Brane SUSY Breaking and Inflation: Implications for Scalar Fields and CMB Distorsion

I elaborate on a link between the string--scale breaking of supersymmetry that occurs in a class of superstring models and the onset of inflation. The link rests on spatially flat cosmologies supported by a scalar field driven by an exponential potential. If, as in String Theory, this potential is steep enough, under some assumptions that are spelled out in the text the scalar can only climb up as it emerges from an initial singularity. In the presence of another mild exponential, slow--roll inflation is thus injected during the ensuing descent and definite imprints are left in the CMB power spectrum: the quadrupole is systematically reduced and, depending on the choice of two parameters, an oscillatory behavior can also emerge for low multipoles l < 50, in qualitative agreement with WMAP9 and PLANCK data. The experimentally favored value of the spectral index, n_s ~ 0.96, points to a potentially important role for the NS fivebrane, which is unstable in this class of models, in the Early Universe.Comment: 9 pages, 4 figures. The original version was based on the talk presented at Rencontres de Moriond EW2013, La Thuile, March 2 - 9 2013. The new version is also based on the talks presented at the "Two-day PLANCK Meeting" and at the "18th Claude Itzykson Meeting". It includes some improved plots and a discussion of the possible role of more general brane

Higher Spins and Current Exchanges

The simplest higher-spin interactions involve classical external currents and symmetric tensors \phi_{\m_1 ... \m_s}, and convey three instructive lessons. The first is a general form of the van Dam-Veltman-Zakharov discontinuity in flat space for this class of fields. The second is the rationale for its disappearance in (A)dS spaces. Finally, the third is a glimpse into an option which is commonly overlooked in Field Theory, and which both higher spins and String Theory are confronting us with: one can well allow in the Lagrangians non-local terms that do not spoil the local nature of physical quantities.Comment: 7 pages, LATEX. Lecture presented at the 9th Hellenic School on Elementary Particle Physics and Gravity, Corfu 200

Observational Hints of a Pre--Inflationary Scale?

We argue that the lack of power exhibited by cosmic microwave background (CMB) anisotropies at large angular scales might be linked to the onset of inflation. We highlight observational features and theoretical hints that support this view, and present a preliminary estimate of the physical scale that would underlie the phenomenon.Comment: 7 pages, LaTeX, 2 eps figures. Essay Written for the 2015 Gravity Research Foundation Awards for Essays on Gravitation. Selected for Honorable Mentio

Some Pathways in non-Linear Supersymmetry: Special Geometry Born-Infeld's, Cosmology and dualities

This review is devoted to some aspects of non-linear Supersymmetry in four dimensions that can be efficiently described via nilpotent superfields, in both rigid and curved Superspace. Our focus is mainly on the partial breaking of rigid $N=2$ Supersymmetry and on a class of generalized Born-Infeld systems that originate from Special Geometry and on some prototype cosmological models, starting from the Supergravity embedding of Starobinsky inflation. However, as an aside we also review briefly some interesting two-field extensions of the Born-Infeld Lagrangian whose field equations enjoy extended duality symmetries.Comment: Contribution to the Proceedings of "Group Theory, Probability, and the Structure of Spacetime", A Conference on the Occasion of Professor V.S. Varadarajan's Retirement, UCLA Mathematics Department, November 7-9, 2014. To appear in a special issue of "p-Adic Numbers, Ultrametric Analysis and Applications". 35 pages LaTeX, 1 eps figure. Typos corrected, reference adde

A String-Inspired Model for the Low-ℓ\ell CMB

We present a semi--analytic exploration of some low--$\ell$ angular power spectra inspired by "Brane Supersymmetry Breaking". This mechanism splits Bose and Fermi excitations in String Theory, leaving behind an exponential potential that is just too steep for the inflaton to emerge from the initial singularity while descending it. As a result, the scalar generically bounces against the exponential wall, which typically introduces an infrared depression and a pre--inflationary peak in the power spectrum of scalar perturbations. We elaborate on a possible link between this phenomenon and the low--$\ell$ CMB. For the first 32 multipoles, combining the hard exponential with a milder one leading to $n_s\simeq 0.96$ and with a small gaussian bump we have attained a reduction of $\chi^{\,2}$ to about 46% of the standard $\Lambda$CDM setting, with both WMAP9 and PLANCK 2013 data. This result corresponds to a $\chi^{\,2}/DOF$ of about 0.45, to be compared with a $\Lambda$CDM value of about 0.85. The preferred choices combine naturally quadrupole depression, a first peak around $\ell=5$ and a wide minimum around $\ell=20$. We have also gathered some evidence that similar spectra emerge if the hard exponential is combined with more realistic models of inflation. A problem of the preferred examples is their slow convergence to an almost scale--invariant profile.Comment: 12 pages, latex, 7 figures. Power and limitations of the models and of the semi-analytic approach stressed, misprints corrected. Final version to appear in Mod. Phys. Lett.

Massive Born--Infeld and Other Dual Pairs

We consider massive dual pairs of p-forms and (D-p-1)-forms described by non-linear Lagrangians, where non-linear curvature terms in one theory translate into non-linear mass-like terms in the dual theory. In particular, for D=2p and p even the two non-linear structures coincide when the non-linear massless theory is self-dual. This state of affairs finds a natural realization in the four-dimensional massive N=1 supersymmetric Born-Infeld action, which describes either a massive vector multiplet or a massive linear (tensor) multiplet with a Born-Infeld mass-like term. These systems should play a role for the massive gravitino multiplet obtained from a partial super-Higgs in N=2 Supergravity.Comment: 17 pages, LaTeX. Misprints corrected. Final version to appear in JHE

Doubly Self-Dual Actions in Various Dimensions

The self-duality of the N=1 supersymmetric Born--Infeld action implies a double self-duality of the tensor multiplet square-root action when the scalar and the antisymmetric tensor are interchanged via Poincare' duality. We show how this phenomenon extends to D space-time dimensions for non-linear actions involving pairs of forms of rank p and D-p-2. As a byproduct, we construct a new two-field generalization of the Born-Infeld action whose equations of motion are invariant under a U(1) duality. In these systems, the introduction of Green-Schwarz terms results in explicit non-linear mass-like terms for dual massive pairs.Comment: 17 pages, LaTeX. References added, duality group of eq. (4.16) changed to SU(2). Final version to appear in JHE

Cosmology and Supergravity

Abdus Salam was a true master of 20th Century Theoretical Physics. Not only was he a pioneer of the Standard Model (for which he shared the Nobel Prize with S. Glashow and S.Weinberg), but he also (co)authored many other outstanding contributions to the field of Fundamental Interactions and their unification. In particular, he was a major contributor to the development of supersymmetric theories, where he also coined the word "Supersymmetry" (replacing the earlier "Supergauges" drawn from String Theory). He also introduced the basic concept of "Superspace" and the notion of "Goldstone Fermion"(Goldstino). These concepts proved instrumental for the exploration of the ultraviolet properties and for the study of spontaneously broken phases of super Yang-Mills theories and Supergravity. They continue to play a key role in current developments in Early-Universe Cosmology. In this contribution we review models of inflation based on Supergravity with spontaneously broken local supersymmetry, with emphasis on the role of nilpotent superfields to describe a de Sitter phase of our Universe.Comment: 20 pages, Latex. Contribution to the Proceedings of the "Memorial Meeting for Nobel Laureate Prof. Abdus Salam's 90th Birthday", Nanyang Technological University, Singapore, 25-28 January 2016. arXiv admin note: text overlap with arXiv:1509.0150