Thirty years ago inflation was a highly speculative idea about the origin of the hot big bang, born from navigating questions about the early evolution of the universe with modern ideas about particles and fields. I will explain how a dynamical scalar field can drive an accelerated expansion, altering the causal structure of the early Universe. This altered causal structure, combined with the uncertainty principle of quantum mechanics, leads to early density flucutations with the right properties to explain a number of features of the observed universe. I will focus on observations of the cosmic microwave background, from the Planck satellite in particular, because they allow us to probe the density fluctuations in the linear regime, where their evolution is analytically tractable.
These extraordinary empirical successes motivate us to search for the siblings of these density fluctuations, the inflationary gravitational waves, via their signature in the polarization of the CMB. Their discovery would open up an observational window on quantum gravitational effects, extremely early times, and extremely high energies.