Relaxing theCosmological Moduli Problem
by Low-scale Inflation
Shu-Yu Ho(Tohoku University, Japan)

In collaboration with F. Takahashi (Tohoku. U.) and Y. Wen (KAIST)
Based on JHEP 1904 (2019) 149, ArXiv:1901.01240
14 May 2019, 2 day mini-workshop : Axion Cosmology
Resonant instabilities in cosmology
and their observational consequences

Introduction

Modulus Fieldl String theory predicts many light scalar moduli fields

through compactification.
l In SUSY, a modulus forms a chiral supermultiplet, !.

! = # + %& Axion

Some of modulus fields
are stabilized bySUSY effect'# ~ ')/+

Non-perturbative effect'& ≪ ')/+#

Shift symmetry : & → & + .

&Dynamics of Modulus Fieldl After inflation ends!(") ≫ #modulus is frozen
by Hubble friction

modulus$%&% ≠ ( )* +!(") : Hubble parameter# : modulus mass(!%&, ≫ #)

Dynamics of Modulus Fieldl After inflation ends!("#$% ) ≈ 'oscillation
modulus()*) ≈ +,- #. /3
3 3 The energy density of modulus
01#2 ≈ ' +,- #. ' / may dominate the Universe.
3Moduli Abundancel We consider only one (string) axion ! with a potential

l At "(#$%& ) ≈ (!

The axion abundance )! can be suppressed if !*+* is sufficiently small.

Cosmological Moduli Problem (CMP)l If the modulus is stable on a cosmological scale.
ü Its abundance may exceed the observed DM density.

Cosmological Moduli Problem (CMP)l If the modulus is stable on a cosmological scale.
ü Its abundance may exceed the observed DM density.
l If the modulus is unstable and can decay into photons.
ü It may spoil the success of big bang nucleosynthesis (BBN)ü due to the photo-dissociation of the light elements.
ü It may overproduce X-ray or gamma-ray fluxes.

Astrophysical & Cosmological Constraints

Cosmological Moduli Problem (CMP)l If the modulus is stable on a cosmological scale.
ü Its abundance may exceed the observed DM density.
l If the modulus is unstable and can decay into photons.
ü It may spoil the success of big bang nucleosynthesis (BBN)ü due to the photo-dissociation of the light elements.
ü It may overproduce X-ray or gamma-ray fluxes.

moduli problems in cosmology

Simple Solutions to Moduli Problem
Yamamoto ‘86 Lyth& Stewart ‘96

l Entropy production (e.g. thermal inflation)l  It may also dilute pre-existing baryon asymmetryl Adiabatic suppression  It is not so efficientl Very low scale inflation with !"#$ ≪ &'l Bunch-Davies (BD) distribution[cf. Graham & Scherlis (1805.07362) andLinde ‘96
K. Nakayama et al. 2011
Randall & Thomas ‘95

S.Y.H, Takahashi & Wen 2019

Takahashi, Wen & Guth (1805.08763) applied to the QCD axion]&' ≪ !"#$

What we didBunch-Davies Distribution

Bunch & Davies ̀78

l Suppose that the axion already acquires its massl (or potential) during inflation.
l The quantum diffusion prevents the axion from falling
l into the potential minimum.

lQuantum !"fluctuations

Classicalmotion"

Bunch-Davies Distribution
Quantum fluctuations

Bunch & Davies ̀78

Classical motion
The axion knows
where the minimum isin a probabilistic way.

Gaussiandistribution!

Bunch-Davies Distribution

Bunch & Davies ̀78

l In order to reach the BD distribution, we also assume

l that the inflation lasts sufficiently long (a large number
l of e-folds).

Bunch-Davies Distribution

Bunch & Davies ̀78

l In order to reach the BD distribution, we also assume

l that the inflation lasts sufficiently long (a large numberl of e-folds).
l Such a long period of inflation can be realized byl eternal inflation, a situation where the inflation
l never ends globally but it only ends locally.

A.D. Linde ’86
A.H. Guth 2007

The Axion Abundance with the BD Distributionl The energy density of the axion with BD distribution#($%&' ) ≈ )"l The axionic moduli problem is relaxed if.

One can suppress !" by low inflation scaleUpper Bound on !"#$ for Solving CMPUpper Bound on !"#$ with Different %&Summaryl We have shown that the CMP can be significantly relaxed bylow-scale inflation even !" ≪ $%&' . This is because the value ofthe scalar field follows the BD distribution if the inflation lasted
sufficiently long.
BD distribution"

Back upUpper Bound on !"#$ for lower axion masses