Caption: A cartoon of the divergence of density parameter Ω(t) for FE models with cosmological constant (AKA Lambda, Λ) set to zero.
As a function of cosmic time), Ω(t) always diverges from 1, unless it is exactly 1. In other words, Omega = 1 is an unstable state.
If one adds a cosmological constant, that will eventually cause Ω(t) to converge to 1. However for the observable universe up cosmic time t=10 Gyr???, the cosmological constant (or dark energy) was relatively unimportant. So any significant curvature in the early universe (cosmic time (10**(-12) s -- 377700(3200) y), would have caused strong divergence then of Ω(t) from 1, and so it
|Ω_tot_0-1| < 0.5 at cosmic time t_0 da/dt = da/dt * Ω_tot - k is a rewritten Friedmann equation (Li-55) |Ω_tot - 1| = |k|/(da/dt) ∝ t**(2/3) for matter era using the EdS solution |Ω_tot - 1| = |k|/(da/dt) ∝ t for radiation era using the EdS solution |Ω_tot - 1|_equality < ([10**12 s]/[4*10**(17) s])**(2/3) ≅ 2**(-4) (L-102) and the value gets vastly smaller as you go earlier.The observable universe seems fine-tuned for flatness now. Is this a problem?
Well if |Ω_tot - 1| = 0 exactly as a symmetry of nature, then no.
But if you believe in some complex/chaotic/multiverse universe from which our observable universe and its unobservable surroundings (our pocket universe in multiverse jargon) arose in which curvature is NOT fixed, then a big bang pocket universe needs a flattening process.
Inflation provides this.
Credit/Permission: ©
David Jeffery,
2004 / Own work.
Image link: Itself.
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