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PoS(EDSU2018)043 http://pos.sissa.it/ ∗ [email protected] Speaker. For cosmology we need GeneralRelativity. Relativity. Superstring theory is the isever, next believed natural to theory step be after has the General andimensional most General emergent fundamental Relativity and concept theory cosmology of we requires many know. space-time.some intermediate steps. amount How- If To of in use these , steps it maximalconsequences in for or cosmology, the minimal potentially supportable context or or of intermediate, falsifiable by the is observations. 4- preserved, one finds ∗ Copyright owned by the author(s) under the terms of the Creative Commons c Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). 2nd World Summit: Exploring the Dark25-29 Side June, of 2018 the - Universe EDSU2018 University of Antilles, Pointe-à-Pitre, Guadeloupe, France Renata Kallosh Stanford Institute for andStanford, Department CA of 94305, Physics, USA , E-mail: Supergravity and Cosmology

PoS(EDSU2018)043Moncelsi Lorenzo

r − s n

BICEP2 BICEP2 2014

Renata Kallosh W.Hu ] with nilpotent 1 , 2013

data. σ . The main feature of B<0 RK, RK, Linde, Roest 2

modes 2 - B>0 -

to see polarization B monodromy . , will be validated , will … log r

α 3 axion

. The models at present compatible with the data = 1 1 LSS LSS = 0 2 -

r

2 Escher a?ractor models, R - T, E, B E,T, plane with blue area representing the 2

a T, E

r < r < 10

]. We show the place of these models in Planck 2015 modes are discovered soon with modes rdiscovered are > 10 S 3 - − 4 - Planck XX 2015 XX Planck s f B waves waves at ] which we will describe in the context of supergravity. In fact, I models, infla;on natural models, r scale log about worry to need No to Otherwise, switch we 10 n bound of Inflation of bound 2015 plane in Fig. / Δ

3

r T

models

− Δ mode mode polarization s - Lyth n = B

r Planck ] in Planck 2015 22/3/16 2

-attractors [ α BK14 w201695GHz / Cosmology: from the sky to the fundamental physics thefundamental theto sky from Cosmology: Probes Probes Ekpyrotic Thomson scattering within local quadrupolelocalwithin Thomson scattering linear generates anisotropies Scalar modes modes Tensor Ratio Gravitational create

• • • • • • • . We explain the geometric nature of these models in Fig. Moriond 2 supergravity. The model does so by adding two real gravitino to the photon and Figure 1: 1 = N 8 . In this talk we will describe the recently discovered De Sitter supergravity [ Fundamental idea following the discovery of General Relativity is the idea of local super- However, supergravity models discovered in 1976 with linearly realized supersymmetry tend = these models is a particular choiceis a of corresponding the Escher’s moduli picture space where geometry, which is a Poincaré disk. There superfield and based on it inflationarytent model with building. Planck We 2015 present [ inflationaryinclude models the still so-called consis- the most advanced geometric version oftent these multiplet models and are using a de Kähler Sitterplane function supergravity in with [ a Fig. nilpo- symmetry. Einstein’s dream of unifyingextended electromagnetism and was realized starting with Short Title for header the . The first breakthrough intocation: finiteness an of quantum explicit supergravity calculation occurred of via photon-photoncoupled this scattering bosonic unifi- which Maxwell-Einstein was system known yielded to begravitinos a divergent cancelled dramatic in the result the divergences : found the previously.quantum new Many diagrams loop more involving divergences unexpected cancellation were of discoveredN the later in extended maximal supergravities with upto to have an easy descriptions ofdifficulty anti-de in Sitter describing vacua with the negative Universe cosmologicalof we constant. the see The positive in have cosmological observations, constant, wheregeometry for we describing example a need via slow-roll to potentials a explain in de the inflationary Sitter cosmology. origin vacua, as well as near de Sitter PoS(EDSU2018)043 (2.1) (1.1) Renata Kallosh . The new targets 3 F − 2 θ 10 n 2 ×  ) + x φ ( α 2 3 . 3 √ θψ e − 2 − √ 1 +  ) 0 and 10 of the order 3 x V ( 2 F r − 2 = E ψψ V ) = 2 θ , ]. When such a multiplet is present in the action , x 1 ( n between 10 2 S r  α 6 φ √ ⇒ tanh and Higgs inflation, with  0 2 0 V R 1 supersymmetry in four dimensions, as discovered by Gol’fand and = = ) = T θ , V N x ( 2 S below a scan the region of 3 ] and therefore also with de Sitter supergravity. 5 1 there are theorems, under certain conditions, supporting anti-de Sitter vacua with unbroken -attractor models These models have an interesting property that the potentials for canonical fields are for T- In 1996 J. Polchinski discovered in the non-perturbative objects, called D- Standard linear Meanwhile, starting with 1998 discovery of the dark energy it become clear that de Sitter space We will explain the new M-theory/String theory inspired targets for B-modes beyond the well ≥ α 2. models and E-models, respectively and a year later itVolkov-Akulov type was is recognized a that property thealso of recognized theory the that of world-volume the non-linearly actions KKLT of uplifting realizedmultiplet, mechanism all [ supersymmetry in D-branes. of string the theory Therefore is it associated was with a nilpotent one finds that even inspontaneously absence broken of supersymmetry. scalar fields such supergravity actions have de Sitter vacua with Lichtman in 1971 and By Wess anddecades. Zumino in LHC 1974 was was expected the major tofor paradigm produce in each super-partners particle of complex physics known for scalar particles, andto one vice explain Majorana if versa. fermion the So super-partnerssupersymmetry far are was we heavier realized than have in predicted. not theN seen context In them, of any cosmology. which case, of In anothersupersymmetry all course issue and linearized is with forbidding supersymmetries easy de linear with Sitter vacua with spontaneously broken supersymmetry. offers a is a simpleDuring explanation the of last two the decades Einsteinis all equations still data a with points possible a explanation towards of positive theof the cosmological fact cosmological standard constant. that data. linearized a The difficulties positive supersymmetry (inrealization cosmological to absence supersymmetry constant of which produce scalar was fields) such in fact theoriesThis discovered long theory forced time is us by equivalent Volkov to and todegree Akulov study of in a freedom 1972. a theory is non-linear with present, and a a constrained scalar field chiral is multiplet a where bilinear of only the a fermion fermionic one shown in Fig. 1. De Sitter supergravity known satellite targets like Short Title for header To explain a consistency between aessary positive cosmological to constant promote and Volkov-Akulov theory, supersymmetry or it aa was theory nec- local with supersymmetry. the nilpotent multiplet, This to was a theory done with in [ PoS(EDSU2018)043 ) 3 / ' =1 (( ). It 1 7. ¯ T =1 , N Sf = 6 (2.2) , + ↵ 5 ) one can , ] that if N T ' )+ . 4 6 ( as shown , according ' α 2 3 ( ln( K r , g F 2 ↵ R , Renata Kallosh 3 , and from LHC 1 = depending on the -attractors [8–16]. can be arbitrary, r ↵ = α ↵ W data. = and waiting for the σ s K n 2 Escher 1, shown by two yellow R ¯ T = 0 for n dT d σ 2 ) ¯ T> ¯ T ↵ ) into phenomenological and an arbitrary SUSY breaking 3 + to identify the value of + T r ( ⇤ T 2.1 2 = RK, Linde RK, 12 N 2 . ds ¯ α Z geometry . Another, also geometric, interpretation Z ≈ ↵ 2 3 symmetry r Kahler is expected to be a playground for the satellite ) 3 plane - R − , 3 = half (2 , – which we will refer to as Killing-adapted form. or there is a T-model with K 2 N SL 1 1 Disk R r and 10 3 − Escher in the Sky, Sky, in the Escher 2015 2 plane with blue area representing the 2 ¯ ) for the potentials K¨ahler described in Section 3. The Z 1 8 supergravity in d=4, the situation changes. Only integer − 10 r -attractor models are inside 2 ( ≈ dZd = related to the curvature of the Kähler manifold ⇡ − 2 -attractor cosmological models the value of s f s α ) K n n Curvature of the in space of the moduli Curvature ¯ ⌘ 9, which corresponds to the GL model [18,19]. From α Z 2 R N b 1 / ↵ Z 3 3 = 4 superconformal theory, [17], one would expect 1 independent 2 Escher disk + − R (1 =1 S = N 7 are possible. We have shown the corresponding values of = ¯ ⇣ = 60. All Z< , ↵ 2 Poincaré ) have a cosmological constant α 6 Z ↵ , = = ds ' 1 potential is very simple, just 3 Hyperbolic geometry of a 5 ( Planck 2015 these models have simple observables , N = F 4 W α , n . These seven targets correspond to Escher’s disks of between between 10 3 in these models, for which the K¨ahler potential 3 , r 2 )= ↵ , ' 1 50 and ( Figure 2: 0 we explain some of the properties of these models in geometric terms. The T-models = f 2 = α is not restricted, it can take any value. However, it was recently discovered in [ N is the number of e-foldings. In Fig. 2 ) in the Fig. N In Fig. The region of . This corresponds to the unit radius Escher disk [15], as well as a target of the 2.2 3 . We find this to be a compelling framework for the discussion of the crucial new data -attractor supergravity models that make manifest an inflaton shift-symmetry by virtue ↵ to ( values of 3 Here supergravity. The value of in Fig. one derives the corresponding kinetic terms starting fromd=11, the superstring maximal theory supersymmetry: in M-theory d=10, in in geometric variables have a non-canonicaland for kinetic example term the defined by the metric of a Poincaré disk lines for discovery of primordial gravitational waves, or new bounds on B-mode missions. In the context of as long as we only consider the embedding of the models in ( Short Title for header At sufficiently small 3. New B-mode targets 10 , and attraction ⇡

↵ r

, illustrated by the Escher’s picture Circle Limit IV [15, 16]. As clarified in these references,

at the minimum. In Section 5 we study more general class of models with ↵ The paper is organized as follows. We begin in Section 2 with a brief review of key vocabulary and 3

with future space mission for B-modeinteresting simplifications detection, occur as for specified in CORE (Cosmic ORigins Explorer). Some

p describes the moduli space curvatureof [9] given this by parameter is in terms of thefrom Poincar´edisk the model fundamental of pointoriginal of a view, theory. hyperbolic there geometry From are with the particularly the maximal interesting radius values of

2.1 There is a key parameter regard to initial conditions for inflation,breaking analogous and to the dark ones energy. studied We in close [28] for in models Section without 6 SUSY with a summary of2Review what we have accomplished. reconstruct the superpotential resulting models with M and the same potential. K¨ahler Fordata these as models well it is as also dark possible energy to and get SUSY agreement with breaking. the Moreover, Planck these models have nice properties with features of these andpresent related the models with referencesof to having the more potential K¨ahler in-depth inflaton Section treatments. 4 presents In a Section universal 3 rule: we given a bosonic inflationary potential of the form the minimum on cosmology and particle physicsalready expected discussed during the in next [14]. few years. Some models of this type were the construction of newcosmological models data of [2] chaotic as inflationof well [1] the in as potential supergravity involving [3–7].either compatible a string with In theory controllable or the this supersymmetry extended supergravity current paper breaking consderations,Here known we we at as will cosmological will the develop enhance minimum supergravity them models with of a inflation controllable motivated supersymmetry by breaking and at

During the next few years weeither might detecting expect some primordial dramatic gravity newdiscovery/non-discovery information waves of from or B-mode low establishing experiments scale athese supersymmetry. new important factors upper in A bound cosmology theoretical on and particle framework physics to has discuss been proposed both recently. of It is based on 1 Introduction a S4 -

CMB PoS(EDSU2018)043 plane (4.17) r 55, for ⇠ , no. 12, s , 057 (2013) n -models with 94 N E 1707 (2017) 144 -attractor models 1311 Renata Kallosh D3 and dS,” ↵ =1inaseven-disk , no. 8, 085040 1 supergravity,” ↵ 1704 92 = (2015) no.14, plane for r N 114 =const =const =const =const =const =const 7 7 7 7 7 7 s ⌧ ⌧ ⌧ ⌧ ⌧ ⌧ n ⌧ = = = = = modes,” Phys. Rev. D inside it corresponding to a highest -Attractors,” JHEP 6 6 6 6 6 B , which is expected to be probed by ⌘ ⌧ ⌧ ⌧ ⌧ ⌧ Seven Seven new targets 3 α , T 7 − -models. The quadratic ⌧ ⌧ = = = = T 5 5 5 5 = ⌘ ⌧ ⌧ ⌧ ⌧ =7. , 6 6 and 10 ↵ ⌧ ⌧ ⌧ = = = 2 4 4 4 -models, see [2]. We show them as a navy circle − = = ⌘ ⌧ ⌧ ⌧ T , 5 5 5 are between these two. They all describe the class ⌧ ⌧ ⌧ ⌧ -attractors, and = = 3 induced geometric inflation,” JHEP α } 3 3 D = = = ⌘ 7 ⌧ ⌧ 7 4 , , 4 4 4 4 6 plane for the future data. The grey band shows one of the ⌧ ⌧ ⌧ ⌧ ⌧ = , r 5 2 between 10 , = = = = ⌘ ⌧ − 4 r , s , 3 3 3 3 3 2 ), so-called quadratic ⌧ 3 ⌧ ⌧ ⌧ ⌧ ⌧ n -attractor models [2, 3, 4] with the seven-disk geometry , ↵ 2 6 ↵ 12 N = = = = = ⌘ , , p 1 2 2 2 2 2 2 / { , no. 6, 069901 (2016)] doi:10.1103/PhysRevD.93.069901, ⌧ ⌧ ⌧ ⌧ ⌧ ⌧ ⌧ ↵ ' , 117 (2014) doi:10.1007/JHEP12(2014)117 [arXiv:1411.1121 ( 93 = 2 ⌘ ======E = 1 1 1 1 1 1 1 ↵ ⌧ ⌧ ⌧ ⌧ ⌧ ⌧ ⌧ T T 1412 tanh in string theory ⇠ V ↵ =1 : =7 : =6 : =5 : =4 : =3 : =2 : =1andforthemaximalvalue3 3 [Planck Collaboration], “Planck 2015 results. XX. Constraints on inflation,” Astron. ,r ↵ ↵ ↵ ↵ ↵ ↵ ↵ ↵ (2016) A20 doi:10.1051/0004-6361/201525898 [arXiv:1502.02114 [astro-ph.CO]]. 3 3 3 3 3 3 3 3 tend to be slightly to the right of the - 2 - 2 et al. N 2 = 7 and the purple one corresponding to the lowest preferred value 3 594 , 106 (2015) doi:10.1007/JHEP10(2015)106 [arXiv:1507.08619 [hep-th]]. , 058 (2015) doi:10.1007/JHEP05(2015)058 [arXiv:1502.07627 [hep-th]]. 10 ) r -attractor models with seven-disk geometry in the 10 inside it. ↵ ↵ ↵' E 3 / 1510 1505 2 This Figure is taken from [16], it represents a forecast of CMB-S4 constraints in the The CMB-S4 figure represents the p , no. 4, 041301 (2015) doi:10.1103/PhysRevD.92.041301 [arXiv:1504.05557 [hep-th]]. e =1 JHEP 198 doi:10.1007/JHEP11(2013)198 [arXiv:1311.0472 [hep-th]]. M. Galante,and R. D. Kallosh, Roest, A. “Unity Linde of Cosmological141302 Inflation doi:10.1103/PhysRevLett.114.141302 Attractors,” [arXiv:1412.3797 Phys. [hep-th]]. Rev. J. Lett. J.R. M. Kallosh, Carrasco, A. Linde and D.92 Roest, “Hyperbolic geometry of cosmological attractors,” Phys. Rev. D Astrophys. 10.1103/PhysRevD.92.085040 [arXiv:1507.08264 [hep-th]]. F. Hasegawa and Y.“Component Yamada, action of nilpotent multiplet coupled to matter in 4 dimensional 126015 (2016) doi:10.1103/PhysRevD.94.126015 [arXiv:1610.04163 [hep-th]]. R.T. Kallosh, Wrase A. and Linde, Y. Yamada, “Maximal Supersymmetrydoi:10.1007/JHEP04(2017)144 and [arXiv:1704.04829 B-Mode [hep-th]]. Targets,” JHEP (2015) Erratum: [Phys. Rev. D (2017) doi:10.1007/JHEP07(2017)057 [arXiv:1705.09247 [hep-th]]. in KKLT dS Vacua,” JHEP [hep-th]]. E. A. Bergshoeff, K. Dasgupta,JHEP R. Kallosh, A. Van Proeyen and T. Wrase, “ s (1 -attractor models with -attractor models. One can see the orange targets there for the Starobinsky and Higgs models. The seven n [2] P. A. R. Ade [4] R. Kallosh, A. Linde, D. Roest and Y. Yamada, “ [3] R. Kallosh, A. Linde and D. Roest, “Superconformal Inflationary [1] E. A. Bergshoeff, D. Z. Freedman, R. Kallosh and A. Van Proeyen, Phys. Rev. D [6] S. Ferrara and R. Kallosh, “Seven-disk manifold, [5] R. Kallosh and T. Wrase, “Emergence of Spontaneously Broken Supersymmetry on an Anti-D3- ↵ ⇠ References the satellite missions. These targets are derived from M-theory/String theory. α new targets at various colors scan the region of Figure 3: Short Title for header the minimal value 3 5 Values of Here we will showthe how derivation to of derive non-compact the symmetries 7-disk in geometry string (4.13) theory in following string [17], theory. [18]. We The start toroidal with We illustrate in Fig.using 1 the the features recent of discussionpredictions of of B-modes in the CMB-S4 Science Book [16]. We show in Fig. 1 with the letter by requiring that Figure 1: for a fiducial model[2, with r 3, = 4]. 0.01.preferred Here value We the 3 have greygeometry. added band shows to All predictions this of intermediateof the figure cases sub-class a 3 of blueV circle with the letter