Inflation from radion gauge-Higgs potential at Planck scale

1. Inflation from radion gauge-Higgs potential at Planck scale Yugo Abe (Shinshu University) GRaB100@NTU, July 10, 2015 In collaboration with T. Inami (NTU), Y. Kawamura (Shinshu U), Y. Koyama (NCTS) YA, T. Inami, Y. Kawamura, & Y. Koyama, [arXiv:1504.06905]

2. 0 Our focus We propose the inflationary cosmology based on the 5-dimensional gravity + gauge theory. In our model, two scalar fields, radion and gauge-Higgs , are obtained from 5d-gravity field and 5d-gauge field after compactification. • Can the effective potential be identified with inflaton potential? • If possible, which scalar fields has the role of inflaton? • Where didinflaton comefrom? Gravity, gauge theory or both? • In string theory point of view, radionappears from closed string and gauge-Higgs appears from open string.

3. 1 Problem 2 Fine-tuning problem on inflationary cosmology Cause What kind of symmetry can control scalar potential? 3 Our solution 5D gravity + gaugetheory 1-loop scalar potential (finite) = inflaton potential 5D gauge symmetry 5D general coordinate transformation invariance

4. 1 Slow-roll inflation scenario -0 Inflation theory is the dynamics of scalar field(s) “inflaton”. Inflation is the rapidly accelerated expansion of space at early stage of our universe. From the particle physics point of view, the slow-roll inflation can be explained using a scalar potential(inflatonpotential). Slow-roll approximation( )gives vacuum conditions and , where and . Friedmanneqs. : scale factor : Newton const. : curvature inflation solution

5. 1 Constraints on inflaton potential -1 • slow-roll conditions : flatness of potential • spectral index : amount of scale dependence of fluctuation • e-foldingnumber: period in which inflation continues • curvature perturbation : reproduce the temperature fluctuations of CMB • tensor to scalar ratio :energy scale of inflation • quantum gravity correction is negligible. (observations) (observations) (observations) (*: at the horizon exit) ( : observations)

6. 1 Fine-tuning problem on inflational cosmology -2 Fine-tuning parameters of inflatonpotential The inflaton potential is just given by hand or is derived from a theory. our way. I will explain later. If we take the inflaton potential as . is required by inflation constraints. However considering quantum effects, all of terms which allowed by symmetries may appear. Coefficients should be fine-tuned. Furthermore, inflation occurs where …. ( : reduced Planck mass) ( : cut-off)

7. 2 What kind of symmetry can control scalar potential? -0 Where does the fine-tuning come from? Scalar field doesn’t have a 4d symmetry of controlling the potential. The serious divergent term appears from the quantum correction. We must balance the relation between and . On the other hand, The gauge and gravity field doesn’t have the mass term, thanks to the gauge symmetry and general coordinate transformation invariance.

8. 2 Our answer : Higher-dimensional theory -1 Howcontrol to 4d scalar potential? Onlytoevaluate . ・Higher-dimensional gauge symmetry ・Higher-dimensional general coordinate transformation invariance Quantum level Tree level cf. 4d gauge symmetry

9. 3 5-dimensional gauge and gravity field -0 Scalar fields are the extra components of the higher-dimensional fields. 5d gauge field includes 4d gauge field and 4d scalar field . Gauge-Higgs 5d gravity field includes 4d gravity field , 4d U(1) gauge fieldand 4d scalar field . (V.E.V of radion is related to the size of the extra space) , Radion

10. 3 5d gauge theory -1 at tree level (after compactification) where, expansion 5D gauge symmetry control the potential of 4D scalar filed. 1-loop level where V.E.V. of 4D scalar field :

11. 3 5d gravity theory -2 at tree level (after compactification) expansion 5D general coordinate transformation invariance control the potential of 4D scalar filed. 1-loop level where V.E.V. of 4D scalar field :

12. 3 Inflation from higher-dimensional theory -3 • 5d U(1) gauge theory : Extranatural inflation model (2003. N. Arkani-Hamed et al.) where, Incomplete: Gauge coupling const. is too small. • 5d gravity theory : Radion inflation model (2013. Fukazawa, Inami, Koyama) Incomplete: 4D cosmological const. is introduced by hand.

13. 3 5d gravity + gauge theory -4 5d gravity + gauge theory : Our model ( YA, T. Inami, Y. Kawamura & Y. Koyama, PTEP 2014 [arXiv:1404.5125] ) where, Both Gauge-Higgs and Radion are higher-dimension origin. However, each property and behavior differ from each other. We can calculate the finite one-loop potential , thanks to the 5D gauge symmetry and 5D general coordinate transformation invariance. Can our potential fulfilltheconstraintsofinflationparameters?

14. 3 Loop diagrams -5 + + + + + +

15. 3 Our one-loop potential -6 : compactificationcircumference : number of U(1)charged matter Radion : U(1)charged matter mass Gauge-Higgs : number of neutral matter : neutral matter mass : 5d cosmological constant

16. 3 Possibilities of our inflation model -7 What kind of inflation did we choose? We investigate which scalar field has the dominant contribution to the inflaton potential and can be identified with the inflaton. a. Single field inflation a-1. inflaton = radion a-2. inflaton = gauge-Higgs b. Hybrid inflation b-1. inflaton = radion, waterfall = gauge-Higgs b-2. inflaton = gauge-Higgs, waterfall = radion c. Multi inflaton inflation (Future work : We need complex analyses.)

17. 3 a. Single field inflation a-1. radion inflation -8 inflaton ( : reduced radion field) a-2. gauge-higgs inflation (Extranatural) inflaton

18. 3 a. Single field inflation a-1. radion inflation -8 The case of radion inflation does not fulfill the slow-roll conditions. inflaton ( : reduced radion field) a-2. gauge-higgs inflation (Extranatural) inflaton

19. 3 b. Hybrid inflation b-1. radionhybrid inflation -9 inflaton waterfall b-2. gauge-higgs hybrid inflation (Extranatural) inflaton waterfall

20. 3 b. Hybrid inflation b-1. radionhybrid inflation -9 The case of radion hybrid inflation does not fulfill the slow-roll conditions. inflaton waterfall b-2. gauge-higgs hybrid inflation (Extranatural) Besides the vacuumof potential, radion direction is the first rolling direction. inflaton waterfall

21. 3 Summary -F In our model, gauge-Higgs inflation can occur. This model is large field inflation. However, we could evaluate the potential without serious fine-tuning. Radionis very important in determining the physical parameters, especially gauge coupling, matter masses and compactificationscale. Gauge-Higgs is inflaton. What is the role of radion? chargedfermionmass neutral fermion mass 1/( circumference) inflaton mass 4d gauge coupling tensor to scalarratio

22. 4 Our focus again Our effective potential can cause inflation. • Can the effective potential be identified with inflaton potential? • If possible, which scalar fields has the role of inflaton? • Where didinflaton comefrom? Gravity, gauge theory or both? • In string theory point of view, radion appears from closed string and gauge-Higgs appears from open string. Gauge-Higgs is inflaton. Inflation appears from gauge field. However, radion is also essential. What is the origin of inflaton?“ClosedstringVSOpenstring” Our result could indicate that the quantum theory of gravity such as string theory is necessary to understand the mechanism of inflation more properly. • It would be interesting to study the inflation based on the effective potential relating several scalar fields such as the dilaton, the moduli (including the radion) and the gauge-Higgs in the framework of string theory.

23. E Shape of our potential x.1 The matter mass ratio change the shape of our effective potential. : U(1)charged matter mass : neutral matter mass Multi field inflation case If , , and are larger than Planck.

24. E Multi inflaton inflation x.2 For example, the trajectrysomething like this is expected.