What is the difference between the Big Bang Model and the Λ-CDM Model?Well, it's subtle. On that page, I explained the difference between the ΛCDM model and the more general term, the big bang theory.
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 ΛCDM Model?
The former is more detailed than the latter; it also says that there's a big positive cosmological constant (Λ in ΛCDM) and cold dark matter (CDM) in the Universe. Cosmologists are generally certain about the big bang and almost all of them think that ΛCDM is basically correct as well. But there are various uncertainties, various degrees of certainty about different questions, and "consensus" is just an inappropriate word to talk about science.
Even if we added the cosmic inflation, the majority of active cosmologists would probably say "Yes". But no specific "subtype" of inflation would already get over 50% of all cosmologists, I think. And what is the dark matter composed of? WIMP would be the winner but whether it would score more than 50% is debatable. It's been reported that the younger generation of cosmologists is much more willing to abandon WIMP theories. This particular evolution seems reasonably defensible to me, unlike some others.
The word "consensus" is used by people who don't have powerful enough evidence. If they had powerful enough evidence, they would talk about this evidence because it's more convincing than some questionable talk about the consensus.
Syed Ali comes from a part of the world where people generally think differently than Westerners. I am sure that he is much closer to the Western – and Western scientific – thinking than a big majority of his compatriots. But there's still a difference.
When we think why people and which people talk about the "consensus" in science, most of us in the West probably think of the climate change debate. The global warming is real because there is a "consensus", we often hear. The actual consensus doesn't apply to the things that are controversial, however, such as the question whether the human civilization is the reason of most of the climate changes in the last 100 years, or whether there is any problem to be afraid of.
However, in the Muslim World, this is not the primary example of a "consensus". The consensus has to exist about most questions and it's normally the religious leaders who are determining it. At the top, I embedded the famous video of the Saudi preacher Bandar Al-Khaybari who demonstrates that the Earth isn't spinning.
First, the Quran makes it clear that it isn't spinning. Second, the religious monster minds have a consensus that it isn't spinning. Third, one can also show a non-religious proof that the Earth is neither spinning nor orbiting around the Sun. Muslims also have brains so they can't be brainwashed by some Western theories. Take a glass of water and imagine that you fly from a Muslim airport to China. You lift the glass and if the Earth were spinning, you would land at a wrong airport, or something like that, so the Earth can't be spinning. And by the way, Mohammed has also revealed that the celestial house of angels is located in the heaven #7 which falls to Kaaba, and if the Earth were spinning, the house would fall to the ocean or the dry land instead. (At this point, his argumentation starts to sound like Tim Maudlin's.) In that way, it's easy to see that the U.S. Moon landing was shot in Hollywood or somewhere.
The complete consensus about this question may also be demonstrated by beheading everyone who would dare to disagree. Incidentally, other Muslim scholars gave their diverse views on whether or not the Quran says that the Earth is spinning. It's clearly one of the hottest questions of the contemporary Muslim science and the most open ones among the Muslim countries have seen huge public debates on the question whether the Earth is spinning (one is shown in the video).
But in the comments under my answer, CuriousOne added a fun twist. He pointed out that Syed Ali wasn't necessarily the first author of the term "cosmological consensus model". It could have been an inaccurate back-translation of the "concordance model". As far as I know, the term "concordance model" goes back to 1995 when Steinhardt and Ostriker were already giving the first versions of the famous chart above.
It shows that several cosmological observations are imposing constraints on the cosmological parameters and two of them are enough to determine the values. However, the third one happens to go through the intersection, too. That's a nontrivial consistency check of the theory. It's a piece of evidence that we're not just fitting parameters but that the theory – with its limited set of parameters – could actually be right. I think that the word "concordance" primarily refers to the agreement between the different types of cosmological observations – the ability of a theory with some parameters to agree with all of them.
Steinhardt and Ostriker wrote the paper – which also suggested that 65% of the energy density in the Universe is the cosmological constant – some 3 years before the first "experimental discovery" of the cosmological constant emerged. I think it's right to say that they were ahead of the time. And I do think that the usual ΛCDM model is indeed what the people also call the "concordance model".
But as you can see, the name has nothing to do with any sociology – with any consensus in the human or political sense or with the personal opinions about the people. These things simply aren't arguments that belong to scientific papers. And cosmology is not only a science. Since these insights, it has joined the prestigious family of quantitative if not precision sciences.