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 Einstein equations: Perfect fluid: Expansion law: Continuity equation:

(k=0) w=1/3 : radiation w=0 : matter

Brief thermal history of the Universe

T

Radiation dominated era w=1/3 ~1 MeV (10^10 K) Big-bang Hot & dense thermal state all particles are in thermal equilibrium decoupling of some particles (example: Dark Matter) Big-bang nucleosynthesis Matter dominated era w=0 ~1 eV ~ 0.1 eV ~0.0001 eV Equal epoch (radiation density = matter density) Recombination



origin of CMB Present

Problems of Big-Bang Cosmology

Big-Bang Cosmology: w=1/3 : radiation w=0 : matter

Flatness problem Fine-tuning of density parameter is necessary

Decelerating expansion

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 1. Inflation at slow-roll era 2. End of Inflation 3. Coherent oscillations 4. Decays to Standard Model particles 5. Reheating



Big-Bang Cosmology Oscillations & decay

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



CMB anisotropy



inflaton potential, initial condition 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

Model 1 : Model 2 : Model 2 N=60 Model 1

We calculate the slow-roll parameters for each model and find predictions

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

V =const

for a large inflaton VEV

Predictions of non-minimal phi^4 model

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



Minimal model N. O.,Rehman & Shafi Phys. Rev. D 82, 043502 (2010)

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 (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

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 M

R

Thank you very much for your attention!