Since its discovery by A. Linde and others, cosmic inflation -- exponential expansion of the universe driven by the potential energy contained in an `inflaton' field -- has become a successful paradigm of early universe cosmology and the origin of structure in the universe. At the same time, it leads to great theoretical problems which remain unsolved. This is a paradigm in search of a theory, and SITP members (including Dimopoulos, Kachru, Kallosh, Linde, Senatore, and Silverstein) have led a major upgrade of our understanding of the dynamics of inflation, taking into account the sensitivity of inflationary theory to quantum gravity that follows from the enormous expansion of the universe and range of the inflaton field during the process. At the same time, SITP theorists discovered an elegant characterization of observables that are captured by low energy quantum fields, and determined precisely how they are constrained by possible symmetries of nature, including a special candidate known as supersymmetry.

Among the major discoveries by SITP members are methods for stabilization of the extra dimensions of string theory to produce accelerated expansion in line with the observed late-universe cosmological constant, several canonical early-universe inflationary mechanisms, and a low energy effective theory of the quantum fluctuations produced during inflation. This includes the recent discovery that string theory naturally produces inflation at large field range (large as compared to the Planck scale of quantum gravity) along ubiquitous highly symmetric `axion' directions in field space, via a mathematical structure known as monodromy -- a fancy version of a spiral staircase. Microwave background experiments are actively testing the signatures of this and several other inflationary mechanisms discovered at Stanford, an unprecedented interface between quantum gravity research and data.

Despite the success of inflation as a theory of the origin of structure, it presents big conceptual challenges. Several SITP members (including Linde, Senatore, Shenker, Silverstein, and Susskind) pursue the difficult problem of deriving a more complete framework for inflationary cosmology. One set of approaches involves upgrading the AdS/CFT correspondence to cosmological backgrounds, taking into account the basic structure of the string landscape. Several interesting lessons have emerged, including remnants of lower-dimensional gravity surviving at least temporarily in the dual description, along with a pair of quantum field theory sectors. This has also led to potential observational predictions -- negative spatial curvature and signatures of exotic bubble collisions -- which apply if the early-universe inflationary expansion is minimal. A recent SITP paper (done in collaboration with a gravitational expert in KIPAC) has discovered on the other hand that the onset of inflation is quite robust even in the presence of large variations in the initial conditions, given sufficient field range. There is clearly much more to learn in this direction.

Accelerated expansion of the universe is implied by observations, and theoretically cosmological backgrounds massively dominate among the solutions of string theory (compared to the more extensively studied anti de Sitter and flat spacetimes). Current and near-future cosmic microwave background and large-scale structure measurements provide sensitive observational probes of early universe physics (as well as much interesting astrophysics). The subject is full of interesting and important challenges. As a result, this area will remain a major component of SITP research for the foreseeable future.