The Unity of the Universe
Portsmouth UK June 2009 Outline • How current and future observa ons in cosmology and experiments in par cle physics have affected and will affect our understanding of `founda ons’ of theore cal physics
• String cosmology On chao c infla on and B‐modes
• Standard model infla on with and supersymmetry
• Recent drama c progress in N=8 four‐dimensional supergravity Quantum Gravity Planck length :
B‐modes from infla on
The highway across the desert Gerard ‘t Hoo GUTs
Today’s LHC Limit … SUPERSYMMETRY Cosmology, ten‐dimensional superstring theory and effec ve four‐dimensional supergravity
Kähler potential and the Superpotential
Generic poten al of N=1 supergravity depends on a number of complex scalar fields which have geometric meaning of coordinates in Kähler geometry
+ D-terms String Theory • String theory is the best known candidate for the theory of all interac ons, including gravity.
• Since 1987 it was known that string theory has many (10500‐101500) solu ons defining string theory vacua (Lerche, Lust, Schellekens 1987; Bousso, Polchinsky 2000). This was a source of embarrassment for string theory, a emp ng to explain our universe in the best tradi ons of the old paradigm: a dream to explain just one world we live in.
• However, all of these vacua were unstable, they had nega ve energy density, and therefore they could not describe our world. This problem became especially urgent when cosmologists found that the vacuum energy density (the cosmological constant) is posi ve.
• This problem was resolved in 2003 in the KKLT scenario based on many other efforts of string community in this direc on. The volume stabilization problem: A potential of the theory obtained by compactification in string theory of type IIB:
X and Y are canonically normalized field corresponding to the dilaton field and to the volume of the compactified space; φ is the field driving inflation
The potential with respect to X and Y is very steep, these fields rapidly run down, and the potential energy vanishes. We must stabilize these fields.
Dilaton stabilization: Giddings, Kachru, Polchinski 2001 Even now the dilaton was Volume stabilization: KKLT construction not yet stabilized in heterotic string theory Kachru, RK, Linde, Trivedi 2003 Long Term Problem of Moduli Stabilisation And Supersymmetry Breaking
4D Compactifications: String theory is consistent in 10D. One of the moduli is the total volume of extra dimensions, it tend to have a runaway behavior. If this volume becomes infinite, we cannot explain the current cosmological observations which require an effective 4D! Examples of Calabi-Yau 3-folds
Other moduli: size of cycles 1) Start with a theory with a typical stringy runaway potential 2) Bend this potential down due to nonperturbative quantum effects 3) Uplift the minimum to the state with a positive vacuum energy by adding a positive energy of a D brane in warped Calabi-Yau geometry
Solving the cosmological constant problem
Among 10500 vacua one can always find many vacua with vacuum energy smaller than 10‐120. We cannot live in the vacua with vacuum energy much greater than 10‐120.
Thus a combina on of infla onary theory, string theory and anthropic reasoning can solve the cosmological constant problem.
At the moment, we do not have any alterna ve solu ons. Inflation in string theory
To produce a reasonable cosmology in string theory it was necessary to stabilize all moduli but the inflaton (or two, for non-gaussianity). In 4d theory such moduli are scalar fields. In string theory and supergravity they often have physical and geometrical meaning as volumes of extra dimensions and various cycles in topologically non- trivial extra dimensions. The inflaton can also be related to a distance between branes. Brane inflation
Modular inflation Brane inflation with monodromy KKLMMT brane-anti-brane inflation Two-throat model
Dirac-Born-Infeld inflation
Hybrid D3/D7 brane inflation (Stringy D-term inflation) Modular Infla on models
Racetrack inflation
,
Kahler modular inflation Roulette inflation A simple working model of the moduli inflation Blanco-Pilado, Burgess, Cline, Escoda, Gomes-Reino, R.K., Linde, Quevedo
Superpotential:
Kähler potential: 2003 η-problem ( ) requires fine-tuning of terms After that, the model works and has interesting properties, such as light cosmic strings
2007
Baumann, Dymarsky, Klebanov, Maldacena, McAllister, Murugan, Steinhardt:
Stringy corrections do not remove terms as originally expected. With fine-tuning one can find an inflection point and slow-roll inflation. “Delicate inflation.”
2008 Baumann, Dymarsky, Kachru, Klebanov, McAllister
Improved understanding of quantum corrections
If there are some discrete symmetries, the original KKLMMT scenario with inflaton mass tuned is valid. Haack, RK, Krause, Linde, Lust, Zagermann 2008
Stringy version of the D-term inflation. Naturally flat inflaton direction, string theory corrections under control, eternal inflation regime, a controllably small amount of cosmic strings. Silverstein, Westphal, 2008, McAllister, Silverstein, Westphal 2008
Type IIA string
Type IIB, CY Type IIB CY
June 2009 MEASUREMENT OF CMB POLARIZATION POWER SPECTRA FROM TWO YEARS OF BICEP DATA
B-mode spectrum is consistent with zero Directly from CMB B-mode polarization
IMPROVED MEASUREMENTS OF THE TEMPERATURE AND POLARIZATION OF THE CMB FROM QUAD
WMAP+ACBAR +QUaD
From CMB alone r =0.1 +…
Add Where is dark matter and how supersymmetry will affect this conclusion ??? Standard Model + Supersymmetry: impossible with 1 Higgs, minimum 2 Higgs fields
Standard model Higgs inflation with non-minimal + supersymmetry 1. It is not possible to simply add to standard supergravity action
+ fermions
2. Need many new terms in the action proportional to
Work in progress Quantum Gravity??? N=8 supergravity in four dimensions during the last 25 years was believed to be UV divergent: all-loop geometric counterterms, candidates for UV divergences, are known RK; Howe, Lindstrom (1981). The onset of divergences was less clear.
During the last few years studies of mul ‐par cle amplitudes in QCD (N=0) were simplified using N=4 super Yang‐Mills theory. This, in turn, led to significant progress in computa on of QFT amplitudes in N=8 supergravity. Some spectacular cancella ons of UV divergences were discovered at the 3‐loop level in 2007 and at the 4‐loop level in 2009.
Is N=8 supergravity UV finite? If the answer is "yes" what would it mean for Quantum Gravity? Bern, Carrasco, Dixon, Johansson, Kosower, Roiban (2007)
Bern, Carrasco, Dixon, Johansson, Roiban (2008, 2009)
• Major surprise:
• The 3‐loop and 4‐loop computa on show much be er UV than expected
• Arguments about all‐loop finiteness At 3 loops N=8 supergravity seems to have the same UV behavior as N=4 SYM gauge theory.
• Dc = 6 at L=3 same as for N=4 SYM!
• Will the same happen at higher loops, so that the formula
N=4 SYM
continues to be obeyed by N=8 supergravity as well?
• If so, N=8 supergravity may represent a perturbatively finite, pointlike theory of quantum gravity Several striking features of the 3‐loop 4‐point amplitude answer
• There are no UV log divergent terms of the form log Λ ( R….)4
• There are no terms of the form 1/Λ2 D2( R….)4 • There are no terms of the form 1/Λ4 D4( R….)4 • The first non‐vanishing terms are of the form 1/Λ6 D6( R….)4 + higher deriva ves 4‐loop computa on
Predic on: if N=8 SG at the 4‐loop level behaves as N=4 SYM they must find 3‐types of cancella on: log Λ
1/Λ2 Superfiniteness is not a necessary condition for the all- loop UV finiteness in d=4, however, it is extremely unlikely 1/Λ4 to be accidental
If the last term is not vanishing, it indicates that D=5 L=4 maximal SG is divergent Howe, Stelle: UV divergent Computation: UV finite terms in 3-loop diagram. There is a reason why this hasn’t been evaluated.
This single 5-loop diagram has terms prior to evaluating any integrals. More terms than atoms in the brain!
Brute force computations are totally hopeless! Maximal supergravity
DeWit, Freedman (1977); Cremmer, Julia, Scherk (1978); Cremmer, Julia (1978,1979); De Wit, Nicolai (1982)
• Theory has 28 = 256 massless states. • Multiplicity of states, vs. helicity, from coefficients in 8 binomial expansion of (x+y) – 8th row of Pascal’s triangle
SUSY charges
Qa, a=1,2,…,8 shift helicity by 1/2 Bern, Dixon, Dunbar and Kosower, 1994
Two-particle cut:
Three- particle cut:
Generalized unitarity:
Apply decomposition of cut amplitudes in terms of product of tree amplitudes. 3 loop N=8 supergravity computation, 2007 4 loop N=8 supergravity computation, May 2009
It continues to be as well behaved as N=4 SYM gauge theory.
What is next? Understanding the reason for cancellation of UV divergences,
use light-cone superfields, E7(7) symmetry At present we are unaware of any natural way to accommodate in string theory a future detec on of B‐modes and, simultaneously, a possible future experimental iden fica on of the gravi no as par cles with mass much smaller than 1013 GeV.
Even if B‐modes are not detected, there is s ll a tension between string cosmology and light gravi no, par cularly if it forms dark ma er.
New ideas are required. • Supersymmetry? • Is dark energy a cosmological constant? • Non‐gaussianity • More on spectral index • Cosmic strings • B‐modes ? • Mass of gravi no ? • Test of superstring theory? We are waiting for LHC and Planck, dark matter and B-mode experiments data