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

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

In Einstein frame

=const for a large inflaton VEV

V

Predictions of non-minimal phi^4 modelN. O.,Rehman & ShafiPhys. Rev. D 82, 043502 (2010)

Minimal model

N. O.,Rehman & ShafiPhys. Rev. D 82, 043502 (2010)

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

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

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

From the seesaw relation

by using

The CMB data tells

Homework

Extend the model to a GUT model

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

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Planck satellite experiment is on-going and plans to release the data in 2013

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Planck may tell us MR

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Thank you very much for your attention!