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Non-minimal inflation and SUSY GUTs
Nobuchika Okada
University of Alabama
International Workshop on Grand Unification
Yukawa Institute of Theoretical Physics
March 15-17, 2012
In collaboration with
Masato Arai, Shinsuke Kawai,
Mansoor Ur Rehman, Qaisar Shafi
The Standard Big-Bang Cosmology
The success of the Standard Big-Bang Cosmology
Hubble expansion
Hubble’s law: expansion of the Universe
Cosmic Microwave Background (CMB)
2.725K radiation, Planck distribution
Big-Bang nucleosynthesis
Success in synthesizing light nuclei in the early Universe
General theory of relativity
Homogeneous & isotropic universe
 Friedmann-Robertson-Walker metric
(k=0)
Einstein equations:
Perfect fluid:
Expansion law:
Continuity equation:
w=1/3 : radiation
w=0 : matter
Brief thermal history of the Universe
T
Big-bang
Hot & dense thermal state
all particles are in thermal equilibrium
Radiation
dominated
era
w=1/3
Matter
dominated
era
w=0
decoupling of some particles
(example: Dark Matter)
~1 MeV
(10^10 K)
Big-bang nucleosynthesis
~1 eV
Equal epoch (radiation density = matter density)
~ 0.1 eV
Recombination  origin of CMB
~0.0001 eV
Present
Problems of Big-Bang Cosmology
Big-Bang Cosmology:
w=1/3 : radiation
w=0 : matter
Decelerating
expansion
Flatness problem
Fine-tuning of density parameter is necessary
Horizon problem
Observed CMB is isotropic
nevertheless two regions have never contacted
with each other
Origin of density fluctuation
need the seed of density fluctuation for the large scale
structure formation of the Universe
Basic Idea of Inflationary Universe
Suppose the existence of a stage in the early universe
with
``Inflation’’
Accelerating Expansion
Simple example: de Sitter space
Positive cosmological constant (vacuum energy)
Expansion law:
Continuity equation:
Exponential expansion (Inflation) solves
flatness problem  spatial curvature flattened
horizon problem  small causal region expanded
Simple model of inflation
 scalar field called ``inflaton’’
Quantum fluctuation of inflaton
 origin of primordial density fluctuation
Simple inflation model
The picture we seek….
Inflation before Big-Bang  Big-bang cosmology
Slow-roll inflation
A scalar field (inflaton) slowly-rolling down to its potential
minimum
Slow-roll
End of inflation
Oscillations & decay
1. Inflation at slow-roll era
2. End of Inflation
3. Coherent oscillations
4. Decays to Standard Model particles
5. Reheating  Big-Bang Cosmology
Primordial density fluctuation
Slow-roll
End of inflation
During inlaftion era,
quantum fluctuation of
inflaton is enlarged by
inflation
Oscillations & decay
Inflaton fluctuation  curvature fluctuation
 structure formation, CMB anisotropy
Inflaton fluctuation  inflaton potential, initial condition
CMB anisotropy  precision measurement by observation
CMB Observations:
Wilkinson Microwave Anisotropy Probe (WMAP)
The observational
cosmology is now a
precision science!
Inflationary Predictions VS. WMAP
inflationary scenario
Slow-roll parameters
These are very small during inflation
End of inflation 
Number of e-foldings
N > 50-60 is necessary to solve
horizon & flatness problem
Inflationary Predictions VS. WMAP (cont’d)
Conditions to fix parameters in inflation model
Power spectrum
WMAP 7yr
e-foldings
= 50 -60
By these conditions, the slow-roll parameters are fixed
Predictions
Spectral index:
Tensor-to-scalar ratio:
Example models
We calculate the slow-roll
parameters for each model
and find predictions
Model 1:
Model 2:
N=60
Model 2
Model 1
WMAP 7yr
contours
Inflation models with non-minimal gravitational coupling
It is generally possible to add the non-minimal
gravitational coupling to Einstein-Hilbert action
Let us consider the model 2 with the non-minimal coupling
In Jordan frame
In Einstein frame
In Einstein frame
=const
V
for a large inflaton VEV
Predictions of non-minimal phi^4 model
N. O.,Rehman & Shafi
Phys. Rev. D 82, 043502 (2010)
N. O.,Rehman & Shafi
Phys. Rev. D 82, 043502 (2010)
Minimal model
Higgs Inflation
Replace phi H
Bezrukov & Shaposhnikov,
PLB 659 (2008) 703;
JHEP 07 (2009) 089
Analysis beyond tree-level (RGE improved effective potential)
De Simone, Hertzberg &
Wilczek, PLB 678 (2009)1
Barvinsky et al., JCAP 0912
(2009) 003
Realization of the non-minimal inflation model
in supersymmetric model
The Standard Model of elementary particle physics
The best theory we know so far in describing
elementary particle physics @ E=O(100 GeV)
Quarks & leptons
Gauge interactions
QCD, weak, E&M
Higgs  masses of particles
However,
Experimental results which cannot be explained by the SM
ex) neutrino masses & mixings
non-baryonic dark matter,…
Theoretical problems
ex) The gauge hierarchy problem (stability of EW scale)
Origin of electroweak symmetry breaking
Fermion mass hierarchy, etc.
We need to extend the SM, New
Physics beyond the SM
E ~ 1 TeV or higher
New Physics beyond the Standard Model takes
place at high energies
Remember: inflation occurs at very high energies
We need to consider inflation scenario in the
context of physics beyond the Standard Model
Supersymmetric theory is one of the promising candidate
of new physics beyond the Standard Model
 Inflation model in the context of SUSY (Supergravity)
Minimal Supersymmetric Standard Model (MSSM)
SUSY version of SM
quark, lepton (1/2)
squark, slepton (0)
gauge boson (1)
gaugino (1/2)
Higgs
Higgsino (1/2)
(0)
SM particles
Superpartners
SUSY Grand Unification is strongly supported by
measurement of Standard Model gauge couplings
Gauge coupling unification
@
The Minimal SUSY SU(5) GUT
Particle contents
Standard Gauge Interactions are unified
into SU(5) GUT gauge interaction
All quarks & leptons in the MSSM are
unified into 5*+10
Higgs fields in the MSSM are included
New Higgs field to break SU(5) to the SM
Higgs inflation in the minimal SUSY SU(5) GUT
Arai, Kawai & N.O.,
PRD 84 (2011) 123515
Supergravity Lagrangian in superconformal framework
Compensating multiplet:
Minimal SUSY SU(5) model (Higgs sector)
We are interested in a special direction of the scalar potential
SU(5) SM
*Normalized by reduced Planck scale
S is almost constant
during inflation
Phi^4 inflation model with non-minimal coupling!
* This structure has been first pointed out by
Ferrara, Kallosh, Linde, Marrani & Van Proeyen
(PRD 82 (2010) 045003, PRD 83 (2011) 025008)
in the context of Next-to-MSSM
Predictions
We also examined quantum corrections, but their effects
are found to be negligible
Extension to other GUT models is possible which includes
SU(5) as a subgroup
(Example) SO(10) model
Another example
Arai, Kawai & N.O.
arXiv:1112.239
MSSM + right-handed neutrino
(For simplicity, we consider the 1 generation case)
Again, we have non-minimal phi^4 inflation
From the seesaw relation
by using
The CMB data tells
Homework
Extend the model to a GUT model
Summary
We study the inflationary scenario in the context of the
minimal SUSY SU(5) GUT
We have found that the inflation model with non-minimal
gravitational coupling is naturally implemented in the
minimal SUSYT SU(5) GUT etc. with an appropriate Kahler
potential
The predicted cosmological parameters are consistent
(almost best fit) with WMAP 7yr data
In the near future, on-going Planck satellite experiment
will provide us with more precise data which can
discriminate different inflation models
Planck satellite experiment is on-going and plans to
release the data in 2013
?
Planck may tell us MR
Thank you very much
for your attention!