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)