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Cosmological solutions of string theory
No full textRendre compte de l'expansion accélérée de l'univers durant la phase actuelle d'énergie noire ou pendant l'inflation dans le cadre de la théorie des cordes est notoirement difficile. Cette thèse de doctorat présente de nouvelles perspectives sur certains des aspects de ce problème. La première partie de la thèse explore les compactifications avec flux des supergravités de type II à dix dimensions sur des variétés de groupe avec orientifolds et D-branes. Nous classifions les solutions possibles permises par ce cadre, et cherchons des vides maximalement symétriques, en se concentrant plus particulièrement sur les solutions de de Sitter. Nous développons ensuite les outils nécessaires pour analyser la stabilité du potentiel scalaire effectif, la séparation d'échelle, la quantification des flux, la compacité de la variété interne ainsi que le régime perturbatif des solutions. La deuxième partie est consacrée à l'étude des compactifications avec flux dépendant du temps de la supergravité de type IIA à dix dimensions sur différentes classes de variétés à six dimensions (Calabi-Yau, Einstein, Einstein-Kähler), afin de construire des solutions cosmologiques où l'espace-temps à quatre dimensions est de type Friedmann-Lemaître-Robertson-Walker. Les cosmologies que nous présentons sont universelles en ce sens qu'elles ne dépendent pas des caractéristiques détaillées de la variété interne. Une fois les équations du mouvement réécrites sous la forme d'un système dynamique approprié, l'existence de solutions présentant une phase d'expansion accélérée est rendue manifeste. Les points fixes de ce système dynamique ainsi que les trajectoires sur le bord de l'espace des phases correspondent à des solutions analytiques que nous déterminons explicitement. En outre, certaines des cosmologies résultantes présentent une accélération éternelle ou semi-éternelle, alors que d'autres permettent un contrôle paramétrique du nombre de e-folds. Nous obtenons également plusieurs cosmologies présentant un nombre infini de périodes alternées d'expansions accélérées et décélérées. La troisième et dernière partie de la thèse se concentre sur les effets des compactifications "déformées" sur le spectre d'ondes gravitationnelles. Lorsque des sources Op/Dp non-moyennées sont incluses dans la théorie à dimensions supplémentaires, le facteur de déformation a des effets non triviaux sur la tour de Kaluza-Klein d'ondes gravitationnelles. Nous étudions le profil du facteur de déformation lorsque l'on s'éloigne d'une source, et nous développons une méthode pour déterminer le spectre d'ondes gravitationnelles, en surpassant les difficultés dues à la région où le facteur de déformation devient négatif.Accounting for the accelerated expansion of the universe during the current dark energy era or the early phase of inflation within the framework of string theory is an open and notoriously difficult problem. This thesis presents new perspectives on some aspects of this long-standing challenge. The first part explores flux compactifications of ten-dimensional type II supergravities on group manifolds with orientifolds and D-branes. We classify the possible solutions allowed by this framework, and look for maximally symmetric backgrounds, with a particular emphasis on de Sitter solutions. We then develop the tools required to analyze the stability of the effective scalar potential, the scale separation, the flux quantization, the compactness of the internal manifold as well as the perturbative regime of the solutions. The second part is devoted to the study of time-dependent flux compactifications of ten-dimensional type IIA supergravity on various classes of six-dimensional manifolds (Calabi-Yau, Einstein, Einstein-Kähler), in order to construct cosmological backgrounds where the four-dimensional spacetime is Friedmann-Lemaître-Robertson-Walker. The cosmologies we present are universal in that they do not depend on the detailed features of the compactification manifold. Once the equations of motion are rewritten as an appropriate dynamical system, the existence of solutions featuring a phase of accelerated expansion is made manifest. The fixed points of this dynamical system, as well as the trajectories on the boundary of the phase space, correspond to analytic solutions which we determine explicitly. Furthermore, some of the resulting cosmologies exhibit eternal or semi-eternal acceleration, whereas others allow for a parametric control on the number of e-foldings. We also obtain several cosmologies featuring an infinite number of cycles of alternating periods of accelerated and decelerated expansions. The third and last part of the thesis focuses on the effects of warped compactifications on the spectrum of gravitational waves. When non-smeared Op/Dp sources are included in the higher-dimensional theory, the warp factor has non-trivial effects on the Kaluza-Klein tower of gravitational waves. We study the profile of the warp factor when moving away from a source, and develop a method to determine the gravitational wave spectrum which overcomes the difficulties due to the region where the warp factor becomes negative
MASSIVE IIA SUPERGRAVITIES
No full textWe perform a systematic search for all possible massive deformations of IIA supergravity in ten dimensions. We show that there exist exactly two possibilities: Romans supergravity and Howe-Lambert-West supergravity. Along the way we give the full details of the ten-dimensional superspace formulation of the latter. The scalar superfield at canonical mass dimension zero (whose lowest component is the dilaton), present in both Romans and massless IIA supergravities, is not introduced from the outset but its existence follows from a certain integrability condition implied by the Bianchi identities. This fact leads to the possibility for a certain topological modification of massless IIA, reflecting an analogous situation in eleven dimensions
M-theory on eight-manifolds revisited: N=1 supersymmetry and generalized Spin(7) structures
No full textThe requirement of supersymmetry for M-theory backgrounds of the form of a warped product , where is an eight-manifold and is three-dimensional Minkowski or AdS space, implies the existence of a nowhere-vanishing Majorana spinor on . lifts to a nowhere-vanishing spinor on the auxiliary nine-manifold , where is a circle of constant radius, implying the reduction of the structure group of to . In general, however, there is no reduction of the structure group of itself. This situation can be described in the language of generalized structures, defined in terms of certain spinors of . We express the condition for supersymmetry in terms of differential equations for these spinors. In an equivalent formulation, working locally in the vicinity of any point in in terms of a `preferred' structure, we show that the requirement of supersymmetry amounts to solving for the intrinsic torsion and all irreducible flux components, except for the one lying in the of , in terms of the warp factor and a one-form on (not necessarily nowhere-vanishing) constructed as a bilinear; in addition, is constrained to satisfy a pair of differential equations. The formalism based on the group is the most suitable language in which to describe supersymmetric compactifications on eight-manifolds of structure, and/or small-flux perturbations around supersymmetric compactifications on manifolds of holonomy
Relative scale separation in orbifolds of S and S
No full textInternational audienceIn orbifold vacua containing an S/Γ factor, we compute the relative order of scale separation, r, defined as the ratio of the eigenvalue of the lowest-lying Γ-invariant state of the scalar Laplacian on S, to the eigenvalue of the lowest-lying state. For q = 2 and Γ finite subgroup of SO(3), or q = 5 and Γ finite subgroup of SU(3), the maximal relative order of scale separation that can be achieved is r = 21 or r = 12, respectively. For smooth S orbifolds, the maximal relative scale separation is r = 4.2. Methods from invariant theory are very efficient in constructing Γ-invariant spherical harmonics, and can be readily generalized to other orbifolds
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Consistent truncation on Calabi-Yau and Nearly-Kähler manifolds
No full textInternational audienceWe complete and extend the analysis of arXiv:1903.10504 in several directions: we put the 4dtheory, arising from the IIA consistent truncation of the universal sector of Calabi-Yau compactification, in a form manifestly consistent with 4d N = 2 supergravity. We go beyond the universal sector and construct the 4d effective action of IIA compactified on Calabi-Yau’s with h11 = 1, h21>=1, in the presence of background flux and fermionic condensates. For ALE gravitational instantons, we show that the putative quartic gravitino condensate is non-negative, as required for the existence of (formal) de Sitter solutions of the 4d theory. We discuss some of the issues in promoting these formal solutions to full-fledged string theory de Sitter solutions. We also extend the Nearly-Kähler consistent truncation of arXiv:1810.06344 to the complete bosonic sector of one vector multiplet and one hypermultiplet
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