1

Cosmic string scenario was the first mechanism to provide the origin of density fluctuations that seeded cosmic large-scale structures from fundamental physics.

Zel’dovich 1980, Vilenkin 1981, & participants of this workshop with age > 0.5C yrs

Another proposal for the origin of density fluctuations was quantum fluctuations from inflation.

610G

～

A single parameter explains everything…

Mukhanov&Chivisov, Starobinsky, Hawking, Guth-Pi 1982,…

As of early 1990s cosmic strings inflation

spectrum of fluctuations

scale invariant scale invariant

amplitude of fluctuations

fine-tuning

dark matter cold or hot requires CDM

monopole problem

incompatible naturally solved

horizon & flatnessproblems

no explanation naturally solved

610G

Cosmic string scenario explained the origin of fluctuations at least equallywell compared with inflation models (or even better if DM was hot),but cannot explain global properties (i.e. homogeneity & isotropy) of theUniverse at all.

So in order to make a fully consistent cosmology, I thought cosmic stringsshould be formed during or after inflation.

Oriental Medicinetreat the body as a whole system

Occidental Medicinetreat each sick partseparately

22† 21( )( ) [ ], [ ]

4 2D D F F V V v

stringL Abelian Higgs model

2 2 21 1( ) [ ], [ ]2 2

U U M inflationL simple massive scalar chaotic inflationas an example (Linde 1983)

Introduce a nonminimal coupling term to χ with the scalar curvature

22 22[ ]2cV v R 22 2[ ]

2V v

0

R

Symmetry of χ restored for or 2R v 2 24

2 16

14

10

4 4Plv M

M

value of the inflaton φ2

at the end of inflation

16 1610 GeV

vv for

2

610Pl

vG

M

14 1410 GeV

MM since we did not know

T

T

44 10 If ,cosmic strings are producedafter inflation.e.g. conformal coupling 1 6

During inflation2

2 22

1612 ( )

Pl

MR H t

M

large and gradually decreasing

Cosmic strings are naturally produced after inflation.

Furthermore, string density can be controlled if phase transition occurs during inflation rather than after inflation.

(JY 1988)

(JY 1989)

cf Previous models of string formation after inflation introduced interactions between the inflaton and the string-forming field. (Shafi, Vilenkin 1984, Vishniac, Olive, Seckel 1987,…)

I expected everyone working on cosmic strings would like the idea, and use it….

But in fact, no one used it.

Because they did not care horizon/flatness/monopole problems.

Because cosmic string scenario was a rival against inflation, so they did not want to have a help from its adversary.

Do we need an adversary to do physics??

8

We propose a new mechanism of string formation during inflation withoutintroducing direct coupling between the inflaton and the U(1)-breaking scalar field in a F-term inflation model in Supergravigy. (Kamada, Miyamoto, JY 2012)

Kähler potential and Superpotential define a model.K W

iji jK

kinetic term F term scalar potential

with

F term inflation

canonical kinetic term

2

ii

K V

F term inflation

canonical kinetic term

2

ii

K VThe scalar potential contains a Hubble-induced mass termsimilar to that induced by the nonminimal coupling in the previous model.

Model building No direct interaction between inflation and string sectors

Charge assignments

Im : inflaton

shift symmetry along the imaginary direction

string forming fields

the inflaton

Introducing canonically normalized mass eigenstates

We find

Symmetry breaking (=string formation) startswhen becomes negative.inflation

String tension in this model

Hubble parameter at string formation

Phase transition and string formation can take place during inflation, and strings are diluted and stretched to some extent by subsequent inflation.

Phase transition is triggered by quantum fluctuations rather thanthermal fluctuations, and the phase of is fixed at the time potentialforce surpasses stochastic force from quantum fluctuations. (Nagasawa & JY 1992)

2

2

mc

M

12

2,

3 3f

c cH M

EXTRADILUTION

Number of e-folds of inflation thereafter

Typical separation & characteristic length of strings at redshift

scale factor at the end of inflation

initial separation of strings 1400H

Loop formation by intercommutation will not start until this scale fallsshorter than the Hubble radius.

Formation of small loops is suppressed, and we can evade pulsar constraints on gravitational waves from loops.

t

GW energy density vs redshift at the beginning of the scaling regime

For single loop size

Numerical simulations in conventional scaling scenario shows that α iswidely distributed between 10-7 and 0.1

(Blanco-Pillado, Olum, Shlaer 2011&2014)

But in our scenario, strings are stretched and small-scale structures aresmoothed out by inflation until well after the scaling regime is achieved, so we assume hereafter. 0.1

3

Constraint on G as a function of the beginning of scaling regime

(Miyamoto, Yamauchi, JY 2014, preliminary)

In terms of model parameters…

G

dilution

c

71.3 10G

Cosmology must be self consistent.

Cosmic string formation should be considered in inflationary cosmology.

We proposed some natural mechanisms of string formation in this context.

Pulsar constraints can be evaded while future CMB experiment maydetect traces of cosmic strings.

Physics with no potential adversary

I wish someone will do numericalsimulations of a string network starting from “inflationary” initialcondition, namely, from a diluteand straight configuration.