1. From String Theory to the LHC via No-Scale Inflation
Big Bang
What
happened here?
And the connection
with here?
13.8 Billion Years
1028 cm
Today
John Ellis

2. Cosmological Inflation in Light of Planck
A scalar in the sky? Supersymmetry/supergravity?

3. The Spectrum of Fluctuations in the Cosmic Microwave Background
The position of the first peak
 total density ΩTot
The other peaks
depend on density of
ordinary matter Ωatoms
& dark matter ΩDark

4. Cosmological Inflation in Light of BICEP2
Quantum gravity radiation in the sky?

5. Planck sees Polarized Dust
BICEP2 claim crumbles into dust

6. Cosmological inflation
Some Big Questions
Why is the Universe so big and old?
Why is it (almost) homogeneous on large scales?
Why is its geometry (almost) Euclidean?
What is the origin of structures in the Universe?
A possible answer:
Cosmological inflation
What do the data tell us?
Models of inflation

7. Primordial Perturbations
“Cosmological constant” due to vacuum energy in “inflaton” field ϕ: Λ ~ V(ϕ) ≠ 0
Quantum fluctuations in ϕ cause perturbations in energy density (scalar) and metric (tensor)
(Almost) independent of scale size
Visible in cosmic microwave background (CMB)

8. Inflationary Perturbations in a Nutshell
Universe expanding like de Sitter
Horizon  information loss  mixed state
Effective ‘Hawking temperature’ H/2π
Expect quantum fluctuations:
<ϕϕ>, <hh> ~ H2
(inflaton, gravitational field: gμν = ημν + hμν) Scalar (density), tensor perturbations
Should have thermal spectrum
Scalars enhanced by evolution of ϕ  r ~ ε

9. Slow-Roll Inflation Expansion driven by cosmological constant:
Getting small density perturbations requires a “small” potential:
That is almost flat: , small
so as to get sufficient e-folds of expansion:
Main observables of scalar and tensor pert’ns:
Scalar tilt: , tensor/scalar ratio:
Perturbations ~ Gaussian: look for deviation (fNL)

10. Inflationary Landscape
Monomial
Single-field
potentials
Planck +
other data ϕ3 ϕ2 ϕ
Starobinsky
R + R2 model
ϕ2/3

11. Challenges for Inflationary Models
Links to low-energy physics?
Only SM candidate for inflaton is Higgs
BUT negative potential, ….
Link to other physics?
SUSY partner of RH (singlet) neutrino?
Some sort of axion?
Links to Planck-scale physics?
Inflaton candidates in string theory?
Inflaton candidates in compactified string models?

12. Inflationary Models in Light of Planck
Planck CMB observations consistent with inflation
Tilted scalar perturbation spectrum (rolling down):
ns = ± 0.006
BUT strengthen upper limit on tensor perturbations: r < 0.12
Challenge for many simple
inflationary models
Starobinsky R2 to rescue?
Higgs/Supersymmetry/supergravity to rescue?

13. Starobinsky Model
Non-minimal general relativity (singularity-free cosmology):
No scalar!?
Inflationary interpretation, calculation of perturbations:
Conformally equivalent to scalar field model:
Starobinsky, 1980
Mukhanov & Chibisov, 1981
Stelle; Whitt, 1984

14. Higgs Inflation: a Single Scalar?
Bezrukov & Shaposhnikov, arXiv:
Standard Model with non-minimal coupling to gravity:
Consider case : in Einstein frame
With potential:
Similar to Starobinsky, but not identical
Successful inflationary potential at

15. Higgs Inflation: a Single Scalar?
Successful inflation for
BUT:
Requires λ > 0 beyond MP: need MH > 127 GeV?
How natural is such a large value of ξ? Unitarity?
Bezrukov & Shaposhnikov, arXiv:

16. Theoretical Constraints on Higgs Mass
Large Mh → large self-coupling → blow up at low-energy scale Λ due to
renormalization
Small: renormalization
due to t quark drives
quartic coupling < 0
at some scale Λ
→ vacuum unstable
Vacuum could be stabilized by Supersymmetry
1011.1±1.1 GeV
Degrassi, Di Vita, Elias-Miro, Giudice, Isodori & Strumia, arXiv:

17. Inflation Cries out for Supersymmetry
Want “elementary” scalar field
(at least looks elementary at energies << MP)
To get right magnitude of perturbations
prefer mass << MP
(~ 1013 GeV in simple φ2 models)
And/or prefer small self-coupling λ << 1
Both technically natural with supersymmetry
JE, Nanopoulos, Olive, & Tamvakis: 1983

18. Sneutrino Inflation?
See-saw model of neutrino masses requires massive singlet (right-handed) neutrinos
In supersymmetric models would be accompanied by massive sneutrinos, with m2ϕ2 potential
Decay of sneutrino inflaton
gives efficient leptogenesis
Disfavoured by Planck?
Not necessarily …
Multiple sneutrinos …
Different trajectories for different v
JE, Raidal & Yanagida: hep-ph/

19. From Supersymmetry to Supergravity
The only good symmetry is a local symmetry
(cf, gauge symmetry in Standard Model)
Local supersymmetry = supergravity
Early Universe cosmology needs gravity
Supersymmetry + gravity = supergravity
Superpartner of graviton is gravitino fermion
Gravitino condensation? (cf, quarks in QCD)
Mechanism for inflation?

20. No-Scale Supergravity Inflation
Supersymmetry + gravity = Supergravity
Include conventional matter?
Potentials in generic supergravity models have ‘holes’ with depths ~ – MP4
Exception: no-scale supergravity
Appears in compactifications of string
Flat directions, scalar potential ~ global model + controlled corrections
JE, Nanopoulos & Olive, arXiv: ,

21. First No-Scale Supergravity Model of Inflation
No ‘holes’ in effective potential with negative cosmological constant
JE, Enqvist, Nanopoulos, Olive & Srednicki, 1984

22. No-Scale Supergravity Inflation Revived
Simplest SU(2,1)/U(1) example:
Kähler potential:
Wess-Zumino superpotential:
Assume modulus T = c/2 fixed by ‘string dynamics’
Effective Lagrangian for inflaton: :
Modifications to globally supersymmetric case
Good inflation possible …
JE, Nanopoulos & Olive, arXiv:

23. No-Scale Supergravity Inflation
Inflationary potential for
Special case = Starobinsky
JE, Nanopoulos & Olive, arXiv:

24. If it looks and smells like Starobinsky …
Is there more profound connection?
Starobinsky model:
After conformal transformation:
Effective potential:
Identical with the no-scale Wess-Zumino model for the case
… it actually IS Starobinsky
JE, Nanopoulos & Olive, arXiv:

25. Beyond Starobinsky Exponential approach to constant potential:
Relations between observables:
E.g., multiple no-scale moduli:
Characteristic of generic string compactifications
Tensor/scalar ratio may be < prediction of
Starobinsky
model:
String phenomenology via the CMB?
JE, Nanopoulos & Olive, arXiv:

26. See also … Nakayama, Takahashi & Yanagida – arXiv:1305.5099
Kallosh & Linde – arXiv:1306:3214
Buchmuller, Domcke & Kamada – arXiv:
Kallosh & Linde – arXiv:
Farakos, Kehagias and Riotto – arXiv:
Roest, Scalisi & Zavala – arXiv:
Kiritsis – arXiv:
Ferrara, Kallosh, Linde & Porrati – arXiv: …

27. New Higgs Inflation in No-Scale SUSY GUT
JE, He & Xianyu, arXiv:
Grand Unification within SU(5)
Embed in no-scale supergravity
Inflation via a combination of 5, 5* Higgs fields
Avoids the problems of the original Higgs inflation model: potential positive
Interpolates between
the Starobinsky model
(Planck) and a quadratic
potential (BICEP2)

28. A No-Scale Inflationary Model to Fit Them All
JE, García, Nanopoulos & Olive, arXiv:
A no-scale supergravity model of inflation that interpolates between Planck and BICEP2:
Identify inflaton with components of modulus T:
Effective Lagrangian:
Motivated by orbifold compactification
Starobinsky
Quadratic

29. A No-Scale Inflationary Model to Fit Them All
JE, García, Nanopoulos & Olive, arXiv:
Starobinsky
+ term to fix direction
in complex T plane
Starobinsky
Quadratic

30. A No-Scale Inflationary Model to Fit Them All
JE, García, Nanopoulos & Olive, arXiv:
A No-Scale Inflationary Model to Fit Them All
Quadratic limit
Starobinsky limit
Circling the drain

31. A No-Scale Inflationary Model to Fit Them All
JE, García, Nanopoulos & Olive, arXiv:
Starting angle interpolates between limits

32. A No-Scale Inflationary Model to Fit Them All
JE, García, Nanopoulos & Olive, arXiv:
Predictions for general initial conditions
ns, r as functions of initial values
Time will tell what Nature has chosen!

33. Two-Field Analysis of No-Scale Inflationary Model
JE, García, Nanopoulos & Olive, arXiv:
Isocurvature effects on curvature perturbations may suppress tensor/scalar ratio r
ns, r, non-Gaussianity dependences on initial values

34. How many e-Folds of Inflation?
General expression:
In no-scale supergravity models:
Amplitude of
perturbations
Inflaton
decay rate
Equation of state
during inflaton decay
JE, García, Nanopoulos & Olive, in preparation

35. How many e-Folds of Inflation?
Dependence on inflaton decay rate of density after reheating
Dependence on inflaton decay rate of effective equation of state
JE, García, Nanopoulos & Olive, in preparation

36. Inflaton Decays in No-Scale Models
Two-body decay in sneutrino inflation:
Three-body decays in no-scale:
Decays into vector bosons:
Connection with
sparticle masses
How do data constrain models?
JE, García, Nanopoulos & Olive, in preparation

37. Planck Constraints on # of e-Folds
JE, García, Nanopoulos & Olive, in preparation

38. Planck Constraints on # of e-Folds
JE, García, Nanopoulos & Olive, in preparation

39. No-Scale Framework for Particle Physics & Dark Matter
Incorporating LHC constraints, Higgs mass, flavour, supersymmetric dark matter, Starobinsky-like inflation, leptogenesis, neutrino masses, …
JE, Nanopoulos & Olive, arXiv:

40. No-Scale Framework for Particle Physics & Dark Matter
Incorporating LHC constraints, Higgs mass, flavour, supersymmetric dark matter, Starobinsky-like inflation, leptogenesis, neutrino masses, …
JE, Nanopoulos & Olive, arXiv:

41. Summary
Inflation may solve some of the biggest problems in cosmology: age, size, homogeneity, flatness, …
Open season for building inflationary models
Inflation cries out for supersymmetry
Cosmology requires supergravity
Natural framework: no-scale supergravity
Derived from string theory
CMB data can constrain models of particle physics
Will the LHC discover supersymmetry?