We outline the construction of metastable de Sitter vacua of type IIB string theory. Our starting point is highly warped IIB compactifications with nontrivial NS and RR three-form fluxes. By incorporating known corrections to the superpotential from Euclidean D-brane instantons or gaugino condensation, one can make models with all moduli fixed, yielding a supersymmetric AdS vacuum. Inclusion of a small number of $\overline{\mathrm{D}3}$-branes in the resulting warped geometry allows one to uplift the AdS minimum and make it a metastable de Sitter ground state. The lifetime of our metastable de Sitter vacua is much greater than the cosmological time scale of ${10}^{10}\mathrm{yr}.$ We also prove, under certain conditions, that the lifetime of dS space in string theory will always be shorter than the recurrence time.

/pdf/de-sitter-vacua-in-string-theory-2gp3ty8kg8.pdf

De Sitter vacua in string theory

The observable universe could be a 1 + 3-surface (the “brane”) embedded in a 1 + 3 + d-dimensional spacetime (the “bulk”), with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the d extra spatial dimensions could be very large relative to the Planck scale, which lowers the fundamental gravity scale, possibly even down to the electroweak (∼ TeV) level. This revolutionary picture arises in the framework of recent developments in M theory. The 1 + 10-dimensional M theory encompasses the known 1 + 9-dimensional superstring theories, and is widely considered to be a promising potential route to quantum gravity. General relativity cannot describe gravity at high enough energies and must be replaced by a quantum gravity theory, picking up significant corrections as the fundamental energy scale is approached. At low energies, gravity is localized at the brane and general relativity is recovered, but at high energies gravity “leaks” into the bulk, behaving in a truly higher-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting and potentially testable implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a phenomenological way to test some of the novel predictions and corrections to general relativity that are implied by M theory. This review discusses the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional brane-worlds based on the Randall-Sundrum models.

Brane-World Gravity

We argue that in the simplest version of the KKLT model, the maximal value of the Hubble constant during inflation cannot exceed the present value of the gravitino mass, Hm3/2. This may have important implications for string cosmology and for the scale of the SUSY breaking in this model. If one wants to have inflation on high energy scale, one must develop phenomenological models with an extremely large gravitino mass. On the other hand, if one insists that the gravitino mass should be O(1 TeV), one will need to develop models with a very low scale of inflation. We show, however, that one can avoid these restrictions in a more general class of KKLT models based on the racetrack superpotential with more than one exponent. In this case one can combine a small gravitino mass and low scale of SUSY breaking with the high energy scale of inflation.

Landscape, the scale of SUSY breaking, and inflation

Cosmological consequences of the brane world scenario are reviewed in a pedagogical manner. According to the brane world idea, the standard model particles are confined on a hypersurface (a so-called brane), which is embedded in a higher-dimensional spacetime (the so-called bulk). We begin our review with the simplest consistent brane world model: a single brane embedded in a five-dimensional anti-de Sitter spacetime. Then we include a scalar field in the bulk and discuss in detail the difference with the anti-de Sitter case. The geometry of the bulk spacetime is also analysed in some depth. Finally, we investigate the cosmology of a system with two branes and a bulk scalar field. We comment on brane collisions and summarize some open problems of brane world cosmology.

http://fma.if.usp.br/~amsilva/Artigos/Branes/branes-review.pdf

Cosmology and brane worlds: a review

Recent developments in the physics of extra dimensions have opened up new avenues to test such theories. We review cosmological aspects of brane world scenarios such as the Randall–Sundrum brane model and two-brane systems with a bulk scalar field. We start with the simplest brane world scenario leading to a consistent cosmology: a brane embedded in an anti-de Sitter space–time. We generalize this setting to the case with a bulk scalar field and then to two-brane systems.We discuss different ways of obtaining a low-energy effective theory for two-brane systems, such as the moduli space approximation and the low-energy expansion. A comparison between the different methods is given. Cosmological perturbations are briefly discussed as well as early universe scenarios such as the cyclic model and the born-again brane world model. Finally we also present some physical consequences of brane world scenarios on the cosmic microwave background and the variation of constants.

Brane world cosmology

The radion on the de Sitter brane is investigated at the linear perturbation level, using the covariant curvature tensor formalism developed by Shiromizu, Maeda and Sasaki. 1) It is found that if there is only one de Sitter brane with positive tension, there is no radion, and thus ordinary Einstein gravity is recovered on the brane, with the exception of corrections due to the massive Kaluza-Klein modes. As a by-product of the covariant curvature tensor formalism, it is immediately seen that cosmological scalar, vector and tensor type perturbations all have the same Kaluza-Klein spectrum. On the other hand, if there are two branes, one with positive tension and another with negative tension, the gravity on each brane receives corrections from the radion mode in addition to the Kaluza-Klein modes, and the radion is found to have a negative mass-squared proportional to the curvature of the de Sitter brane. This is in contrast to the flat brane case, in which the radion mass vanishes and becomes degenerate with the 4-dimensional graviton modes. To relate our result with the metric perturbation approach, we derive the second-order action for the brane displacement. We find that the radion identified in our approach indeed corresponds to the relative displacement of the branes in the Randall-Sundrum gauge and describes the scalar curvature perturbations of the branes in Gaussian normal coordinates around the branes. The implications of our results with regard to the inflationary brane universe are briefly discussed.

Radion on the de Sitter Brane

We consider a wave-function approach to the false vacuum decay with gravity and present a new method to calculate the tunneling amplitude under the WKB approximation. The result agrees with the one obtained by the Euclidean path-integral method, but gives a much clearer interpretation of an instanton (Euclidean bounce solution) that dominates the path integral. In particular, our method is fully capable of dealing with the case of a thick wall with the radius of the bubble comparable to the radius of the instanton, thus surpassing the path-integral method whose use can be justified only in the thin-wall and small bubble radius limit. The calculation is done by matching two WKB wave functions, one with the final state and another with the initial state, with the wave function in the region where the scale factor of the metric is sufficiently small compared with the inverse of the typical energy scale of the field potential at the tunneling. The relation of the boundary condition on our wave function for the false vacuum decay with Hartle-Hawking's no-boundary boundary condition and Vilenkin's tunneling boundary condition on the wave function of the universe is also discussed.

False vacuum decay with gravity in the non-thin-wall limit

We consider the force acting on a spinning charged test particle (probe particle) with mass m and charge q in a slowly rotating Kerr-Newman-de Sitter (KNdS) black hole with mass M and charge Q . We consider the case in which the spin vector of the probe particle is parallel to the angular momentum vector of the KNdS spacetime. We take account of the gravitational spin-spin interaction under the slow rotation limit of the KNdS spacetime. When Q = M and q = m , we show that the force balance holds including the spin-spin interaction and the motion is approximately the same as that of a particle in de Sitter spacetime. This force cancellation suggests the possibility of the existence of an exact solution of a spinning multi-KNdS black hole.

http://iopscience.iop.org/article/10.1088/0264-9381/17/6/303/pdf

A probe particle in a Kerr-Newman-de Sitter cosmos

We consider the force acting on a spinning charged test particle (probe particle) with the mass m and the charge q in slow rotating the Kerr-Newman-deSitter(KNdS) black hole with the mass M and the charge Q. We consider the case which the spin vector of the probe particle is parallel to the angular momentum vector of the KNdS space-time. We take account of the gravitational spin-spin interaction under the slow rotating limit of the KNdS space-time. When Q=M and q=m, we show that the force balance holds including the spin-spin interaction and the motion is approximately same as that of a particle in the deSitter space-time. This force cancellation suggests the possibility of the existence of an exact solution of spinning multi-KNdS black hole.

A Probe Particle in Kerr-Newman-deSitter Cosmos

We define spacetimes which are asymptotic to radiation-dominated Friedman-Robertson-Walker spacetimes at timelike infinity and study the asymptotic structure. We discuss the local asymptotic symmetry and give a definition of the total energy from the electric part of the Weyl tensor.

Uchida Gen

Papers

Radion on the de Sitter Brane

False vacuum decay with gravity in the non-thin-wall limit

A probe particle in a Kerr-Newman-de Sitter cosmos

A Probe Particle in Kerr-Newman-deSitter Cosmos

Spacetimes which are asymptotic to certain Friedman-Robertson-Walker spacetimes at timelike infinity