Eternal Inflation with alpha'-Corrections

Higher-order alpha'-corrections are a generic feature of type IIB string compactifications. In KKLT-like models of moduli stabilization they provide a mechanism of breaking the no-scale structure of the volume modulus. We present a model of inflation driven by the volume modulus of flux compactifications of the type IIB superstring. Using the effects of gaugino condensation on D7-branes and perturbative alpha'-corrections the volume modulus can be stabilized in a scalar potential which simultaneously contains saddle points providing slow-roll inflation with about 130 e-foldings. We can accommodate the 3-year WMAP data with a spectral index of density fluctuations n_s=0.93. Our model allows for eternal inflation providing the initial conditions of slow-roll inflation.Comment: 24 pages, 5 figures, LaTeX, v4: includes comparison with 3-year WMAP data and values for the tensor ratio r and the running of n_

String Cosmology - Large-Field Inflation in String Theory

This is a short review of string cosmology. We wish to connect string-scale physics as closely as possible to observables accessible to current or near-future experiments. Our possible best hope to do so is a description of inflation in string theory. The energy scale of inflation can be as high as that of Grand Unification (GUT). If this is the case, this is the closest we can possibly get in energy scales to string-scale physics. Hence, GUT-scale inflation may be our best candidate phenomenon to preserve traces of string-scale dynamics. Our chance to look for such traces is the primordial gravitational wave, or tensor mode signal produced during inflation. For GUT-scale inflation this is strong enough to be potentially visible as a B-mode polarization of the cosmic microwave background (CMB). Moreover, a GUT-scale inflation model has a trans-Planckian excursion of the inflaton scalar field during the observable amount of inflation. Such large-field models of inflation have a clear need for symmetry protection against quantum corrections. This makes them ideal candidates for a description in a candidate fundamental theory like string theory. At the same time the need of large-field inflation models for UV completion makes them particularly susceptible to preserve imprints of their string-scale dynamics in the inflationary observables, the spectral index $n_s$ and the fractional tensor mode power $r$. Hence, we will focus this review on axion monodromy inflation as a mechanism of large-field inflation in string theory.Comment: 34 pages, 1 figure, LaTeX, v2: typos fixed, 3 references added, agrees with published version in "Perspectives in String Phenomenology" and "International Journal of Modern Physics A

Moduli Stabilization in Meta-Stable Heterotic Supergravity Vacua

We revisit the issue of moduli stabilization in a class of N=1 four dimensional supergravity theories which are low energy descriptions of standard perturbative heterotic string vacua compactified on Calabi-Yau spaces. In particular, we show how it is possible to stabilize the universal dilaton and Kahler moduli in a de Sitter/Minkowski vacuum with low energy supersymmetry breaking by means of non-perturbative gauge dynamics, including recent results by Intriligator, Seiberg and Shih. The non-SUSY vacua are meta-stable but sufficiently long-lived.Comment: 1+31 pages, LaTeX, uses JHEP3 class, v2: references corrected and added, version published in JHE

Non-Equilibrium Random Matrix Theory : Transition Probabilities

In this letter we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large $N$ limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.Comment: REVTeX, 5 pages, 2 figure

Inflation with a graceful exit in a random landscape

We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound $N\ll 10$ on the number of light fields $N$ participating during inflation from the non-observation of negative spatial curvature.Comment: Published versio

Higher-Derivative Supergravity and Moduli Stabilization

We review the ghost-free four-derivative terms for chiral superfields in $\mathcal{N}=1$ supersymmetry and supergravity. These terms induce cubic polynomial equations of motion for the chiral auxiliary fields and correct the scalar potential. We discuss the different solutions and argue that only one of them is consistent with the principles of effective field theory. Special attention is paid to the corrections along flat directions which can be stabilized or destabilized by the higher-derivative terms. We then compute these higher-derivative terms explicitly for the type IIB string compactified on a Calabi-Yau orientifold with fluxes via Kaluza-Klein reducing the $(\alpha')^3 R^4$ corrections in ten dimensions for the respective $\mathcal{N}=1$ K\"{a}hler moduli sector. We prove that together with flux and the known $(\alpha')^3$-corrections the higher-derivative term stabilizes all Calabi-Yau manifolds with positive Euler number, provided the sign of the new correction is negative.Comment: Latex, 44+1 pages; v2: References and comments added; estimates of scales added to sec. 4.

Moduli stabilization and SUSY breaking in heterotic orbifold string models

In this paper we discuss the issues of supersymmetry breaking and moduli stabilization within the context of E_8 x E_8 heterotic orbifold constructions and, in particular, we focus on the class of "mini-landscape" models. In the supersymmetric limit, these models admit an effective low energy field theory with a spectrum of states and dimensionless gauge and Yukawa couplings very much like that of the MSSM. These theories contain a non-Abelian hidden gauge sector which generates a non-perturbative superpotential leading to supersymmetry breaking and moduli stabilization. We demonstrate this effect in a simple model which contains many of the features of the more general construction. In addition, we argue that once supersymmetry is broken in a restricted sector of the theory, then all moduli are stabilized by supergravity effects. Finally, we obtain the low energy superparticle spectrum resulting from this simple model.Comment: LaTeX, v2: 57+1 pages, 4 figures, 8 Tables, added references; this version i) discusses volume moduli stabilization with exponentials of both sign (as sometimes mandated by modular invariance); ii) includes the anomalous U(1)_A D-term & the leading Coleman-Weinberg 1-loop correction into the MSSM soft masses to prevent tachyonic results

On uplifts by warped anti-D3-branes

In this note we outline the arguments against the ten-dimensional consistency of the simplest types of KKLT de Sitter vacua, as given in arXiv:1707.08678. We comment on parametrization proposals within four-dimensional supergravity and express our disagreement with the recent criticism by the authors of arXiv:1808.09428.Comment: Latex, revtex, 4 pages, 1 figure, v2: references added, minor clarification

Chaotic Inflation in Supergravity after Planck and BICEP2

We discuss the general structure and observational consequences of some of the simplest versions of chaotic inflation in supergravity in relation to the data by Planck 2013 and BICEP2. We show that minimal modifications to the simplest quadratic potential are sufficient to provide a controllable tensor mode signal and a suppression of CMB power at large angular scales.Comment: 13 pages, 6 figures, minor references change