Renata Kallosh DESY Workshop, September 2014 with Linde and with Cecotti, Ferrara, Porrati, Van Proeyen, Bercnocke, Roest, Westphal, Wrase We discuss inflationary models which are flexible enough to fit the data (Planck 2013 or BICEP2 or in between), which can be implemented in string theory/supergravity, and which may tell us something interesting and instructive about the fundamental theory from the sky We describe new models of inflation and dark energy/cc. New results on de Sitter Landscape: how to avoid tachyons in string theory motivated supergravities Recent new tools have allowed us to construct new simple models of inflation with dS uplifting in the context of spontaneously broken supersymmetry A nilpotent chiral multiplet, Volkov-Akulov goldstino A New Game In Town! and D-brane physics BICEP2 - Planck Drama IsIs ItIt DDuusst?t? IsIs ItIt DDuusst?t? Mortonson, Seljak Flauger, Hill, Spergel May-June 2014 (Flauger, Hill, & Spergel, arXiv:1405:7351) (Flauger, Hill, & Spergel, arXiv:1405:7351) Genus Topology and Cross-Correlation of BICEP2 and Planck 353 GHz B- Modes: Further Evidence Favoring Gravity Wave Detection Colley and Gott, September 15, 2014 Still preliminary as it is based on redigitized plots of both BICEP2 and Planck. However the basic idea to check Cross- Correlation of BICEP2 and Planck is a good one. This is what BICEP2 and Planck are doing now, using the actual combined data. And we are waiting… Planck intermediate results. XXX. The angular power spectrum of polarized dust emission September 19 at intermediate and high Galactic latitudes Details on dust in the BICEP2 patch of the sky. Talk by Bouchet here on September 22. Current conclusion: there is a lot of dust, however, we need a joint analysis with BICEP Sean Carroll blog‪ Sep 21 Planck Speaks: Bad News for Primordial Gravitational Waves? Results in from Planck: seems likely that the famous BICEP2 results were dust, not gravitational waves. George Efstathiou comment September 21, 2014 As a member of the Planck Science Team, I would urge caution concerning the interpretation. What we are saying is that polarised dust emission in the BICEP2 field is high. But it may be that there is something left in the BICEP2 signal that can be attributed to gravitational waves. We need to cross-correlate the Planck maps with the BICEP2 maps. This analysis is underway. r ??? new version of Mortonson and Seljak the updated contours on r including the new Planck dust 353GHz prior: the new limits are r<0.09 (95% cl), r>0.14 is excluded at 99.5% Chaotic Inflation in Supergravity: shift symmetry Kawasaki, Yamaguchi, Yanagida 2000 Kahler potential and superpotential The potential is very curved with respect to S and Im F, so these fields vanish. But Kahler potential does not depend on The potential of this field has the simplest form, as in chaotic inflation, without any exponential terms: RK, Linde, Rube 2010 Superpotential must be a REAL holomorphic function. (We must be sure that the potential is symmetric with respect to Im , so that Im = 0 is an extremum (then we will check that it is a minimum). The Kahler potential is any function of the type The potential as a function of the real part of at S = 0 is FUNCTIONAL FREEDOM in choosing inflationary potential Here S is a goldstino multiplet: supersymmetry is broken only in the goldstino direction FUNCTIONAL FREEDOM in choosing inflationary potential in supergravity allows us to fit any set of ns and r. Why there is so much discussion of a large field inflation, and fundamental theory? Large r means large field, but not the other way around. Starobinsky model, Higgs inflation, and all recently discovered supersymmetric attractors are large field models (inflation at canonical field > 5 Mp), and yet they lead to r of the order 0.003, not to be ruled out in the next 10 years. 10 Planck Collaboration: Constraintson inflation Model Parameter Planck+WP Planck+WP+lensing Planck+WP+high- Planck+WP+BAO n 0.9624 ± 0.0075 0.9653 ± 0.0069 0.9600 ± 0.0071 0.9643 + 0.0059 ΛCDM+tensor s r0.002 < 0.12 < 0.13 < 0.11 < 0.12 −2∆lnLmax 0 0 0 -0.31 Table4. Constraintson theprimordial perturbationparametersintheΛCDM+r model fromPlanckcombinedwithother datasets. −1 Theconstraintsaregiven at thepivot scalek∗ = 0.002 Mpc . 5 5 2 . potential V(φ),take a square root of it,makeits Taylor 0 series ex pansion and thus construct a real holomorphic function which approximate V(φ) with great accuracy. 0 ) 2 2 . 0 C 0 0 However, one should be careful to obey the rules of the . onvex 0 r ( Concave game as formulated above. o i 5 t 1 a . For example, suppose one wants to obtain a fourth de- 0 R m 2 φ2 r a gree polynomial potential of thetype of V(φ)= (1+ l 2 a 2 c 0 aφ + bφ ) in supergravity. One may try to do it by tak- S 1 . - 2 i ✓ 0 o ¯ ¯ t ing K =(Φ + Φ) / 2+ SS) and f (Φ) = mΦ(1 + ce Φ) - r o [52]. For general ✓,this choice violates our conditions for s n 5 e 0 f (Φ). In this case, the potential will be a fourth degree . T 0 polynomial with respect to ImΦ if ReΦ = 0.However, in this model the flat direction of the potential V(Φ) 0 0 . (and, correspondingly, the inflationary trajectory) devi- 0 0.94 0.96 0.98 1.00 ate from ReΦ = 0.(Also, in addition to the minimum at Primordial Tilt (ns) Sunday, March 31, 13 Φ = 0, the potential will develop an extra minimum at − 1 − i ✓ Fig.1. Marginalizedjoint 68% and95% CL regionsfor ns andr0.002 fromPlanckincombinationΦwith=other− cdataesetscompared.) Asatoresult, thepotential along theinfla- thetheoretical predictionsof selectedinflationary models. FIG. 1: T he green area describes observational consequences of tionary trajectory is not exactly polynomial, contrary to inflation in the Higgs model (10) with v 1 (a ⌧ 1), for the thef expectations of [52, 53]. Moreover, the kinetic terms reheating priors allowing N∗ < 50 could reconcile thismodel leadtoinflationwitha(t) ∝ exp(At ), withA> 0and0< f < 1, withintheflaPlanctionkadata.ry regime when the field rolls down fromwherethefm=a4x/i(4mu+mβ)oandf β >o0f. Inthintermediatee fields wiinflationll betherenon-canonical and non-diagonal. the potential. T he continuation of this area upwisanordnaturals correendsp otoninflation,ds but if theexit mechanismleaves to the prediction of inflation which begins when ttheheinflationaryfield φ initiallypredictions on cosmological perturbations un- Exponential potential and power lawinflation This may not be a big problem, since the potential in is at the sl ope of the potential at |v − φ| v.Inmodified,the limthisit vclass! of1 models, thpredictse direr ≈c−tion8β(nsorth− 1)/(βogon− 2) al to the inflationary trajectory is Inflationwhicwithh canorreexponentialsp onds potentialto a ! 0, the predictions (cBarrooincwid&e Liddlewith,t1993he ). It is disfavoured, being outside the joint 95% CL contour for anyβe.xponentially steep. Therefore the deviation of this field predictions of the si mplest cφhaotic inflation model with a quadratic 2 4 from ReΦ = 0 will not be large, and for sufficiently large potential m Vφ(φ2).= Λ exp −λ (35) 2 Mpl Hill-top models values of the inflaton field χ the potential will be ap- Inanother interestingclassof potentials, theinflatonrollsaway is called power law inflation (Lucchin & Matarrese, 1985), proximap tel y given by the si mple polynomial ex pression because the exact solution for the scale factor is given by froman unstableequilibriumas inthefirst new2inflationarymod- a(t) ∝ t2/λ2. This model is incomplete, since inflation would els(Albrecht & Steinhardt, 1982|f;(Lindeχ/ , 19822)|)..BWeconsiderut in order to make a full investigation of not end without an additional mechanismto stop it. Assuming inflφationp in such models one would need to study evo- an inflationary regime when the field φ rolls from Vth(φe) ≈ Λ4 1− + ... , (37) such a mechanism exists and leaves predictions for cosmo- µp logicalmaximperturbationsum ofunmodified,the potenthis clastialsofatmodelsφ =0predicts,as in new inflation lution of all fields numerically, and make sure that all r = −8(ns − 1) andisnowoutsidethejoint 99.7%CL contour. wheretheellipsisindicateshigherst abiorderlittermsy condinegligibletionsduringare satisfied. An advantage of the scenario. Nat ural initial conditions for iinflation,nflationbut neededin thitosensurethepositivenessof thepotential model are easily set by tunneling from laternothingon. An exponentinto aof p = metho2isalloweddsonlydevaselopalargeedfieldin [38, 39] is that all fields but one Inverse power lawpotential 3 inflationary model and predicts n −1≈ −4M2/µ2 + 3r/8 and universe with spatial topology T ,see e.g. [24] and the vans ish duriplng inflation, all kinetic terms are canonical r ≈ 32φ2M2/µ4. This potential leads to predictions in agree- Intermediatemodels(Barrow, 1990; Muslimov, 1990) with in- ∗ pl and diagonal along the inflationary trajectory, and in- versedpoiswercuslaswiopotentialsn in [51]. The results of investigation of the ob- ment withPlanck+WP+BAOjointvest95%igaCLtiocontoursn of stforabsuperility- is straightforward. servat ional consequences of this model [Planckian38, 42,values48]ofarµ,ei.e., µ& 9Mpl . φ −β Modelswith p ≥ 3predict n − 1 ≈ −(2/N)(p− 1)/(p− 2) described byV(φt)he= Λg4reen area in Figur(36)e 1. Predict ions of s Mpl when r ∼ 0. Thehill-top potentialFowithrtupn=at3eliesly,outsideone cthean obtain an exactly polynomial po- thismodel arein good agreement with observational data tential V(φ) in the theories with K = K ((Φ − Φ¯)2,SS¯) for a certain range of values of the parameter a ⌧ 1. using the met hods of [38, 39], if the polynomial can be However, this does not mean that absolutely any po- represented as a square of a polynomial function f (φ) tential V(φ) can be obtained in this si mple contex t, or with real coefficients. As a simplest example, one may 2 that one has a full freedom of choice of the functions consider f (Φ) = mΦ 1 − cΦ + dΦ .