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Chapter 26: Problem 15

Some people refer to the Hubble constant as "the Hubble variable." In what sense is this justified?

Short Answer

Expert verified
The term 'Hubble variable' is justified because the Hubble constant isn't a true constant. It changes over time, decreasing as the universe expands and ages. Although these variations are slow on a human timescale, naming it as 'Hubble variable' acknowledges this temporal variability.

Step by step solution

01

Understanding the Hubble Constant

The Hubble constant, \(H_0\), is a parameter that indicates the rate at which the universe is expanding. It can be understood as the rate of change of the scale factor, which measures the size of the universe in Big Bang cosmology. Currently, its estimated value is around 70 kilometers per second per megaparsec.
02

The Hubble 'Variable'

Even though it's called a 'constant', in reality, the value of the Hubble constant isn't truly constant everywhere or at all times. It is dependent on the scale factor of the universe, which changes with time as the universe expands. Back when the universe was half its present size, the Hubble 'constant' was twice its current value. That means, the constant decreases as the universe expands and ages. This is why it is sometimes referred to as the Hubble 'variable'.
03

Justification for the term 'Hubble variable'

Given that the Hubble constant varies with time and isn't the same everywhere, referring to it as the 'Hubble variable' is justified. However, it's worth mentioning that despite this variability, the variations are very slow on a human timescale and the Hubble constant can be considered approximately constant for relatively short periods.

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Most popular questions from this chapter

Use Wien's law (Section \(5-4\) ) to calculate the wavelength at which the cosmic microwave background \((T=2.72 .5 \mathrm{~K})\) is most intense.

4 Calculate the mass density of radiation \(\left(\rho_{\mathrm{rad}}\right)\) in each of the following situations, and explain whether each situation is matter-dominated or radiation-dominated: (a) the photosphere of the Sun \(\left(T=5800 \mathrm{~K}, \rho_{\mathrm{m}}=3 \times 10^{-4} \mathrm{~kg} / \mathrm{m}^{3}\right) ;(\) b \()\) the center of the Sun \(\left(T=1.55 \times 10^{7} \mathrm{~K}, \rho_{\mathrm{m}}=1.6 \times 10^{5} \mathrm{~kg} / \mathrm{m}^{3}\right)\); (c) the solar corona \(\left(T=2 \times 10^{6} \mathrm{~K}, \rho_{\mathrm{m}}=5 \times 10^{-13} \mathrm{~kg} / \mathrm{m}^{3}\right)\).

What is a cosmological constant? Why did Einstein introduce it into cosmology?

Estimate the age of the universe for a Hubble constant of (a) \(50 \mathrm{~km} / \mathrm{s} / \mathrm{Mpc}\), (b) \(75 \mathrm{~km} / \mathrm{s} / \mathrm{Mpc}\), and (c) \(100 \mathrm{~km} / \mathrm{s} / \mathrm{Mpc}\). On the basis of your answers, explain how the ages of globular clusters could be used to place a limit on the maximum value of the Hubble constant.

Search the World Wide Web for information on a European Space Agency mission called Planck. In what ways is Planck an improvement over the WMAP mission? Has it been launched? If yes, what have scientists learned from Planck? If no, what do they hope plan to learn?
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