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
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
all particles are in thermal equilibrium
~1 MeV(10^10 K) Big-bang nucleosynthesis
~1 eV
Recombination origin of CMB
Equal epoch (radiation density = matter density)
~ 0.1 eV
Present~0.0001 eV
decoupling of some particles (example: Dark Matter)
Hot & dense thermal state
Radiation dominated era
Matter dominated era
w=1/3
w=0
Problems of Big-Bang Cosmology
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
Big-Bang Cosmology:
w=1/3 : radiation w=0 : matter
Decelerating expansion
Basic Idea of Inflationary Universe
Suppose the existence of a stage in the early universe with
Simple example: de Sitter space
Positive cosmological constant (vacuum energy)
Expansion law:
Continuity equation:
``Inflation’’ Accelerating Expansion
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
Oscillations & decay
During inlaftion era, quantum fluctuation of inflaton is enlarged by inflation
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
Number of e-foldings
N > 50-60 is necessary to solve horizon & flatness problem
These are very small during inflation
End of inflation
Inflationary Predictions VS. WMAP (cont’d)
Power spectrum
Conditions to fix parameters in inflation model
WMAP 7yr
e-foldings
= 50 -60
Predictions
By these conditions, the slow-roll parameters are fixed
Spectral index:
Tensor-to-scalar ratio:
Example models
We calculate the slow-roll parameters for each model and find predictions
WMAP 7yr contours
Model 1:
Model 2:
N=60
Model 1
Model 2
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
Higgs InflationReplace phi H
Analysis beyond tree-level (RGE improved effective potential)
Bezrukov & Shaposhnikov, PLB 659 (2008) 703; JHEP 07 (2009) 089
De Simone, Hertzberg & Wilczek, PLB 678 (2009)1Barvinsky 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 (0) Higgsino (1/2)
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
Standard Gauge Interactions are unified into SU(5) GUT gauge interaction
All quarks & leptons in the MSSM are unified into 5*+10
Particle contents
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
Supergravity Lagrangian in superconformal framework
Compensating multiplet:
Minimal SUSY SU(5) model (Higgs sector)
Arai, Kawai & N.O., PRD 84 (2011) 123515
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
Another example
MSSM + right-handed neutrino (For simplicity, we consider the 1 generation case)
Again, we have non-minimal phi^4 inflation
Arai, Kawai & N.O.arXiv:1112.239
SummaryWe 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