TASI lectures on cosmological observables and string theory

TL;DR

This work surveys how inflation can be embedded in a UV-complete framework provided by string theory, emphasizing the sensitivity of inflation to Planck-scale physics and the need for a full effective description. It expounds multiple string-theoretic inflationary mechanisms—especially axion monodromy, Kahler-moduli dynamics, warped brane inflation, and DBI scenarios—along with their distinctive observational signatures in the tensor-to-scalar ratio, non-Gaussianity, and higher-point correlations. The notes outline how moduli stabilization, fluxes, warping, and uplift mechanisms shape viable inflationary potentials and predict rich phenomenology testable with current and upcoming data, including potential heavy-field imprints and oscillatory features. A broader framework is presented that integrates these top-down constructions with bottom-up cosmological probes, exploring holographic uplifts of de Sitter space and emphasizing the continued dialogue between theory and data in exploring the early universe.

Abstract

These lectures provide an updated pedagogical treatment of the theoretical structure and phenomenology of some basic mechanisms for inflation, along with an overview of the structure of cosmological uplifts of holographic duality. A full treatment of the problem requires `ultraviolet completion' because of the sensitivity of inflation to quantum gravity effects, including back reaction and non-adiabatic production of heavy degrees of freedom. Cosmological observations imply accelerated expansion of the late universe, and provide increasingly precise constraints and discovery potential on the amplitude and shape of primordial tensor and scalar perturbations, and some of their correlation functions. Most backgrounds of string theory have positive potential energy, with a rich but still highly constrained landscape of solutions. The theory contains novel mechanisms for inflation, some subject to significant observational tests. Although the detailed ultraviolet completion is not accessible experimentally, some of these mechanisms directly stimulate a more systematic analysis of the space of low energy theories and signatures relevant for analysis of data, which is sensitive to physics orders of magnitude above the energy scale of inflation as a result of long time evolution (dangerous irrelevance) and the substantial amount of data. Portions of these lectures appeared previously in Les Houches 2013, "Post-Planck Cosmology" .

Figures (2)

• Figure 1:
• Figure 2: The structure of the string landscape -- specifically its metastability -- leads to a brane construction for de Sitter spacetime which nontrivially agrees with the macroscopic structure of de Sitter as a two-throated warped compactification. This would not have happened if string theory admitted a hard cosmological constant parameter. The left panel depicts AdS/CFT dual pairs arising from compactification on a positively curved Einstein space. This leads to the leading negative term in its potential, and appears as the base of the cone in the brane construction, D-branes probing the tip of a cone whose size satisfies a radial Friedmann equation. Trading the branes for flux and geometry, the resulting AdS solution has a warp factor that extends to the deep UV. The right panel depicts the effect on all this of uplifting to a metastable de Sitter solution. The leading term in the potential is now positive, e.g. coming from negative curvature. This combined with the second, negative term in the potential (e.g. from orientifolds) leads to a de Sitter analogue of the brane construction whose radial Friedmann equation implies that the size grows to a finite maximum before contracting. This fits perfectly with the dS/dS slicing of macroscopic de Sitter spacetime, which exhibits two warped throats cutoff at a finite UV scale. This structure occurs also in the computation of observables in the dS/CFT approach, which requires integrating over the $d-1$ dimensional metric. All this suggests that the matter sector in the appropriate holographic dual to de Sitter is a theory that is not UV complete (perhaps analogous to QED), in contrast to gauge/gravity duals with asymptotic boundaries.