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# Advances in Theoretical and Mathematical Physics

## Volume 21 (2017)

### Number 7

### Special Issue: Proceedings of the Strings 2016 Conference in Beijing

Guest Editors: J. Maldacena (Institute for Advanced Study), H. Ooguri (California Institute of Technology), H. Babak (Harvard University), S. Li (Tsinghua University), W. Song (Tsinghua University), and H. Lin (Tsinghua University)

### Why the cosmological constant is so small: A string theory perspective

Pages: 1803 – 1818

DOI: https://dx.doi.org/10.4310/ATMP.2017.v21.n7.a9

#### Author

#### Abstract

With no free parameter (except the string scale $M_S$), dynamical flux compactification in Type IIB string theory determines both the cosmological constant (vacuum energy density) $\Lambda$ and the Planck mass $M_P$ in terms of $M_S$, thus yielding their relation. Following elementary probability theory, we find that a good fraction of the meta-stable de Sitter vacua in the cosmic string theory landscape tend to have an exponentially small cosmological constant $\Lambda$ compared to either the string scale $M_S$ or the Planck scale $M_P$, i.e., $\Lambda \ll M^4_S \ll M^4_P$. Here we illustrate the basic stringy idea with a simple scalar field $\phi^3$ (or $\phi^4$) model coupled with fluxes to show how this may happen and how the usual radiative instability problem is bypassed (since there are no parameters to be fine-tuned). These low lying semi-classical de Sitter vacua tend to be accompanied by light scalar bosons/axions, so the Higgs boson mass hierarchy problem may be ameliorated as well.

Published 19 March 2018