What is the significance of dark energy in determining the age of the universe?

Question

BlackTom AI · Accepted Answer

Dark energy causes the cosmic expansion to accelerate, so its primary significance for the universe’s age is that it changes the expansion history and leads to an accelerating expansion today.

1) Relevant knowledge points and concepts
- Friedmann equations govern expansion. The acceleration equation: ä/a = −(4πG/3)(ρ + 3p/c^2). Negative pressure (p) can produce positive acceleration.  
- Equation-of-state parameter w = p/(ρc^2). For a cosmological constant (dark energy) w ≈ −1, so ρ + 3p/c^2 = ρ(1 + 3w) ≈ ρ(1 − 3) = −2ρ → positive ä.  
- The age t0 of the universe depends on the integral of 1/H(z): t0 = ∫0^∞ dz / [(1+z)H(z)], with H(z)=H0 sqrt(Ωm(1+z)^3 + ΩΛ + ...). Different energy components change H(z) and thus t0.

2) Step-by-step reasoning
- If the universe were matter-dominated (Ωm=1, ΩΛ=0), the analytic age is t0 = 2/(3H0).  
- If dark energy (ΩΛ>0) is present, H(z) evolves differently and the integral yields a larger t0 for the same present H0 because expansion has been accelerating in recent epochs.

3) Calculation with intermediate steps (illustrative numerical example)
- Use H0 = 70 km/s/Mpc. H0^-1 = 9.78×10^9 yr × (100/70) ≈ 13.97×10^9 yr ≈ 14.0 Gyr.  
- Matter-only age: t0 = 2/(3H0) = 0.6667 × 14.0 Gyr ≈ 9.33 Gyr.  
- For a flat ΛCDM with Ωm ≈ 0.3, ΩΛ ≈ 0.7, the age factor ≈ 0.964 so t0 ≈ 0.964 × 14.0 Gyr ≈ 13.5 Gyr. Thus adding dark energy increases the inferred age and implies late-time acceleration.

4) Why the correct answer is correct
The statement “It leads to an accelerating expansion today” directly reflects the effect of dark energy’s negative pressure (w ≈ −1) producing positive cosmic acceleration, confirmed by supernova, CMB and BAO observations. That acceleration changes the expansion history and so affects age estimates.

5) Why other options are incorrect
- “It eliminates the need for the Big Bang”: incorrect — the Big Bang framework remains; dark energy modifies later expansion, not the initial singularity concept.  
- “It slows expansion over time”: opposite of reality; dark energy causes acceleration, not slowing.  
- “It causes galaxies to stop moving”: incorrect — expansion acceleration increases recession speeds at large scales; galaxies do not “stop moving” because of dark energy.

6) Conclusion
The correct choice is “It leads to an accelerating expansion today,” which matches the provided answer.

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