIMPs (Weakly Interacting Massive Particles) would still be the most widespread single choice but its believers could be above 50% or below 50%, depending on the set of people who are asked, and people may have different opinions on whether this number is above 50% etc. Most people in the field are uncertain about WIMPs as individuals. There is nothing "objective" about the question whether some at least somewhat controversial idea is supported by more than 50%, by a majority, or by a "consensus".
To return to your question, you shouldn't use the term "consensus model" because consensus is not a method by which scientists think – moreover, there exists a different level of "consensus" about different questions, so one can't say that one of your terms is right and the other is wrong as a description of the "consensus". (The percentage of cosmologists who take The Big Bang Theory seriously is overwhelming, and the percentage who think that the $\Lambda{\rm CDM}$ model is at least "basically right" is still a majority, although the devil may hide in the details.) And you shouldn't use "The Big Bang Theory" and the $\Lambda{\rm CDM}$ model in standalone sentences because as your question indicates, the usage of some terms means that you would use phrases whose meaning is unknown to you, and it is generally a very bad habit to do such things.
If you talk or write about some things, especially if you want to make your text intimidating by words such as "consensus", you should better have a good enough idea what you're talking about which apparently isn't your case in this situation. I think that your question indicates that you should only use the terms "The Big Bang Theory" and "$\Lambda{\rm CDM}$ model" in sentences in which you say that the cosmologists and physicists use these terms. With an introduction such as the comment above, one may get some idea what the terms mean but it's still not enough to justify too "authoritative" statements about these theories.
Update
CuriousOne has pointed out that maybe the term "consensus model" wasn't quite invented by the OP but was heard somewhere and it came from an inaccurate back-translation of the "concordance model". That's indeed the term that was used basically for the $\Lambda{\rm CDM}$ model. The first appearance was in 1995, in a paper by Steinhardt and Ostriker:
They studied the experimental constraints in the 2-dimensional parameter plane involving the Hubble constant (or the age of the Universe) and the cosmological constant, and were already able to guess that the cosmological constant seemed to be 65% of the energy density or so (and all the constraints seemed to be consistent with these choices), some three years before the "discovery" of this fact was officially made by the experimenters. The "concordance" refers purely to the agreement between the models and the observations – there is nothing "sociological" or "about people's opinions" in this term.
A nice picture I borrowed from the question on this server
How do scientists calculate the percentage of dark energy in the universe?
The fact that the thin ellipses (experimental constraints) intersect was and is nontrivial. Two of them are enough to determine the point. The fact that the third ellipse also intersects the point is already a nontrivial check i.e. evidence that we're not just fitting parameters but that it's more likely than before that it actually makes sense to describe the data by the given 2-parameter theory. And this nontrivial agreement is perhaps the real reason why the word "concordance" was used.
Luboš Motl
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