Reinterpretation of the Starobinsky-type inflation models

Based on Kohri and Kei-ichi Maeda in preparation Asaka, Iso, H. Kawai, Kohri, Noumi, and Terada, arXiv:1507.04344 [hep-th]

Kazunori Kohri (KEK and Sokendai)

Messages to the communities

l  A detection of r ~ O(10-3) tests the (trans-)Planck-scale physics of the field values in large-field inflation models

l  By LiteBIRD, we will be able to test the Starobinsky model, and check a variety of Starobinsky-type models with combining 21cm line observation by SKA

l  By LiteBIRD, we can measure nt within a sensitivity of 0.2

l E-folding number

l Tensor to scalar ratio at the CMB scale

Lyth bound (rough estimation)

r =

Ptensor

Pscalar CMB

= 16εCMB !

< 16ε(φ)

Boubekeur and Lyth (2005)

Trans-Planckian?

!!dN = d lna =Hdt = Hdφ

!φ

!!!!/φ +3H !φ = −

dVdφ

=V 'Slowroll condition

!!N = ln

aendaCMB

⎛

⎝⎜⎞

⎠⎟

Observations l  Planck2015 satellite reported;

l  Power spectrum of curvature perturbation

l  Spectral index

l  Running of n(k)

Pζ= P

scalar= V

24π 2mGε= (3.091 ± 0.025) ×10−10 ~ (ΔT /T )2

n

s=

d lnPζ

dlnk+1 == 1 + 2η − 6ε = 0.9639 ± 0.0047 (1σ )

α

s= dn

d lnk= 24ε 2 −16εη − 2ξ (2) = 0.009 ± 0.010 (1σ )

ns-1 ~ - 0.04

M

G= M

p/ 8π

ξ(2) ≡V '''V 'm

G4 /V 2

Tensor to scalar ratio Planck and BICEP/Keck + BAO

Planck 2015 results. XX. Constraints on inflation

1/2m2φ2 Chaotic inflation model was excluded at 95%

(February, ２０１５)

Keck Array and BICEP2 Collaborations: P. A. R. Ade, et al, arXiv:1510.09217 [astro-ph.CO]

PlanckTT+lowP+lensing+ext. +Bicep2/Keck Array 150GHz+95GHz

r < 0.07 at 95% at 0.05Mpc-1

Hazumi-san’s slide

LiteBIRD + Simons Array

l  LiteBIRD single: without lensing for ell<=1500 for TT, TE, EE, BB

l  LiteBIRD + Simons Array: with lensing for ell<=3000, + Temp.-fluctuation

Forecast of r v.s. ns by LiteBIRD

Oyama, Kohri, Hazumi et al, in preparation

Forecast of r v.s. nt by LiteBIRD

Oyama, Kohri, Hazumi et al, in preparation !!nt =

d lnPtensord lnk

= −2ε

Starobinsky Inflation Model

Starobinsky Inflation Model l Action

See also K. Maeda, Phys. Rev. D 37, 858 (1988).

is a big number

Transformation from Jordan to Einstein frame

l Action

l After the Legendre transformation

l Effective Potential

Transformation from Jordan to Einstein frame

l Conformal transformation

l Potential

Starobinsky Inflation in Einstein frame

l Action

l Potential

General potential shapes

Q.-G. Huang, 2013

M

Starobinsky-like model from extra dimensions

l Action in D-dimension

l Action in 4D after a compactification,

l  If we take

L=30/Λ

Λ is a cutoff scale

Asaka, Iso, Kawai, Kohri, Noumi, Terada, 2015

Starobinsky-like Inflation

l Einstein term

l  Including higher-order terms

b1 ~O(10−4 )

b = b1b3

Asaka, Iso, Kawai, Kohri, Noumi, Terada, 2015

As we will see later,

Starobinsky-like Inflation l Potential

l Predictions

βs = dα s / d ln k

α s = dns / d ln k

Asaka, Iso, Kawai, Kohri, Noumi, Terada, 2015

b = b1b3b3 ~O(1)b ~ b1

Future observations

22

nupper

nlower

~ Exp − ΔET

S

⎡

⎣⎢⎢

⎤

⎦⎥⎥

Cosmological  21cm  line  was  emi0ed  at  the  reioniza6on  epoch,    Temperature  T  ~  0.003eV  –  0.01  eV

23

 

 

 

 

Detail of ionization history

gives us power spectrum

21cm line power spectrum P21(k,µ) traces the baryon power spectrum

　µ: cosine with respect to line of sight

25

26

2

Sensitivities on running spectral index by future cosmological 21cm obs. for small scales

27

Kohri, Oyama, T.Takahashi, T.Sekiguchi, 2013

Tensor to scalar ratio vs spectral index

Asaka, Iso, Kawai, Kohri, Noumi, Terada, 2015

b = b1b3

Starobinsky Inflation

Asaka, Iso, Kawai, Kohri, Noumi, Terada, 2015

Running will be observed by future 21cm line with the precison of 3.E-4 (Kohri, Oyama, T.Takahashi, Sekiguchi, 2015)

b = b1b3

Cut-off scale of this model

l Upper bounds on b1

l  Lower bounds on the cutoff scale

Asaka, Iso, Kawai, Kohri, Noumi, Terada, 2015

Another ways of compactification

l One more scalar field ψ appears because of the compactification

l  If such a degree of freedom can have a relation,

the result does not change (Kohri and Kei-ichi Maeda in preparation)

→conformal transformation → compactification

Conclusion l  The original Starobinsky model fits the observations

very well

l  The higher order R terms may result from an effective theory with a cutoff scale Λ in extra-dimension theories.

l  The big coefficient of the R2 term can come from the volume factor in case of the reduction form 10D to 4D.

l  The small coefficient of R term may result in a breakdown of conformal symmetry or accidental cancellations with the order of O(10-4), which is just a milder tuning

For a bit more specific models Juan Garcia-Bellido, Diederik Roest, Marco Scalisi, Ivonne Zavala (2014)