Gianmassimo Tasinato

General brane geometries from scalar potentials: gauged supergravities and accelerating universes

We find broad classes of solutions to the field equations for d-dimensional gravity coupled to an antisymmetric tensor of arbitrary rank and a scalar field with non-vanishing potential. For an exponential potential we find solutions corresponding to brane geometries, generalizing the black p-branes and S-branes known for the case of vanishing potential. These geometries are singular at the origin with up to two horizons. When the singularity has negative tension or the cosmological constant is positive we find time-dependent configurations describing accelerating universes. Special cases give explicit brane geometries for gauged supergravities in various dimensions, and we discuss their interrelation. Some examples lift to give new solutions to 10D supergravity. Limiting cases preserve a fraction of the supersymmetries of the vacuum. We also consider more general potentials, including sums of exponentials. Exact solutions are found for these with up to three horizons, with potentially interesting cosmological interpretation. Further examples are provided.We find broad classes of solutions to the field equations for d-dimensional gravity coupled to an antisymmetric tensor of arbitrary rank and a scalar field with non-vanishing potential. Our construction generates these configurations from the solution of a single nonlinear ordinary differential equation, whose form depends on the scalar potential. For an exponential potential we find solutions corresponding to brane geometries, generalizing the black p-branes and S-branes known for the case of vanishing potential. These geometries are singular at the origin with up to two (regular) horizons. Their asymptotic behaviour depends on the parameters of the model. When the singularity has negative tension or the cosmological constant is positive we find time-dependent configurations describing accelerating universes. Special cases give explicit brane geometries for (compact and non-compact) gauged supergravities in various dimensions, as well as for massive 10D supergravity, and we discuss their interrelation. Some examples lift to give new solutions to 10D supergravity. Limiting cases with a domain wall structure preserve part of the supersymmetries of the vacuum. We also consider more general potentials, including sums of exponentials. Exact solutions are found for these with up to three horizons, having potentially interesting cosmological interpretation. We give several additional examples which illustrate the power of our techniques.

Lifshitz solutions in supergravity and string theory

We derive Lifshitz configurations in string theory for general dynamical exponents z ≥ 1. We begin by obtaining simple Li × Ω solutions to supergravities in diverse dimensions, with Ω a compact constant curvature manifold. Then we uplift the solutions to ten dimensions, providing configurations that correspond to warped compactifications in Type II string theory.

Selftuning and its footprints

Abstract We reconsider the selftuning idea in brane world models of finite volume. We notice that in a large class of selftuning models, the four-dimensional physics is sensitive to the vacuum energy on the brane. In particular the compactification volume changes each time the tension of the brane is modified: consequently, observable constants, as the effective Planck mass or masses of matter fields, change as well. We notice that the selftuning mechanism and the stabilization mechanism of the size of the extra dimensions are generically in apparent conflict. We focus on a selftuning model in six spacetime dimensions to analyze how the above considerations are explicitly realized.

Scale dependence of local fNL

We consider possible scale-dependence of the non-linearity parameter fNL in local and quasi-local models of non-Gaussian primordial density perturbations. In the simplest model where the primordial perturbations are a quadratic local function of a single Gaussian field then fNL is scale-independent by construction. However scale-dependence can arise due to either a local function of more than one Gaussian field, or due to non-linear evolution of modes after horizon-exit during inflation. We show that the scale dependence of fNL is typically first order in slow-roll. For some models this may be observable with experiments such as Planck provided that fNL is close to the current observational bounds.

General axisymmetric solutions and self-tuning in 6D chiral gauged supergravity

We re-examine the properties of the axially-symmetric solutions to chiral gauged 6D supergravity, recently found in refs. [12] and [13]. Ref. [12] finds the most general solutions having two singularities which are maximally-symmetric in the large 4 dimensions and which are axially-symmetric in the internal dimensions. We show that not all of these solutions have purely conical singularities at the brane positions, and that not all singularities can be interpreted as being the bulk geometry sourced by neutral 3-branes. The subset of solutions for which the metric singularities are conical precisely agree with the solutions of ref. [13]. Establishing this connection between the solutions of these two references resolves a minor conflict concerning whether or not the tensions of the resulting branes must be negative. The tensions can be both negative and positive depending on the choice of parameters. We discuss the physical interpretation of the non-conical solutions, including their significance for the proposal for using 6-dimensional self-tuning to understand the small size of the observed vacuum energy. In passing we briefly comment on a recent paper by Garriga and Porrati which criticizes the realization of self-tuning in 6D supergravity.

Towards Minkowski vacua in type II string compactifications

We study the vacuum structure of compactifications of type II string theories on orientifolds with SU(3) × SU(3) structure. We argue that generalised geometry enables us to treat these non-geometric compactifications using a supergravity analysis in a way very similar to geometric compactifications. We find supersymmetric Minkowski vacua with all the moduli stabilised at weak string coupling and all the tadpole conditions satisfied. Generically the value of the moduli fields in the vacuum is parametrically controlled and can be taken to arbitrarily large values.

Standard 4D gravity on a brane in six-dimensional flux compactifications

We consider a six-dimensional space-time, in which two of the dimensions are compactified by a flux. Matter can be localized on a codimension one brane coupled to the bulk gauge field and wrapped around an axis of symmetry of the internal space. By studying the linear perturbations around this background, we show that the gravitational interaction between sources on the brane is described by Einstein 4D gravity at large distances. Our model provides a consistent setup for the study of gravity in the rugby (or football) compactification, without having to deal with the complications of a deltalike, codimension two brane. To our knowledge, this is the first complete study of gravity in a realistic brane model with two extra dimensions, in which the mechanism of stabilization of the extra space is fully taken into account.

Scale-dependent non-Gaussianity probes inflationary physics

We calculate the scale dependence of the bispectrum and trispectrum in (quasi) local models of non-Gaussian primordial density perturbations, and characterize this scale dependence in terms of new observable parameters. They can help to discriminate between models of inflation, since they are sensitive to properties of the inflationary physics that are not probed by the standard observables. We find consistency relations between these parameters in certain classes of models. We apply our results to a scenario of modulated reheating, showing that the scale dependence of non-Gaussianity can be significant. We also discuss the scale dependence of the bispectrum and trispectrum, in cases where one varies the shape as well as the overall scale of the figure under consideration. We conclude providing a formulation of the curvature perturbation in real space, which generalises the standard local form by dropping the assumption that fNL and gNL are constants.

UV caps and modulus stabilization for 6D gauged chiral supergravity

We describe an explicit UV regularization of the brane singularities for all 4D flat configurations of 6D gauged chiral supergravity compactified on axially symmetric internal spaces (for which the general solutions are known). All such solutions have two or fewer co-dimension two singularities, which we resolve in terms of microscopic co-dimension one cylindrical 4-branes, whose interiors are capped using the most general possible 4D flat solution of the 6D field equations. By so doing we show that such a cap is always possible for any given bulk geometry, and obtain an explicit relationship between the properties of the capped 4-branes and the various parameters which describe the bulk solution. We show how these branes generically stabilize the size of the extra dimensions by breaking the scale invariance which relates classical solutions to 6D supergravity, and we compute the scalar potential for this modulus in the 4D effective theory. The lifting of this marginal direction provides a natural realization of the Goldberger-Wise stabilization mechanism in six dimensions.

Inflationary correlation functions without infrared divergences

Inflationary correlation functions are potentially affected by infrared divergences. For example, the two-point correlator of curvature perturbation at momentum k receives corrections ~ ln (kL), where L is the size of the region in which the measurement is performed. We define infrared-safe correlation functions which have no sensitivity to the size L of the box used for the observation. The conventional correlators with their familiar log-enhanced corrections (both from scalar and tensor long-wavelength modes) are easily recovered from our IR-safe correlation functions. Among other examples, we illustrate this by calculating the corrections to the non-Gaussianity parameter fNL coming from long-wavelength tensor modes. In our approach, the IR corrections automatically emerge in a resummed, all-orders form. For the scalar corrections, the resulting all-orders expression can be evaluated explicitly.