Hubble bubble toil and trouble

EMPEHI

... is  the name of a 1964 hit by English pop group Manfred Mann, a misquote from Shakespeare's Macbeth but for us it is the continued mystery of the Hubble parameter ##H## which we meet at the end of section 8.3 and was discovered by the great astronomer Hubble and predicted by the Friedmann equations.

Carroll wrote his book in 2003 and gives the Hubble constant, ##H_0##, (which is the current value of the Hubble parameter) as ##70\pm10\ \rm{km/sec/Mpc}##. Since then many more measurements of it have been made and there seem to be two values 67 and 73 depending on the measuring technique used and it is not known why. This mystery is called the Hubble tension.

We also meet the Hubble time ##t_H=1/H_0=13.6\ \rm{billion\ years}## which is the age of the Universe and the Hubble distance ##\ d_H=c/H_0=14\ \rm{billion\ lightyears}## which is the size of the visible Universe. Obviously. 

We also meet the deceleration parameter ##q## , the density parameter ##\Omega## and the critical density ##\rho_{crit}##. Recent measurements of the cosmic background anisotropy lead us to believe that ##\Omega## is very close to unity which would mean the Universe is flat and infinite. Nut as Wikipedia says, it might merely be that the universe is much larger than the part we see. Similarly, the fact that Earth is approximately flat at the scale of the Netherlands does not imply that the Earth is flat: it only implies that it is much larger than the Netherlands.

See my notes  at Commentary 8.3 Hubble and more.pdf (4 pages)