During the 12 years of project C6 of the SFB 676 it has achieved a set of significant contributions to our understanding of the dynamics of scalar fields in early universe cosmology and its connection to string theory. In this contribution we describe our results at this interface between theoretical cosmology and fundamental high-energy theory in their impacts on `string inflation'~ consequences of multi-field inflation in string theory inspired random potentials', `pole inflation, $f(R)$-gravity, and exponential inflationary plateaus', the `phenomenological consequences of features before and during inflation', `false-vacuum tunneling and its consequences for the initial conditions of inflation', connections between slow-rolling scalar fields and electroweak symmetry breaking due to couplings between the Standard Model (SM) Higgs field and inflation, `moduli stabilization and de Sitter (dS) vacua in string theory', as well as the connection of dS vacua to `sequestering as a solution to the cosmological constant problem', and on the connection between measurements of ${\rm \Lambda CDM}$ parameters from the CMB as well as local data such as the local $H_0$ determinations, and effects from large-scale structure such as weak gravitational lensing. We finish in section with a summary of a review by one of the PIs on the topic of `String cosmology -- Large field inflation in string theory'.

Louis, Jan "Scalar Fields in Cosmology: Inflation, Dark Matter, Dark Energy" in Particles, Strings and the Early Universe : The Structure of Matter and Space-Time / Haller, Johannes, Grefe, Michael (eds.), Verlag Deutsches Elektronen-Synchrotron : 2018; Hamburg : Verlag Deutsches Elektronen-Synchrotron 341-361 (2018). doi:10.3204/PUBDB-2018-00782/C6

Published by Verlag Deutsches Elektronen-Synchrotron, Hamburg