Physic Labs

Cosmology and astrophysics

Dark energy and accelerated expansion

Use the schematic scale-factor plot a(t)a(t) to see how the matter fraction Ωm\Omega_m reshapes cosmic expansion in a flat Λ\LambdaCDM model, where ΩΛ=1−Ωm\Omega_\Lambda=1-\Omega_m and pΛ=−ρΛc2p_\Lambda=-\rho_\Lambda c^2.

Research

Equipment

  • Schematic expansion-history graph a(t)a(t)
  • Slider “Tỉ phần vật chất Ωₘ” (matter fraction)
  • “Góc nhìn” (view angle) control and draggable canvas
  • “Tạm dừng” (pause) button

Procedure

  1. Read the expansion curve

    Start with the default Ωm\Omega_m and follow the curve a(t)a(t) from the past to today. The slope of aa is the expansion rate; in a matter-dominated era a∝t2/3a\propto t^{2/3}, while dark energy drives faster, roughly exponential growth at late times.

  2. Sweep the matter fraction

    Drag the Ωm\Omega_m slider down and up; since the model is flat, ΩΛ=1−Ωm\Omega_\Lambda=1-\Omega_m adjusts automatically. With Ωm\Omega_m near 1 the curve keeps decelerating, while a small Ωm\Omega_m bends it upward — the signature of accelerating expansion from a¨>0\ddot a>0.

  3. Compare universes

    Set Ωm=1.0\Omega_m=1.0 (matter only) and then a low value like 0.3, matching today's estimates. Describe how the future of a(t)a(t) differs in the two cases, and connect the acceleration to a component with negative pressure, pΛ=−ρΛc2p_\Lambda=-\rho_\Lambda c^2.

Simulation

Experiment history

In 1998, two teams studying distant type Ia supernovae — the High-z Supernova Search Team led by Adam Riess and Brian Schmidt, and the Supernova Cosmology Project led by Saul Perlmutter — reported that the expansion of the universe is accelerating rather than slowing. The result earned them the 2011 Nobel Prize and revived Einstein's cosmological constant as the simplest candidate “dark energy.” Independent evidence soon accumulated: the cosmic microwave background measured by WMAP (2003) and Planck (2013) favors a flat universe, and the growth of large-scale structure matches a flat model with roughly Ωm≈0.3\Omega_m\approx0.3 and ΩΛ≈0.7\Omega_\Lambda\approx0.7. Whether dark energy is truly a constant or evolves remains an open question pursued by surveys such as DESI and Euclid.

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