general holomorphic pure supergravity and its cosmology

GENERAL HOLOMORPHIC PURE SUPERGRAVITY AND

ITS COSMOLOGY

Takahiro Terada

Univ. of Tokyo, Japan

Sergei V. Ketov and TT,

JHEP07(2013)127,

arXiv:1304.4319 [hep-th]

19th International Summer Institute on Phenomenology of Elementary Particles and Cosmology

GENERALIZATION OF

SUPERGRAVITY

SUPERSYMMETRIZATION OF MODIFIED GRAVITY

Ordinary Matter; 4.90% Dark Matter; 26.80%

Dark Energy; 68.30%

Energy Density of The Universe

Ordinary Matter Dark Matter Dark Energy

𝐺𝜇𝜈=8𝜋 𝐺𝑇 𝜇𝜈

Many reasons to do that!!• pure theoretical interests• stringy/quantum corrections• potential applications to pheno• application to inflation• to embed modified gravity into

fundamental theory, etc.

Planck collaboration, arXiv:1303.5082

• A. Einstein, 1915

gravity• A. De Felice and S. Tsujikawa, Living Rev. Rel. 13

(2010) 3 and references therein.

gravity• Our work

• D. Z. Freedman, P. van Nieuwenhuizen and S. Ferrara,

Phys. Rev. D 13 (1976) 3214;• S. Deser and B. Zumino, Phys. Lett. B 62 (1976) 335.

supergravity• S.J. Gates, Jr. and S.V. Ketov, Phys. Lett. B674 (2009) 59

supergravity• Our work

Simple

General

Supersymmetrization

Bosonic sector

NEW NEW

Positioning of the work

ℒ= ∫ d2Θ 2ℰ 𝐹 (ℛ ,𝒲 )+H .c .where is a holomorphic function.

+H.c.

New action for supergravity

gravity and Inflation

𝑓 (𝑅 ,𝐶 )=𝑅− 𝑅2

6𝑀2 +𝑏𝑅𝐶𝜇𝜈𝜌𝜎𝐶𝜇𝜈𝜌𝜎

Starobinsky model + correction term () as a simple non-trivial example:

𝑉=34 𝑀

2 (1−𝑒− √2 /3𝜎+𝑏𝐶𝜇𝜈𝜌𝜎𝐶𝜇𝜈𝜌𝜎𝑒√2 /3𝜎 )2

where is the inflaton mass and is a coupling constant.

𝑆=− 12 ∫ 𝑑4𝑥 √−𝑔 𝑓 (𝑅 ,𝐶)

f(R) gravity Scalar-tensor gravity

f(R,C) gravity scalar-tensor gravity with Weyl tensor

equivalent

equivalent

~𝑏=0.05~𝑏=0.01

~𝑏=0.002~𝑏=0

02~𝑏=−0.01

~𝑏=−0.05

𝑉=34 𝑀

2 (1−𝑒− √2 /3𝜎+~𝑏𝑒√2 /3𝜎 )2

~𝑏≡𝑏𝐶𝜇𝜈𝜌𝜎𝐶𝜇𝜈𝜌𝜎

GENERAL HOLOMORPHIC PURE SUPERGRAVITY AND

ITS COSMOLOGY

Takahiro Terada

Univ. of Tokyo, Japan

Sergei V. Ketov and TT,

JHEP07(2013)127,

arXiv:1304.4319 [hep-th]

19th International Summer Institute on Phenomenology of Elementary Particles and Cosmology

ℒ= ∫ d2Θ 2ℰ 𝐹 (ℛ ,𝒲 )+H .c .SUMMARY• There are many reasons to study modified supergravity.

• We proposed a new type of action for modified gravity and supergravity.

• It’s interesting to compare the results with future CMB data.