[T]he distance at present is<math>d_{\mathrm{max}}(t_0) = \frac{1}{H_0} \int_{0}^{1} \frac{dx}{x^2 \sqrt{\Omega_\Lambda+\Omega_K x^{-2}+\Omega_M x^{-3}}}</math>...[T]here may have been a time before the radiation-dominated era in which there was nothing in the universe but , in which case the particle horizon distance would... be infinite. But as far as telescopic observations... [<math>d_{max}(t_0)</math>] gives the proper distance beyond which we cannot now see.

Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world. ...The most important thing accomplished by the three-degree radiation background in 1965 was to force us to take seriously the idea that there was an early universe.