The cosmological principle states that, on a sufficiently large scale, the universe is both homogeneous and isotropic.
An astronomer proposes several hypothetical observational scenarios to test these fundamental assumptions. Which of the following scenarios describes a universe that is isotropic about an observer on Earth but is not homogeneous?
The average number density of galaxies is found to decrease systematically with increasing radial distance from Earth, while remaining uniform across all angular directions at any given radius.
The Cosmic Microwave Background (CMB) radiation shows a dipole temperature variation, being consistently hotter in one direction of the sky and cooler in the opposite direction.
The Hubble constant is measured to be 73 km s−1 Mpc−173\text{ km s}^{-1}\text{ Mpc}^{-1}73 km s−1 Mpc−1 when observing galaxies in the Northern Celestial Hemisphere, but 67 km s−1 Mpc−167\text{ km s}^{-1}\text{ Mpc}^{-1}67 km s−1 Mpc−1 in the Southern Celestial Hemisphere.
Galaxies are observed to be distributed uniformly throughout a single flat plane that passes through Earth, with completely empty space above and below this plane.
