The idea of eternal cosmic inflation has been argued to provide a possible way to conceptualize the measured values of dimensionless “physical constants”, such as the fine structure constant, the Yukawa couplings and notably the cosmological constant: for if in the fundamental theory these parameters are not really constants but are dynamical fields that just happen to have constant value (“moduli fields”) over large scales, then they might, so the argument, still vary from one “inflationary bubble” to the next. Thereby the idea of eternal inflation combined with that of a fundamental theory that has moduli fields (such as string theory with its landscape of string theory vacua) has been argued to put “physical constants” on the same footing as other more or less random phenomenological parameters, such as for instance the distance of our planets from the sun, etc.

Aleksei Starobinsky, Stochastic de sitter (inflationary) stage in the early universe, In: de Vega H.J., Sánchez N. (eds) Field Theory, Quantum Gravity and Strings. Lecture Notes in Physics, vol 246. Springer, Berlin, Heidelberg (doi:10.1007/3-540-16452-9_6)

Gabriela Barenboim, William Kinney, Wan-Il Park, Eternal Hilltop Inflation, Journal of Cosmology and Astroparticle Physics, Volume 2016, May 2016 (arXiv:1601.08140)