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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. ～ A single parameter explains everything… Mukhanov&Chivisov, Starobinsky, Hawking, Guth-Pi 1982,…

As of early 1990s cosmic stringsinflation spectrum of fluctuations scale invariant amplitude of fluctuations fine-tuning dark mattercold or hotrequires CDM monopole problem incompatiblenaturally solved horizon & flatness problems no explanation naturally solved

Cosmic string scenario explained the origin of fluctuations at least equally well compared with inflation models (or even better if DM was hot), but cannot explain global properties (i.e. homogeneity & isotropy) of the Universe at all. So in order to make a fully consistent cosmology, I thought cosmic strings should be formed during or after inflation. Oriental Medicine treat the body as a whole system Occidental Medicine treat each sick part separately

Abelian Higgs model simple massive scalar chaotic inflation as an example (Linde 1983) Introduce a nonminimal coupling term to χ with the scalar curvature Symmetry of χ restored for or value of the inflaton φ 2 at the end of inflation for since we did not know If, cosmic strings are produced after inflation. e.g. conformal coupling During inflation 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??

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We propose a new mechanism of string formation during inflation without introducing 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. kinetic term F term scalar potential with F term inflation canonical kinetic term

F term inflation canonical kinetic term The scalar potential contains a Hubble-induced mass term similar to that induced by the nonminimal coupling in the previous model. Model building No direct interaction between inflation and string sectors Charge assignments shift symmetry along the imaginary direction string forming fields

the inflaton Introducing canonically normalized mass eigenstates

We find Symmetry breaking (=string formation) starts when 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 than thermal fluctuations, and the phase of is fixed at the time potential force surpasses stochastic force from quantum fluctuations. (Nagasawa & JY 1992) EXTRA DILUTION 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 Loop formation by intercommutation will not start until this scale falls shorter than the Hubble radius. Formation of small loops is suppressed, and we can evade pulsar constraints on gravitational waves from loops. 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 is widely distributed between and 0.1 (Blanco-Pillado, Olum, Shlaer 2011&2014) But in our scenario, strings are stretched and small-scale structures are smoothed out by inflation until well after the scaling regime is achieved, so we assume hereafter.

Constraint on G as a function of the beginning of scaling regime (Miyamoto, Yamauchi, JY 2014, preliminary)

In terms of model parameters… dilution

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 may detect traces of cosmic strings. Physics with no potential adversary I wish someone will do numerical simulations of a string network starting from “inflationary” initial condition, namely, from a dilute and straight configuration.