The critical density depends on the value of Hubble's...

The critical density depends on the value of Hubble's constant $H$ If $H$ turns out to be $65 \mathrm{km} / \mathrm{sec}$ per $\mathrm{Mpc}$, calculate how much the critical density changes compared to $H=71 \mathrm{km} / \mathrm{sec}$ per Mpc.

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Key Concepts

Critical Density

The critical density is a fundamental cosmological parameter that defines the density at which the Universe is spatially flat. It is derived from the Friedmann equations and represents the threshold between an open and a closed universe. Understanding critical density is essential in cosmology as it provides insight into the overall fate and geometry of the Universe.

Hubble's Constant

Hubble's constant is the rate at which the Universe is expanding, expressed in units of velocity per distance. It directly influences calculations of distances in the Universe and plays a key role in determining the critical density. Variations in the measured value of Hubble's constant can lead to recalibrations of cosmological parameters, affecting our models of the Universe's evolution.

Dependence of Critical Density on Hubble's Constant

The critical density is proportional to the square of Hubble's constant; this quadratic relationship means that even small changes in the value of Hubble's constant can significantly affect the estimated critical density. This concept is important for understanding how revisions in cosmological measurements translate into differences in our perception of the Universe's composition and geometry.

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