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One of the successes of theory of inflation is its explanation for the flatness of the Universe at the start of the Big Bang. Simply stated, in the Friedmann equation, the inflation field energy density, $\rho$, in the term $8\pi G\rho/3$, is constant and as the scale length increases exponentially, the curvature term $-kc^2/a^2$ becomes negligible.

My question then is: As the present Universe expands, the vacuum energy (dark energy), which also has constant energy density, will start dominating the matter density more and more. This situation too will drive the Universe towards greater and greater flatness. Is this correct? At present, with matter-dominated universe, the quantity $\Omega-1$, where $\Omega=\rho/\rho_{\text{critical}}$, has increased a factor of $10^{60}$ since the start of the Big Bang. Will this trend reverse?

Sten
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Raghavan Jay Jayakumar
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  • No need to answer this question - it has been answered in https://physics.stackexchange.com/questions/23384/curvature-omega-the-flatness-problem-and-the-evolving-shape-of-the-universe?rq=1. Conclusion - yes, this is correct. – Raghavan Jay Jayakumar Mar 23 '24 at 19:09
  • it is Omega -1, not omega^-1. – Raghavan Jay Jayakumar Mar 23 '24 at 19:11
  • You can think of curvature as an effective fluid component of the Friedman equation with $w=-\frac{1}{3}$. Any fluid with $w<-\frac{1}{3}$ will dominate curvature at late times. This includes dark energy, with $w=-1$. – Andrew Mar 23 '24 at 19:58
  • At present, with matter-dominated universe According to the current standard model of cosmology, the universe is not presently dominated by matter. Dark energy is already 69% of the total energy density, so we live in a dark-energy-dominated universe. – Ghoster Mar 23 '24 at 20:20
  • it is Omega -1, not omega^-1 You can edit your question after you’ve posted it. Just click “Edit” below the question. – Ghoster Mar 23 '24 at 20:51

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