The age of the Universe in the [itex]\Lambda[/itex]CDM cosmology with [itex]\Omega_{matter}=0.26[/itex] and [itex]\Omega_{\Lambda}=0.74[/itex] is the same as in the Milne cosmology which correspods to an almost empty universe. In both cases it is a reciprocal Hubble constant, [itex]1/H_0[/itex], that for now preferred value [itex]H_0=71 km/s/Mpc[/itex] is 13.7 billion years. The most curious coincidence is that at the present time, in the [itex]\Lambda[/itex]CDM model the decelerated expansion is exactly compensated by the accelerated expansion, as if the Universe coast for 13.7 billion years.
Garth said:
Given the current value of the Hubble parameter H = 71, there are other models that give the same result. For example [itex]\Omega_m[/itex] = 0.1, [itex]\Omega_{\Lambda}[/itex] = 0.4. This is a degeneracy as any other. For example, mantaining [itex]\Omega_m[/itex] = 0.3 you get the same age with [itex]\Omega_{\Lambda}[/itex] = 0 and H = 60, which might not be a very unrealistic model (or at least it was not some years ago).gptejms said:If [tex] \Omega_R [/tex] is a very small number,then couldn't there be many combinations of [tex] \Omega_{matter} [/tex] and [tex] \Omega_\Lambda [/tex] that give the same result?
Yes, where [itex] \Omega_R [/itex] is the curvature component, the deviation of the total density parameter from unity.gptejms said:If [tex] \Omega_R [/tex] is a very small number,then couldn't there be many combinations of [tex] \Omega_{matter} [/tex] and [tex] \Omega_\Lambda [/tex] that give the same result?
The "Astonishing Coincidence" refers to the strikingly similar values of the age of the universe predicted by two different cosmological models: the $\Lambda$CDM model and the Milne model. Despite their different assumptions and foundations, both models predict an age of the universe that is within a few percent of each other.
The $\Lambda$CDM model is the currently accepted standard model of cosmology, which includes the presence of dark energy and dark matter, while the Milne model is a simpler model that assumes a flat and empty universe with no dark energy or matter. The Milne model is based on the Special Theory of Relativity, while the $\Lambda$CDM model incorporates both General Relativity and the Standard Model of particle physics.
The currently accepted age of the universe predicted by the $\Lambda$CDM model is about 13.8 billion years, while the Milne model predicts an age of about 18.5 billion years. Despite this large difference, the "Astonishing Coincidence" arises from the fact that the two models predict an age that is within 5% of each other.
The fact that two very different models can predict such a similar value for the age of the universe raises questions about the validity and accuracy of these models. It suggests that there may be underlying principles or physical laws that govern the evolution of the universe that we have yet to discover.
The "Astonishing Coincidence" challenges our current understanding of the universe and raises the possibility of new theories and models that can better explain the observed data. It also highlights the need for further research and exploration in cosmology to fully understand the complex and mysterious nature of our universe.