$\Lambda$CDM obviously includes dark energy (the $\Lambda$) as well as cold dark matter (CDM). Does it also include cosmic inflation?

I've not seen a clear answer to this. Wikipedia's article on Lambda-CDM says in the lede that Lambda-CDM can be extended to include inflation (i.e. it doesn't per se include cosmic inflation). But then in the next section it contradicts itself by saying "The model includes ... an exponential expansion of space [shortly after the big bang] by a scale multiplier of $10^{27}$ or more, known as cosmic inflation." I also suspect most cosmologists will agree that the observational evidence behind inflation is less established than that behind dark matter and dark energy.

Does $\Lambda$CDM include cosmic inflation? If so, why isn't it referred to as $\Lambda$CDMI?

  • $\begingroup$ Would this not be a matter of opinion? Or is there an internationally recognized authority on naming cosmological models? $\endgroup$
    – safesphere
    Oct 16, 2018 at 1:46
  • $\begingroup$ I don't think there's an internationally recognized authority, but people generally have a good idea of what theory they're referring to. For example if someone talked about Newtonian cosmology, nobody would think about Planck's constant - it's just not included in the theory. The question is whether Lambda-CDM includes inflation. $\endgroup$
    – Allure
    Oct 16, 2018 at 2:06
  • $\begingroup$ Further down in the article it says: "The model uses the Friedmann–Lemaître–Robertson–Walker metric, the Friedmann equations and the cosmological equations of state to describe the observable universe from right after the inflationary epoch to present and future. " So I'm pretty sure the answer to your 1st question is "yes." $\endgroup$
    – D. Halsey
    Oct 16, 2018 at 18:41
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    $\begingroup$ @D.Halsey but if it's from "right after the inflationary epoch", then the inflationary epoch itself is not part of the model (?) $\endgroup$
    – Allure
    Oct 16, 2018 at 18:48
  • $\begingroup$ @Allure: I interpret that to mean that the model includes all 3 things (inflation, FLRW metric, & Friedmann equations), using the results of the inflationary calculations as initial conditions for the Friedmann equations (which don't have to be at t=0). $\endgroup$
    – D. Halsey
    Oct 16, 2018 at 18:59

1 Answer 1


The $\Lambda CDM$ cosmological model is a pattern of the evolution of the cosmos parameterized by a cosmological constant $\Lambda$ describing the vacuum energy (dark energy), ordinary matter (baryonic) and cold nonbaryonic dark matter (CDM) inferred to match the observed matter density. The picture in which, as per current cosmological epoch, roughly matter density $\Omega_M = 0.3$, vacuum energy density $\Omega_\Lambda = 0.7$, radiation density $\Omega_R = 0.0001$ (negligible), fits an impressive variety of observational data and implies a flat universe as well.

In itself the model is not asking for cosmic inflation, however the flatness of the universe, its homogeneity and isotropy on a large scale raised the two problems of unnaturalness: the so called "flatness problem" and "horizon problem" (The CMB, cosmic microwave background, is isotropic to a high degree). Why the initial conditions of the universe were so finely tuned? As this seems unlikely, a more likely scenario is a dynamical mechanism that can take a wide spectrum of initial conditions and evolve them toward flatness and homogeneity/isotropy. The inflationary universe provides such mechanism, even if its demonstration is still far to be achieved.

  • $\begingroup$ Your answer omits a term of the Friedmann equation which has FOUR terms represented by \Omega including Omega_k. This term permits analysis of non-flat universe models. Also, a flat universe model has no need for inflation, since the role of inflation is to cause a non-flat universe to become flatter. $\endgroup$
    – Buzz
    Jun 5, 2021 at 22:45
  • $\begingroup$ @Buzz. The $\Lambda CDM$ cosmological model assumes a flat universe, in compliance with current observational data. Therefore the curvature density is not shown. $\endgroup$ Jun 8, 2021 at 8:58

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