Cosmological Attractors from α\alpha-Scale Supergravity

The Planck value of the spectral index can be interpreted as $n_s = 1 - 2/N$ in terms of the number of e-foldings $N$. An appealing explanation for this phenomenological observation is provided by $\alpha$-attractors: the inflationary predictions of these supergravity models are fully determined by the curvature of the Kahler manifold. We provide a novel formulation of $\alpha$-attractors which only involves a single chiral superfield. Our construction involves a natural deformation of no-scale models, and employs these to construct a De Sitter plateau with an exponential fall-off. Finally, we show how analogous structures with a flat Kahler geometry arise as a singular limit of such $\alpha$-scale models.Comment: 6 pages, 3 figures. v3: minor clarifications and refs added. PRD versio

Universality Classes of Scale Invariant Inflation

We investigate the inflationary implications of extensions of Poincare symmetry. The simplest constructions with local scale invariance lead to universal predictions: the spectral index is $n_s = 1-2/N$, in excellent agreement with Planck data, while the tensor-to-scalar ratio is determined by a free parameter to $r = 12 \alpha / N^2$. For the special value $\alpha=1$ one finds symmetry enhancement to the full conformal group. We show that these findings hold both for two-derivative scalar-tensor theories as well as higher-derivative gravity. Therefore scale invariance underlies a promising set of inflationary models.Comment: 6 pages, 1 figur

General sGoldstino Inflation

We prove that all inflationary models, including those with dark energy after the end of inflation, can be embedded in minimal supergravity with a single chiral superfield. Moreover, the amount of supersymmetry breaking is independently tunable due to a degeneracy in the choice for the superpotential. The inflaton is a scalar partner of the Goldstino in this set-up. We illustrate our general procedure with two examples that are favoured by the Planck data.Comment: 6 pages, 6 figures; v2: refs added, published versio

Twin Supergravities

We study the phenomenon that pairs of supergravities can have identical bosonic field content but different fermionic extensions. Such twin theories are classified and shown to originate as truncations of a common theory with more supersymmetry. Moreover, we discuss the possible gaugings and scalar potentials of twin theories. This allows to pinpoint to which extent these structures are determined by the purely bosonic structure of the underlying Kac-Moody algebras and where supersymmetry comes to plays its role. As an example, we analyze the gaugings of the six-dimensional N=(0,1) and N=(2,1) theories with identical bosonic sector and explicitly work out their scalar potentials. The discrepancy between the potentials finds a natural explanation within maximal supergravity, in which both theories may be embedded.Comment: 27 pages. v2: ref added, published versio

The double attractor behavior of induced inflation

We describe an induced inflation, which refers to a class of inflationary models with a generalized non-minimal coupling $\xi g(\phi) R$ and a specific scalar potential. The defining property of these models is that the scalar field takes a vev in the vacuum and thus induces an effective Planck mass. We study this model as a function of the coupling parameter $\xi$. At large $\xi$, the predictions of the theory are known to have an attractor behavior, converging to a universal result independent on the choice of the function $g(\phi)$. We find that at small $\xi$, the theory approaches a second attractor. The inflationary predictions of this class of theories continuously interpolate between those of the Starobinsky model and the predictions of the simplest chaotic inflation with a quadratic potential.Comment: 5 pages, 2 figures; v2: refs added, accepted by JHE

Internal Supersymmetry and Small-field Goldstini

The dynamics of the Goldstino mode of spontaneously broken supersymmetry is universal, being fully determined by the non-linearly realized symmetry. We investigate the small-field limit of this theory. This model non-linearly realizes an alternative supersymmetry algebra with vanishing anti-commutators between the fermionic generators, much like an internal supersymmetry. This Goldstino theory is akin to the Galilean scalar field theory that arises as the small-field limit of Dirac-Born-Infeld theory and non-linearly realizes the Galilean symmetry. Indeed, the small-field Goldstino is the partner of a complex Galilean scalar field under conventional supersymmetry. We close with the generalization to extended internal supersymmetry and a discussion of its higher-dimensional origin.Comment: 12 pages, v2: references added, typos corrected, discussion about a fermionic invariant improve

Moduli Backreaction on Inflationary Attractors

We investigate the interplay between moduli dynamics and inflation, focusing on the KKLT-scenario and cosmological $\alpha$-attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for $\alpha$-attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory, or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there is a universal supersymmetric minimum where the scalars end up, preventing the decompactification scenario. The gravitino mass is independent from the inflationary scale with no fine-tuning of the parameters. The observational predictions conform to the universal value of attractors, fully compatible with the Planck data, with possibly a capped number of e-folds due to the interplay with moduli.Comment: 23 pages, 13 figures. v2: minor clarifications and refs added. PRD versio

An Algebraic Classification of Exceptional EFTs Part II: Supersymmetry

We present a novel approach to classify supersymmetric effective field theories (EFTs) whose scattering amplitudes exhibit enhanced soft limits. These enhancements arise due to non-linearly realised symmetries on the Goldstone modes of such EFTs and we classify the algebras that these symmetries can form. Our main focus is on so-called exceptional algebras which lead to field-dependent transformation rules and EFTs with the maximum possible soft enhancement at a given derivative power counting. We adapt existing techniques for Poincar\'{e} invariant theories to the supersymmetric case, and introduce superspace inverse Higgs constraints as a method of reducing the number of Goldstone modes while maintaining all symmetries. Restricting to the case of a single Goldstone supermultiplet in four dimensions, we classify the exceptional algebras and EFTs for a chiral, Maxwell or real linear supermultiplet. Moreover, we show how our algebraic approach allows one to read off the soft weights of the different component fields from superspace inverse Higgs trees, which are the algebraic cousin of the on-shell soft data one provides to soft bootstrap EFTs using on-shell recursion. Our Lie-superalgebraic approach extends the results of on-shell methods and provides a complementary perspective on non-linear realisations

On the Three Primordial Numbers

Cosmological observations have provided us with the measurement of just three numbers that characterize the very early universe: $1-n_{s}$, $N$ and $\ln\Delta_R^2$. Although each of the three numbers individually carries limited information about the physics of inflation, one may hope to extract non-trivial information from relations among them. Invoking minimality, namely the absence of ad hoc large numbers, we find two viable and mutually exclusive inflationary scenarios. The first is the well-known inverse relation between $1- n_{s}$ and $N$. The second implies a new relation between $1-n_{s}$ and $\ln\Delta_R^2$, which might provide us with a handle on the beginning of inflation and predicts the intriguing $\textit{lower}$ bound on the tensor-to-scalar ratio $r> 0.006$ ($95\%$ CL).Comment: 5 pages, 3 figure

Higher Derivative Field Theories: Degeneracy Conditions and Classes

We provide a full analysis of ghost free higher derivative field theories with coupled degrees of freedom. Assuming the absence of gauge symmetries, we derive the degeneracy conditions in order to evade the Ostrogradsky ghosts, and analyze which (non)trivial classes of solutions this allows for. It is shown explicitly how Lorentz invariance avoids the propagation of "half" degrees of freedom. Moreover, for a large class of theories, we construct the field redefinitions and/or (extended) contact transformations that put the theory in a manifestly first order form. Finally, we identify which class of theories cannot be brought to first order form by such transformations.Comment: 26 pages, 1 figure. v2: minor changes, references added, matches version published in JHE