Ref HAL: hal-02021381_v1
Ref Arxiv: 1610.00363
DOI: 10.1088/1475-7516/2016/12/037
WoS: 000398395400009
Ref. & Cit.: NASA ADS
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11 Citations
Résumé:

The growth index $\gamma$ is an interesting tool to assess the phenomenology of dark energy (DE) models, in particular of those beyond general relativity (GR). We investigate the possibility for DE models to allow for a constant $\gamma$ during the entire matter and DE dominated stages. It is shown that if DE is described by quintessence (a scalar field minimally coupled to gravity), this behaviour of $\gamma$ is excluded either because it would require a transition to a phantom behaviour at some finite moment of time, or, in the case of tracking DE at the matter dominated stage, because the relative matter density $\Omega_m$ appears to be too small. An infinite number of solutions, with $\Omega_m$ and $\gamma$ both constant, are found with $w_{DE}=0$ corresponding to Einstein-de Sitter universes. For all modified gravity DE models satisfying $G_{\rm eff}\ge G$, among them the $f(R)$ DE models suggested in the literature, the condition to have a constant $w_{DE}$ is strongly violated at the present epoch. In contrast, DE tracking dust-like matter deep in the matter era, but with $\Omega_m <1$, requires $G_{\rm eff} > G$ and an example is given using scalar-tensor gravity for a range of admissible values of $\gamma$. For constant $w_{DE}$ inside GR, departure from a quasi-constant value is limited until today. Even a large variation of $w_{DE}$ may not result in a clear signature in the change of $\gamma$. The change however is substantial in the future and the asymptotic value of $\gamma$ is found while its slope with respect to $\Omega_m$ (and with respect to $z$) diverges and tends to $-\infty$.

Commentaires: 16 pages, 5 figure; incorrect reference corrected; v3 matches published version in JCAP; v4: comment added and expanded references. Réf Journal: JCAP 1612, no 12, 037 (2016)

Ref HAL: hal-01927223_v1
DOI: 10.1109/cleoe-eqec.2017.8087591
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Open channels are peculiar incidents modes of the optical field that are transmitted by a highly diffusing medium with high efficiency (100 % in the ideal case). The existence of these modes has been predicted by Dorokhov et al. [1] more than 25 years ago. Although many experiments were made to prepare these modes [2,3], the maxima of transmission obtained in experiments, are ever much lower than 100 %. To test the theory, we have considered here another Dorokhov's prediction: the average transmission of the modes that sustain the transmitted field must be TT=66%, where TT is defined by N2 TT= N1 T (where T is the averaged transmission of energy, and N1 and N2 the number of incident and transmitted modes i.e. the size of the incident and transmitted mode basis). Fig.1 (a) Holographic experimental setup. (b) Residual correlation of the transmitted field. The horizonal axis is SQ'. The sample transverse size is L=70 µm red, 50 µm green, 35 µm blue.... The horizontal grey line is the residual correlation expected for N1=N2. To verify this prediction, we have measured N2 on a slab sample of ZNO powder (transverse size L<=70 µm, thickness 20 µm) [4], by assuming that N1 is given by the sample geometry. The experimental setup is seen in Fig. 1(a). The incident fields are random (there are scrambled by a diffusing liquid DL) and digital holography is used to measure the complex transmitted field E(x,y) for the two polarisations. N2 is measured by analysing the residual correlations of the transmitted field measured for uncorrelated incident fields. Since the average transmission is T=1/25, we expect N2=N1/16. To get this optimal result, the transverse size of sample L must be infinite and the defocusing SQ' of the microscope objective MO2 must be zero (where S is the sample outgoing surface and Q' the plane imaged by MO2). Figure 1 (b) shows the residual correlation (which is proportional to 1/N2) as a function these two parameters. We get N2=N1/12 without extrapolation, and N2=N1/16 with extrapolation to L infinite. Here, the open channel effect is huge (factor 16) and the aggreement with the Dorokhov's prediction is excellent. We acknowledge Labex Numev (convention ANR-10-LABX-20) for funding. References 1. O.N. Dorokhov. On the coexistence of localized and extended electronic states in the metallic phase. Solid state communications, 51(6): 381-384, (1984).

Ref HAL: hal-02096153_v1
DOI: 10.1088/978-1-6817-4301-1
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Ref HAL: hal-02046929_v1
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Résumé:

I’ll present an introduction to the problem of string theory compactifications with an emphasis on the low energy description of compactifications of type II strings on Calabi-Yau manifolds. In particular, I’ll describe the Kaluza-Klein reduction procedure, basic facts about Calabi-Yau manifolds and why they are important in string theory, effective actions arising in the low energy limit, their moduli spaces, their symmetries and dualities between them. Depending on time, I may also touch the problem of quantum corrections and compactifications with fluxes.

Ref HAL: hal-01940773_v1
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The first part of this book introduces the Schubert Cells and varieties of the general linear group Gl (k^(r+1)) over a field k according to Ehresmann geometric way. Smooth resolutions for these varieties are constructed in terms of Flag Configurations in k^(r+1) given by linear graphs called Minimal Galleries. In the second part, Schubert Schemes, the Universal Schubert Scheme and their Canonical Smooth Resolution, in terms of the incidence relation in a Tits relative building are constructed for a Reductive Group Scheme as in Grothendieck's SGAIII. This is a topic where algebra and algebraic geometry, combinatorics, and group theory interact in unusual and deep ways.

Ref HAL: hal-01927313_v1
DOI: 10.1364/dh.2016.dth4c.2
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Résumé:

Open channels are peculiar incidents modes that are transmitted by a diffusing medium with high efficiency (up to 100%). Digital holography is used to analyze the correlations of the transmitted field, and to test open channel theory. Quantitative agreement is obtained.

Résumé:

I'll present a review of what is known about effective low-energy theory arising as a result of compactification of string theory down to 4 dimensions. In particular, I'll discuss why Calabi-Yau manifolds naturally arise as internal compactification manifolds, what is known in this case about quantum corrections, and why these manifolds are not enough from the phenomenological point of view. If time permits, I'll also present basic facts about flux compactifications allowing to get more realistic models.