Conservation of ζ\zeta with radiative corrections from heavy field

In this paper, we address a possible impact of radiative corrections from a heavy scalar field $\chi$ on the curvature perturbation $\zeta$. Integrating out $\chi$, we derive the effective action for $\zeta$, which includes the loop corrections of the heavy field $\chi$. When the mass of $\chi$ is much larger than the Hubble scale $H$, the loop corrections of $\chi$ only yield a local contribution to the effective action and hence the effective action simply gives an action for $\zeta$ in a single field model, where, as is widely known, $\zeta$ is conserved in time after the Hubble crossing time. Meanwhile, when the mass of $\chi$ is comparable to $H$, the loop corrections of $\chi$ can give a non-local contribution to the effective action. Because of the non-local contribution from $\chi$, in general, $\zeta$ may not be conserved, even if the classical background trajectory is determined only by the evolution of the inflaton. In this paper, we derive the condition that $\zeta$ is conserved in time in the presence of the radiative corrections from $\chi$. Namely, we show that when the scaling symmetry, which is a part of the diffeomorphism invariance, is preserved at the quantum level, the loop corrections of the massive field $\chi$ do not disturb the constant evolution of $\zeta$ at super Hubble scales. In this discussion, we show the Ward-Takahashi identity for the scaling symmetry, which yields a consistency relation for the correlation functions of the massive field $\chi$.Comment: 27 pages, 1 figure; v2: updated references and minor revision

Strong restriction on inflationary vacua from the local gauge invariance I: Local gauge invariance and infrared regularity

The primordial perturbation is widely accepted to be generated through the vacuum fluctuation of the scalar field which drives inflation. It is, however, not completely clear what is the natural vacuum in the inflationary universe particularly in the presence of non-linear interactions. In this series of papers, we will address this issue, focusing on the condition required for the removal of the divergence from the infrared (IR) contribution to loop diagrams. We show that requesting the gauge invariance in the local observable universe guarantees the IR regularity of the loop corrections beginning with a simple initial state. In our previous works, the IR regularity condition was discussed using the slow roll expansion, which restricts the background evolution of the inflationary universe. We will show more generally that requesting the gauge invariance/the IR regularity leads to non-trivial constraints on the allowed quantum states.Comment: 14 page

Strong restriction on inflationary vacua from the local gauge invariance III: Infrared regularity of graviton loops

It has been claimed that the super Hubble modes of the graviton generated during inflation can make loop corrections diverge. Even if we introduce an infrared (IR) cutoff at a comoving scale as an ad hoc but a practical way for the regularization, we encounter the secular growth, which may lead to the breakdown of perturbative expansion for a sufficiently long lasting inflation. In this paper, we show that the IR pathology concerning the graviton can be attributed to the presence of residual gauge degrees of freedom in the local observable universe as in the case of the adiabatic curvature perturbation. We will show that choosing the Euclidean vacuum as the initial state ensures the invariance under the above-mentioned residual gauge transformations. We will also show that as long as we consider a gauge invariant quantity in the local universe, we encounter neither the IR divergence nor the secular growth. The argument in this paper applies to general single field models of inflation up to a sufficiently high order in perturbation.Comment: 34 pages; v2: minor revision, published in PTEP. arXiv admin note: text overlap with arXiv:1306.446

Natural selection of inflationary vacuum required by infra-red regularity and gauge-invariance

It has been an issue of debate whether the inflationary infrared(IR) divergences are physical or not. Our claim is that, at least, in single-field models, the answer is "No," and that the spurious IR divergence is originating from the careless treatment of the gauge modes. In our previous work we have explicitly shown that the IR divergence is absent in the genuine gauge-invariant quantity at the leading order in the slow-roll approximation. We extend our argument to include higher-order slow-roll corrections and the contributions from the gravitational waves. The key issue is to assure the gauge invariance in the choice of the initial vacuum, which is a new concept that has not been considered in conventional calculations.Comment: 12 pages; v3: several descriptions are added; v4: accepted version in PT

The Current Status of Knowledge and Behavior Related to STI Prevention among High School Students in Korea

This study explores coping with STIs and related factors including knowledge, sexual behavior, and sex education among Korean adolescents. Anonymous self-administered questionnaires were distributed to 135 male and 150 female high school students. The results showed that 2.1% of participants had had sexual experience. Males had less information than females (p<0.05); 38.5% of males did not consult anyone. In contrast, females acquired information from and consulted with their parents. Although females' sexual abstinence behavior was higher than that of males (p<0.001), there were no significant differences in the STI knowledge test. Regarding sex education, 32.4–59.5% of students had received education on STIs. Students' degree of satisfaction with sexual knowledge was 10.2%, their understanding of STIs was poor, and they could not cope with having a checkup. In conclusion, high school students receive insufficient education to protect themselves from STIs. Their knowledge was not related to sexual abstinence behavior and coping behavior. Therefore, schools in Korea should provide high school students with appropriate education on STI prevention and coping behavior. In addition, an environment that facilitates consultation and clinics for helping young people deal with sexual problems should be provided