Hubble Time
Rough age of the universe from the Hubble constant.
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≈ 14 billion years
How it works
Hubble time is the inverse of the Hubble constant, so it gives a characteristic timescale for cosmic expansion. If galaxies are receding at rates proportional to their distance, then extrapolating that expansion backward suggests a time of order 1/H_0 for the universe to reach its current size. It is only an estimate of the age of the universe because the expansion rate has changed over time due to radiation, matter, and dark energy.
When to use it
Use this when you want a quick order-of-magnitude estimate for the age of the universe from a measured Hubble constant. It is also useful in cosmology when comparing expansion timescales, even though precise ages require a full cosmological model.
Worked example, step by step
Given H_0 = 70 km s^-1 Mpc^-1 Convert 1 Mpc to km: 1 Mpc ≈ 3.086 × 10^19 km So H_0 = 70 / (3.086 × 10^19) s^-1 H_0 ≈ 2.27 × 10^-18 s^-1 Now take the inverse: t_H = 1 / H_0 ≈ 1 / (2.27 × 10^-18) s t_H ≈ 4.41 × 10^17 s Convert seconds to years using 1 yr ≈ 3.156 × 10^7 s: t_H ≈ (4.41 × 10^17) / (3.156 × 10^7) yr t_H ≈ 1.40 × 10^10 yr So the Hubble time is about 14 billion years.
Common mistakes to avoid
- Using H_0 in km/s/Mpc directly without converting to inverse seconds before inverting
- Treating Hubble time as the exact age of the universe instead of a rough estimate
- Forgetting that the result depends on the units used for H_0 and must be converted consistently
Did You Know?
Inverting Hubble's constant gives a rough age of the universe, close to the accepted 13.8 billion years.
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