A3 - Origin of Dark Energy and Dark Matter in String Theory
Contact: Dieter Lüst
, Arthur Hebecker
Aim of the project
We will consider several aspects of string cosmology searching for string realizations of dark matter, dark energy and cosmic inflation through compactifications. Among various compactification schemes with and without branes and/or fluxes, we intend to investigate F-theory compactifications and moduli stabilization on 4-folds with background fluxes. The production of light moduli after reheating in string inflation is another possible new topic of this project. We will also look for possible dark matter candidates in string compactifications. Finally, we are aiming to discuss some general aspects of the string theory landscape such as transitions between metastable vacua.
- Among the most surprising discoveries in cosmology is the late time acceleration of the universe, possibly driven by a non-vanishing vacuum energy. Its equation of state is very close to that of a small and positive cosmological constant.
- This observed value of the cosmological constant appears as a huge fine-tuning in conventional quantum field theory and begs for explanation.
- A potentially useful approach from string theory might be the scanning of the vacuum energy in the string landscape realizing Weinberg's earlier insight on the cosmological constant problem. This requires control of de Sitter vacua in string theory.
- 23% of the universe is made of dark matter.
- In a complete, fundamental cosmological theory the corresponding matter fields should arise from first principles.
- String theory compactifications generally include a number of dark matter candidates such as light moduli, axions or light superpartners of the standard matter fields.
- For a specific string vacuum traditional questions of cosmology such as the overproduction of light fields after reheating can be studied concretely.
Current observations support the inflationary paradigm for the early universe:
- A light scalar field, the inflaton, slowly rolls on a flat potential producing a phase of exponential expansion.
- Its quantum fluctuations generate an almost scale invariant spectrum of adiabatic fluctuations with nearly Gaussian statistics.
- At the end of inflation, reheating occurs and the inflaton decays into Standard Model particles.
Why String Inflation
String theory is a theoretical framework to study inflation:
Cosmology can probe string theory!
- String theory is characterized by a large number of moduli, some of which are suitable inflaton candidates. Fluxes and non-perturbative effects give a potential for these fields.
- Inflation is very sensitive to its UV completion. String models of inflation allow one to analyze and keep under control high energy corrections to the inflationary potential.
- Many string inflationary models make distinctive observable predictions that can be tested in the near future such as for the size of non-Gaussianities, the tensor to scalar ratio or the amount of cosmic strings:
- The coupling of the inflaton to Standard Model particles can be calculated from first principles: a fundamental theory of reheating can be built within string theory.
We set out to look for a 'non-fine-tuned' version of brane-inflation. Our proposal, which we refer
to as 'fluxbrane inflation', can be very briefly summarized as follows: Given a particular flux
choice, some of the D7-brane moduli of a type IIB orientifold compactification may remain unfixed to leading order. Moreover, in the large-complex-structure limit the relevant Kähler potential possesses a shift symmetry (it is the natural shift symmetry of dual Wilson lines of the type IIA mirror model). Thus, we can envision a situation in which the relative distance between two D7-branes is the inflaton. Over most of its field space, the scalar potential is extremely flat.
This stringy version of D-term hybrid inflation can be realized in the type IIB flux landscape, which gives us the opportunity to think in detail about moduli stabilization. One variant that we have worked out relies on the large volume scenario with loop
corrections, stabilizing three large 4-cycles. Some of the ratios of these
cycles are sizable, providing us with a parameter which can be used to
suppress the cosmic string tension - a highly non-trivial achievement
in D-term inflation.
Our investigation of fluxbrane inflation, and especially of its shift-invariance in the light of mirror symmetry, has also lead to an interesting
`spin-off' in Higgs physics and related cosmological questions.
Brane moduli spaces:
The success of our fluxbrane inflation scenario as a non-fine-tuned model of inflation eventually hinges upon the structure of subleading corrections both to the superpotential and
to the Kähler potential of the 7-brane moduli. At leading order, the open and closed moduli spaces are
independent and a suitable choice of gauge fluxes ensures a flat direction in the superpotential of the
open string moduli space. The direct product structure of the open and closed moduli, however, does
not persist if one takes into account the backreaction of 7-branes on the geometry. A crucial question
is to which extent this unavoidable entanglement of open and closed moduli affects the flatness of the inflaton potential.
There are two basically different approaches to this.
First, in the language of Type II compactifications, the open string superpotential can be directly computed by geometric means and via world-sheet techniques. Alternatively, one directly addresses the open-closed entanglement by studying backreacted compactifications with 7-branes in F-theory. In this approach the 7-brane and the closed string moduli are combined into the complex structure moduli of an auxiliary elliptically fibered Calabi-Yau fourfold.
However, an understanding of the F-theoretic analogue of 7-branes with U(1) gauge groups, the associated fluxes and the mechanism of D-term triggered recombination on Calabi-Yau fourfolds turned out to be missing in the literature. We have therefore initiated a systematic and necessarily slightly more mathematical study of 7-branes with abelian gauge symmetry and the associated gauge fluxes in F-theory fourfolds.
This is only a first step towards understanding, directly in F-theory, the more complicated setup of two infinitesimally separated, homologous, fluxed 7-branes, as they appear in fluxbrane inflation. We have been able to construct precisely those gauge fluxes which produce an attractive D-term potential of the required type without inducing at the same time a dangerous open-string moduli-dependent F-term. Furthermore, we have been able to explicitly formulate brane recombination in terms of a complex structure deformation of the F-theory geometry. This will serve as a basis for investigations of the tachyon condensation process triggered by the D-term potential at the end of inflation and thus for studying 7-brane inflation in F-theory geometries.
Beyond conventional geometry:
At a more fundamental level, a proper understanding of de Sitter vacua and thus the cosmological constant in string theory requires a good understanding of spacetime
geometry as probed by string theory. The appropriate mathematical formulation of so-called stringy
geometry is at the moment a field of very active research. Our long-term goal is to investigate
the consequences of such stringy 'non-geometries' with respect to their cosmological properties, in
particular concerning the possibility of de Sitter vacua. As a preparation towards this goal we have
made significant progress in the formal description of stringy geometries.
Infrared issues, non-Gaussianity inflation:
It is well-known that correlation functions of light scalars in de Sitter space are beset by infrared divergences which, however, do not
affect the inflationary power spectrum at leading order. Nevertheless, due to non-linear inflationary
dynamics, these divergences appear in potentially observable curvature perturbations at subleading
order. We decided to look for an intuitive physical understanding of this effect and for appropriate
'infrared safe' observables (as one would do in conventional flat-space quantum field theory). Our
results are very simple: In single-field inflation, IR divergences can be traced to fluctuations of the
Hubble scale during the horizon exit of the relevant observable mode. They can hence be completely
eliminated if one defines the inflationary power spectrum using invariant distances on some late surface
of fixed energy density (e.g. the reheating surface). We were thus lead to the proposal of an 'infrared
safe' power spectrum, which we believe to be a rather fundamental and general result. This 'IR-safe
spectrum' is a conceptually important quantity, resolving at least a significant part of the controversial
discussion of IR divergences in inflation.
A particularly active direction of research, especially in the preparation for the Planck data release, has been the study of possible non-Gaussian features in the power spectrum. Very important contributions in this area have been made by members of our project in collaboration with researchers from other Transregio projects in Heidelberg and from outside. Especially noteworthy is the analyses of the scale dependence of non-Gaussianity in Byrnes et al. 2009, which is among the very first such investigations world-wide.
References and Publications
An up-to-date list of our publications can be found here