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We derive a cutting rule for equal-time in-in correlators including cosmological correlators based on Keldysh $r/a$ basis, which decomposes diagrams into fully retarded functions and cut-propagators consisting of Wightman functions. Our derivation relies only on basic assumptions such as unitarity, locality, and the causal structure of the in-in formalism, and therefore holds for theories with arbitrary particle contents and local interactions at any loop order. As an application, we show that non-local cosmological collider signals arise solely from cut-propagators under the assumption of microcausality. Since the cut-propagators do not contain (anti-)time-ordering theta functions, the conformal time integrals are factorized, simplifying practical calculations., Comment: 36 pages, 2 figures; v2: references added

We quantitatively analyze a basic question: what is the stationary solution of the background plasma temperature profile around a black hole (BH)? One may naively expect that the temperature profile continuously decreases from the Hawking temperature at the surface of the BH towards an outer region. We show analytically and numerically that this is not the case because local thermal equilibrium cannot be maintained near the surface of the BH and also because the high-energy particles emitted from Hawking radiation cannot be instantaneously thermalized into the background plasma. The temperature profile has a plateau within a finite distance from the BH, and even the overall amplitude of background temperature at a distance far away from the BH is significantly suppressed compared with the naive expectation. The main reason for these counterintuitive results comes from the fact that the size of the BH is too small that particles of Hawking radiation goes far away within the typical time scale of interactions., Comment: 24 pages, 9 figures

We present a conceptually simple model to generate asymmetries that are not directly related to baryon nor lepton charges. The model employs a three-Higgs doublet framework, wherein the other two Higgs fields are significantly heavier than the Standard Model (SM) Higgs field. The decay of these heavier Higgs fields generates asymmetry for approximately conserved charges in the Standard Model at a high temperature. These asymmetries will be converted into baryon/lepton asymmetry through $B-L$ violating interactions associated with right-handed neutrinos via the wash-in mechanism., Comment: 21 pages, 4 figures. v2: appendix extended, typos fixed, but results unchanged

We investigate the thermalization of high-energy particles injected from the perturbative decay of inflaton during the pre-thermal phase of reheating in detail. In general, thermalization takes a relatively long time in a low-temperature plasma; therefore, the instantaneous thermalization approximation is not justified, even for the reheating of the Standard Model (SM) sector. We consider a pure Yang-Mills (YM) theory as an approximation of the SM sector or a possible dark sector, considering the Landau-Pomeranchuk-Migdal effect, a quantum interference effect in a finite temperature plasma. We perform the first numerical calculation to solve the time evolution of the system, including the redshift due to the expansion of the Universe, and show the details of the temperature evolution near the maximum and the behavior of the quasi-attractors at later times. The maximal temperature $T_\text{max}$ and time scale $t_\text{max}$ are determined quantitatively, such as $T_\text{max} \simeq 0.05 \times (\Gamma_I M_\text{Pl}^2/m_I^3)^{2/5} m_I$ and $t_\text{max} \simeq 2 \times 10^3 \times (\Gamma_I M_\text{Pl}^2/m_I^3)^{-3/5} m_I^{-1}$ in the SM-like system, where $m_I$ and $\Gamma_I$ are the mass and decay rate of inflaton. We also provide a similar formula for pure $\operatorname*{SU}(N)$ and $\operatorname*{SO}(N)$ YM theories for general values of $N$ and coupling constant $\alpha$, including $T_\text{max} \propto \alpha^{4/5}$ and $t_\text{max} \propto N^{-2} \alpha^{-16/5}$ behaviors and their numerical coefficients. The thermalization occurs in a finite time scale, resulting in a lower maximal temperature of the Universe after inflation than that under the instantaneous thermalization approximation., Comment: 21 pages, 4 figures

We show that various types of scalaron-induced inflation, including the Starobinsky inflation, can be realized in the Einstein-Cartan gravity with the Nieh-Yan term and/or the Holst term. Einstein-Cartan $f(R)$ theory is known not to induce an additional scalar degree of freedom, the scalaron, contrary to the case in the metric formalism. However, there exist geometric quantities other than the Ricci scalar in the Einstein-Cartan gravity, such as the Nieh-Yan and the Holst terms. Once we introduce them in addition to the Ricci scalar and allow general combinations up to their quadratic order, the scalaron can become dynamical to realize inflation. With the rank of the associate matrix of the quadratic part to be one, the models are equivalent to the $\alpha$-attractor inflation and its deformation, including the Starobinsky inflation and quadratic chaotic inflation, etc. For more general cases with the rank greater than one, the models fall into the $k$-essence, realizing the rank one case in a particular limit., Comment: 24 pages, 2 figures

The stochastic gravitational wave background (SGWB) recently detected by the PTA collaborations could be the gravitational waves (GWs) induced by curvature perturbations. However, primordial black holes (PBHs) might be overproduced if the SGWB is explained by the GWs induced by the curvature perturbations that follow the Gaussian distribution. This motivates models associated with the non-Gaussianity of the curvature perturbations that suppress the PBH production rate. In this work, we show that the axion curvaton model can produce the curvature perturbations that induce GWs for the detected SGWB while preventing the PBH overproduction with the non-Gaussianity., Comment: 18 pages, 4 figures, v2: published version, minor revision

We formulate scalar field theories coupled non-conformally to gravity in a manifestly frame-independent fashion. Physical quantities such as the $S$ matrix should be invariant under field redefinitions, and hence can be represented by the geometry of the target space. This elegant geometric formulation, however, is obscured when considering the coupling to gravity because of the redundancy associated with the Weyl transformation. The well-known example is the Higgs inflation, where the target space of the Higgs fields is flat in the Jordan frame but is curved in the Einstein frame. Furthermore, one can even show that any geometry of O$(N)$ nonlinear $\sigma$ models can be flattened by an appropriate Weyl transformation. In this Letter, we extend the notion of the target space by including the conformal mode of the metric, and show that the extended geometry provides a compact formulation that is manifestly Weyl-transformation/field-redefinition invariant. We identify the cutoff scale with the inverse of square root of the extended target space curvature and confirm that it coincides with that obtained from two-to-two scattering amplitudes based on our formalism., Comment: 6+2 pages, 1 table

This paper studies the quantum corrections to the Higgs inflation model in the context of the Einstein-Cartan (E-C) gravity in the large-$ N $ limit with $N$ being the number of real scalar components in Higgs. Recently, it is realized that the Higgs inflation in the E-C formalism smoothly connects those in the metric and the Palatini formalisms in the presence of a non-minimal coupling between the Higgs fields and the Nieh-Yan term. This motivates us to investigate the quantum corrections to the E-C Higgs inflation and to clarify how the Ricci curvature squared $ R^2 $ induced by the quantum corrections succeeds in Ultraviolet (UV)-extending the Higgs inflation in metric formalism while it fails in the Palatini case. We show that a generalized $ R^2 $-term required for the renormalization in the E-C formalism induces a new scalar degree of freedom (DoF), the scalaron, which gradually decouples with the system due to its increasing mass as approaching the Palatini limit. The presence of the scalaron extends the UV cutoff at vacuum of the original model except for the parameter space close to the Palatini limit. This UV-extension is expected to solve the strong coupling problem that may exist during (p)reheating in the absence of the scalaron., Comment: 32 pages, 4 figures, 3 appendices. Matched publication version

We study the evolution of magnetic fields coupled with chiral fermion asymmetry in the framework of chiral magnetohydrodynamics with zero initial total chirality. The initial magnetic field has a turbulent spectrum peaking at a certain characteristic scale and is fully helical with positive helicity. The initial chiral chemical potential is spatially uniform and negative. We consider two opposite cases where the ratio of the length scale of the chiral plasma instability (CPI) to the characteristic scale of the turbulence is smaller and larger than unity. These initial conditions might be realized in cosmological models such as certain types of axion inflation. The magnetic field and chiral chemical potential evolve with inverse cascading in such a way that the magnetic helicity and chirality cancel each other at all times. The CPI time scale is found to determine mainly the time when the magnetic helicity spectrum attains negative values at high wave numbers. The turnover time of the energy-carrying eddies, on the other hand, determines the time when the peak of the spectrum starts to shift to smaller wave numbers via an inverse cascade. The onset of helicity decay is determined by the time when the chiral magnetic effect becomes efficient at the peak of the initial magnetic energy spectrum. When spin flipping is important, the chiral chemical potential vanishes and the magnetic helicity becomes constant, which leads to a faster increase of the correlation length, as expected from magnetic helicity conservation. This also happens when the initial total chirality is imbalanced. Our findings have important implications for baryogenesis after axion inflation., Comment: 24 pages, 21 figures, 6 tables, corrected Fig.17, Phys. Rev. D, in press

We point out that there is a stable configuration of metal plates where the Casimir force is vanishing in axion electrodynamics. We consider a concrete setup involving Weyl semimetals, which hosts an axion-like effect on the electromagnetism, towards the measurement of the axionic effect on the Casimir force. Our setup realizes zero Casimir force between metals and may be useful for the search for new force mediated by light particles at the micrometer scale., Comment: 29 pages, 9 figures; to appear in PRD; typos fixed

CP violation and the violation of baryon-minus-lepton number B-L do not necessarily have to occur simultaneously in order to accomplish successful leptogenesis. Instead, it suffices if new CP-violating interactions at high energies result in primordial charge asymmetries, which are then reprocessed into a nonvanishing B-L asymmetry by right-handed neutrinos (RHNs) at lower energies. In this paper, we study this novel mechanism known as "wash-in leptogenesis", utilizing axion inflation as the source of high-scale CP violation. We specifically consider axion inflation coupled to the Standard Model hypercharge sector, which results in the dual production of hypermagnetic helicity and fermionic charge asymmetries. Although the survival of these charges is endangered by sphaleron processes, magnetic diffusion, and the chiral plasma instability, we find a large range of viable scenarios. We consistently account for RHN flavor effects and coherence among the Standard Model lepton flavors across a wide range of RHN masses. We find a lower bound of 10^(5...9) GeV on the mass of the lightest RHN involved in wash-in leptogenesis, depending on the onset of turbulence in the chiral plasma and the Hubble scale of inflation. Our model is representative of a broader class of new leptogenesis scenarios and suggests interesting observational signatures with regard to intergalactic magnetic fields, primordial black holes, and gravitational waves., Comment: 56 pages, 4 figures, 2 tables. v2: updated references, factor of 2 corrected in Eq. (3.8), matches version published in JHEP

In this paper, we investigate the thermalization of Hawking radiation from primordial black holes (PBHs) in the early Universe, taking into account the interference effect on thermalization of high energy particles, known as Landau-Pomeranchuk-Migdal (LPM) effect. Small PBHs with masses $ \lesssim 10^9 \, \mathrm{g} $ completely evaporate before the big bang nucleosynthesis (BBN). The Hawking radiation emitted from these PBHs heats up the ambient plasma with temperature lower than the Hawking temperature, which results in a non-trivial temperature profile around the PBHs, namely a hot spot surrounding a PBH with a broken power-law tail. We find that the hot spot has a core with a radius much larger than the black hole horizon and its highest temperature is independent of the initial mass of the PBH such as $2 \times 10^{9} \, {\rm GeV} \times (\alpha/0.1)^{19/3}$, where $\alpha$ generically represents the fine-structure constants. We also briefly discuss the implications of the existence of the hot spot for phenomenology., Comment: 20 pages, 4 figures. Coincides with published version

High-energy standard model (SM) particles in the early Universe are generated by the decay of heavy long-lived particles. The subsequent thermalization occurs through the splitting of high-energy primary particles into lower-energy daughters in primordial thermal plasma. The principal example of such processes is reheating after inflation caused by the decay of inflatons into SM particles. Understanding of the thermalization at reheating is extremely important as it reveals the origin of the hot Universe, and could open up new mechanisms for generating dark matter and/or baryon asymmetry. In this paper, we investigate the thermalization of high-energy SM particles in thermal plasma, taking into account the Landau--Pomeranchuk--Migdal effect in the leading-log approximation. The whole SM particle content and all the relevant SM interactions are included for the first time, i.e., the full gauge interactions of SU(3)$_c\times$SU(2)$_L\times$U(1)$_Y$ and the top Yukawa interaction. The distribution function of each SM species is computed both numerically and analytically. We have analytically obtained the distribution function of each SM species after the first few splittings. Furthermore, we demonstrate that, after a sufficient number of splittings, the particle distributions are asymptotic to certain values at low momentum, independent of the high-energy particles injected by inflaton decay. The results are useful to calculate the DM abundance produced during the pre-thermal phase. An example is provided to illustrate a way to calculate the DM abundance from the scattering between the thermal plasma and high-energy particles in the cascade., Comment: 41 pages, 7 figures; v2: minor comments added, published version; v3: numerical errors corrected (see the main text for detail)

A chiral chemical potential present in the early universe can source helical hypermagnetic fields through the chiral plasma instability. If these hypermagnetic fields survive until the electroweak phase transition, they source a contribution to the baryon asymmetry of the universe. In this letter, we demonstrate that lepton flavour asymmetries above $|\mu|/T \sim 9 \times 10^{-3}$ trigger this mechanism even for vanishing total lepton number. This excludes the possibility of such large lepton flavour asymmetries present at temperatures above $10^6$ GeV, setting a constraint which is about two orders of magnitude stronger than the current CMB and BBN limits., Comment: 4 pages, matches journal version

We develop the stochastic formalism for $\mathrm{U}(1)$ gauge fields that has the Chern-Simons coupling to a rolling pseudo-scalar field during inflation. The Langevin equations for the physical electromagnetic fields are derived and the analytic solutions are studied. Using numerical simulation we demonstrate that the electromagnetic fields averaged over the Hubble scale continuously change their direction and their amplitudes fluctuate around the analytically obtained expectation values. Though the isotropy is spontaneously broken by picking up a particular local Hubble patch, each Hubble patch is understood independent and the isotropy is conserved globally by averaging all the Hubble patches., Comment: 15pages, 4 figures, v2 matches the published version

The Maxwell equations imply that, under the background of non-zero $\boldsymbol{B}$, varying $\theta$ term produces $\boldsymbol{E} \cdot \boldsymbol{B}$. An interesting example is the Witten effect where a magnetic monopole becomes a dyon which, however, should disappear in the exact massless limit of the fermion. Underlying mechanism of this phenomenon has been understood by Callan by the presence of an effective axion-like degree of freedom around the monopole, which is roughly the phase of the fermions. The configuration of this axion cancels the effect of the $\theta$ term. Now, the chiral anomaly implies that non-vanishing $\boldsymbol{E} \cdot \boldsymbol{B}$ induces the chiral charge in the system. The question is whether the chiral charge is generated in the massless limit when we take into account the axion-like degree of freedom in the discussion. The discussion is relevant for the mechanism of baryogenesis under the background of time-dependent $\theta$. We solve the system of the massless QED with time dependent $\theta$ by reducing it to the two-dimensional QED. We demonstrate the occurrence of chiral charge generation in the background of static magnetic field for two cases: a magnetic monopole and a uniform magnetic flux. For the monopole case, the chiral charge comes out from the monopole while canceling the Witten effect. For the case of the uniform flux, on the other hand, the effect of the backreaction cannot be ignored, giving a more non-trivial time dependence. We also discuss their implications on baryogenesis., Comment: 33 pages, 2 figures

We consider the transfer of a U(1) charge density between Bose-Einstein condensates of complex scalar fields coupled to a thermal bath, focusing on the case of a homogeneous Affleck-Dine field transmitting the charge stored in its angular motion to an axion field. We demonstrate that in the absence of additional symmetries this charge transfer, aided by cosmic expansion as well as the thermal effective potential of the Affleck-Dine field, can be very efficient. The charge redistribution between the scalar fields becomes possible if the interactions with the thermal bath break the original U(1) x U(1) symmetry down to a single U(1) symmetry; the charge distribution between the two fields is then determined by minimizing the free energy. We discuss implications for cosmological setups involving complex scalars, with applications to axion dark matter, baryogenesis, kination domination, and gravitational wave production., Comment: 31 pages, 7 figures

Particle production induced by a time-dependent background is well understood as the projection of the time-evolved initial state onto a set of final states. While the asymptotic initial and final states are well defined in the usual way, the definition of particles and antiparticles at intermediate times in the presence of external fields is ambiguous. These external fields moreover induce divergences which require regularization. In this paper we clarify some subtleties in the computation of transient effects in physical quantities for fermions in a homogeneous axion background, including Schwinger production in background electromagnetic fields. The presence of the axion requires particular care as well as knowledge of the UV theory when regulating the theory and computing the vacuum contribution to the fermion energy., Comment: 34 pages, 6 figures

The axionic inflaton with the Chern-Simons coupling may generate U(1) gauge fields and charged particles simultaneously. In order to incorporate the backreaction from the charged particles on the gauge fields, we develop a procedure to obtain an equilibrium solution for the gauge fields by treating the induced current as effective electric and magnetic conductivities. Introducing mean field approximation, and numerically solving self-consistency equations, we find that the gauge field amplitudes are drastically suppressed. Interestingly, as the production becomes more efficient, the charged particles gain a larger part of the transferred energy from the inflaton and eventually dominate it. Our formalism offers a basis to connect this class of inflationary models to a rich phenomenology such as baryogenesis and magnetogenesis., Comment: 29 pages, 7 figures; v2: comparison to the previous works is added

Any field, even if it lives in a completely hidden sector, interacts with the visible sector at least via the gravitational interaction. In this paper, we show that a scalar field in such a hidden sector generically couples to the quadratic curvature via dimension five operators, i.e., $\phi R^2$, $\phi R^{\mu\nu} R_{\mu\nu}$, $\phi R_{\mu\nu\rho\sigma} R^{\mu\nu\rho\sigma}$, $\phi R_{\mu\nu\rho\sigma} \tilde R^{\mu\nu\rho\sigma}$, because they can emerge if there exist particles heavier than it. We derive these scalar couplings to the quadratic curvature by integrating out heavy particles in a systematic manner. Such couplings are of phenomenological interest since some of them induce the scalar decay into the graviton pair. We point out that the decay of a scalar field can produce a substantial amount of the stochastic cosmic graviton background at high frequency since the suppression scale of these operators is given by the mass of heavy particles not by the Planck scale. The resultant graviton spectrum is computed in some concrete models., Comment: 30 pages, 2 figures; to appear in JHEP

Charged-lepton flavor violation (CLFV) is a smoking-gun signature of physics beyond the Standard Model. The discovery of CLFV in upcoming experiments would indicate that CLFV processes must have been efficient in the early Universe at relatively low temperatures. In this letter, we point out that such efficient CLFV interactions open up new ways of creating the baryon asymmetry of the Universe. First, we quote the two-loop corrections from charged-lepton Yukawa interactions to the chemical transport in the Standard Model plasma, which imply that nonzero lepton flavor asymmetries summing up to $B-L = 0$ are enough to generate the baryon asymmetry. Then, we describe two scenarios of what we call {\it leptoflavorgenesis}, where efficient CLFV processes are responsible for the generation of primordial lepton flavor asymmetries that are subsequently converted to a baryon asymmetry by weak sphaleron processes. Here, the conversion factor from lepton flavor asymmetry to baryon asymmetry is suppressed by charged-lepton Yukawa couplings squared, which provides a natural explanation for the smallness of the observed baryon-to-photon ratio., Comment: 9 pages, 2 figures; v2: added missing term in transport eq., typos corrected

We study SU($N$) gauge fields that couple to the inflaton through the Chern-Simons term. We provide a general procedure to construct homogeneous, isotropic, and attractor solutions of the gauge fields during inflation. The gauge fields develop various VEVs corresponding to different spontaneous symmetry breaking patterns of SU($N$) where embedded SU($2$) subgroups are broken with the spatial rotation SO($3$) symmetry. As specific examples, we construct the stable solutions for $N = 3$ and $4$. We also numerically solve the gauge field dynamics and confirm that our analytic solutions are complete and attractor. It is straightforward to apply our procedure to the other simple Lie groups., Comment: 8 pages, 6 figures

We perform a complete next-to-leading order calculation of the non-Abelian electric field correlator in a SU($N_c$) plasma, which encodes properties of the plasma relevant for heavy particle bound state formation and dissociation, and is different from the correlator for the heavy quark diffusion coefficient. The calculation is carried out in the real-time formalism of thermal field theory and includes both vacuum and finite temperature contributions. By working in the $R_\xi$ gauge, we explicitly show the results are gauge independent, infrared and collinear safe. The renormalization group equation of this electric field correlator is determined by that of the strong coupling constant. Our next-to-leading order calculation can be directly applied to any dipole singlet-adjoint transition of heavy particle pairs. For example, it can be used to describe dissociation and (re)generation of heavy quarkonia inside the quark-gluon plasma well below the melting temperature, as well as heavy dark matter pairs (or charged co-annihilating partners) in the early universe., Comment: 86 pages, 13 figures

We point out an enhancement of the pair production rate of charged fermions in a strong electric field in the presence of time dependent classical axion-like background field, which we call axion assisted Schwinger effect. While the standard Schwinger production rate is proportional to $\exp(-\pi(m^2+p_T^2 )/E)$, with $m$ and $p_T$ denoting the fermion mass and its momentum transverse to the electric field $E$, the axion assisted Schwinger effect can be enhanced at large momenta to $\exp(-\pi m^2/E)$. The origin of this enhancement is a coupling between the fermion spin and its momentum, induced by the axion velocity. As a non-trivial validation of our result, we show its invariance under field redefinitions associated with a chiral rotation and successfully reproduce the chiral anomaly equation in the presence of helical electric and magnetic fields. We comment on implications of this result for axion cosmology, focussing on axion inflation and axion dark matter detection., Comment: 18 pages + appendices, 5 figures

We present a leptogenesis mechanism based on the standard type-I seesaw model that successfully operates at right-handed-neutrino masses as low as a few 100 TeV. This mechanism, which we dub "wash-in leptogenesis", does not require any CP violation in the neutrino sector and can be implemented even in the regime of strong wash-out. The key idea behind wash-in leptogenesis is to generalize standard freeze-out leptogenesis to a nonminimal cosmological background in which the chemical potentials of all particles not in chemical equilibrium at the temperature of leptogenesis are allowed to take arbitrary values. This sets the stage for building a plethora of new baryogenesis models where chemical potentials generated at high temperatures are reprocessed to generate a nonvanishing B-L asymmetry at low temperatures. As concrete examples, we discuss wash-in leptogenesis after axion inflation and in the context of grand unification., Comment: 5 pages + references and appendix, 1 figure, 2 tables. v2: matches version published in PRL

We discuss a possible connection between the recent NANOGrav results and the primordial black holes (PBHs) for the LIGO-Virgo events. In particular, we focus on the axion-like curvaton model, which provides a sizable amount of PBHs and GWs induced by scalar perturbations around the NANOGrav frequency range. The inevitable non-Gaussianity of this model suppresses the induced GWs associated with PBHs for the LIGO-Virgo events to be compatible with the NANOGrav results. We show that the axion-like curvaton model can account for PBHs for the LIGO-Virgo events and the NANOGrav results simultaneously., Comment: 6 pages, 2 figures, v2: version published in PRL, minor revision

We derive one- and two-loop renormalization group equations (RGEs) of Higgs-$R^2$ inflation. This model has a non-minimal coupling between the Higgs and the Ricci scalar and a Ricci scalar squared term on top of the standard model. The RGEs derived in this paper are valid as long as the energy scale of interest (in the Einstein frame) is below the Planck scale. We also discuss implications to the inflationary predictions and the electroweak vacuum metastability., Comment: 35 pages, 1 figure; v2: references added, version accepted by JHEP

Axion-like particles can source the baryon asymmetry of our Universe through spontaneous baryogenesis. Here we clarify that this is a generic outcome for essentially any coupling of an axion-like particle to the Standard Model, requiring only a non-zero velocity of the classical axion field while baryon or lepton number violating interactions are present in thermal bath. In particular, coupling the axions only to gluons is sufficient to generate a baryon asymmetry in the presence of electroweak sphalerons or the Weinberg operator. Deriving the transport equation for an arbitrary set of couplings of the axion-like particle, we provide a general framework in which these results can be obtained immediately. If all the operators involved are efficient, it suffices to solve an algebraic equation to obtain the final asymmetries. Otherwise one needs to solve a simple set of differential equations. This formalism clarifies some theoretical subtleties such as redundancies in the axion coupling to the Standard Model particles associated with a field rotation. We demonstrate how our formalism automatically evades potential pitfalls in the calculation of the final baryon asymmetry., Comment: 47 pages, 6 figures; v2: references added, published version; v3: a few typos and sign errors fixed

We discuss the footprint of evaporation of primordial black holes (PBHs) on stochastic gravitational waves (GWs) induced by scalar perturbations. We consider the case where PBHs once dominated the Universe but eventually evaporated before the big bang nucleosynthesis. The reheating through the PBH evaporation could end with a sudden change in the equation of state of the Universe compared to the conventional reheating caused by particle decay. We show that this "sudden reheating" by the PBH evaporation enhances the induced GWs, whose amount depends on the length of the PBH-dominated era and the width of the PBH mass function. We explore the possibility to constrain the primordial abundance of the evaporating PBHs by observing the induced GWs. We find that the abundance parameter $\beta \gtrsim 10^{-5} \text{ - }10^{-8}$ for $\mathcal{O}(10^3 \text{ - } 10^5) \, \text{g}$ PBHs can be constrained by future GW observations if the width of the mass function is smaller than about a hundredth of the mass., Comment: 24 pages, 11 figures, v3: acknowledgment added

We point out that a model with scalar fields with a large nonminimal coupling to the Ricci scalar, such as Higgs inflation, can be regarded as a nonlinear sigma model (NLSM). With the inclusion of not only the scalar fields but also the conformal mode of the metric, our definition of the target space of the NLSM is invariant under the frame transformation. We show that the $\sigma$-meson that linearizes this NLSM to be a linear sigma model (LSM) corresponds to the scalaron, the degree of freedom associated to the $R^2$ term in the Jordan frame. We demonstrate that quantum corrections inevitably induce this $\sigma$-meson in the large-$N$ limit, thus providing a frame independent picture for the emergence of the scalaron. The resultant LSM only involves renormalizable interactions and hence its perturbative unitarity holds up to the Planck scale unless it hits a Landau pole, which is in agreement with the renormalizability of quadratic gravity., Comment: 18 pages + appendices, 1 figures; v2: references added; v3: explanation clarified, published version; v4: one reference added

The formation of meta-stable dark matter bound states in coannihilating scenarios could efficiently occur through the scattering with a variety of Standard Model bath particles, where light bosons during the electroweak cross over or even massless photons and gluons are exchanged in the t-channel. The amplitudes for those higher-order processes, however, are divergent in the collinear direction of the in- and out-going bath particles if the mediator is massless. To address the issue of collinear divergences, we derive the bound-state formation collision term in the framework of non-equilibrium quantum field theory. The main result is an expression for a more general cross section, which allows to compute higher-order bound-state formation processes inside the primordial plasma background in a comprehensive manner. Based on this result, we show that next-to-leading order contributions, including the bath-particle scattering, are i) collinear finite and ii) generically dominate over the on-shell emission for temperatures larger than the absolute value of the binding energy. Based on a simplified model, we demonstrate that the impact of these new effects on the thermal relic abundance is significant enough to make it worthwhile to study more realistic coannihilation scenarios., Comment: 38 pages, 20 figures

The thermal decoupling description of dark matter (DM) and co-annihilating partners is reconsidered. If DM is realized at around the TeV-mass region or above, even the heaviest electroweak force carriers could act as long-range forces, leading to the existence of meta-stable DM bound states. The formation and subsequent decay of the latter further deplete the relic density during the freeze-out process on top of the Sommerfeld enhancement, allowing for larger DM masses. While so far the bound-state formation was described via the emission of an on-shell mediator ($W^{\pm}$, $Z$, $H$, $g$, photon or exotic), we point out that this particular process does not have to be the dominant scattering-bound state conversion channel in general. If the mediator is coupled in a direct way to any relativistic species present in the Early Universe, the bound-state formation can efficiently occur through particle scattering, where a mediator is exchanged virtually. To demonstrate that such a virtually stimulated conversion process can dominate the on-shell emission even for all temperatures, we analyze a simplified model where DM is coupled to only one relativistic species in the primordial plasma through an electroweak-scale mediator. We find that the bound-state formation cross section via particle scattering can exceed the on-shell emission by up to several orders of magnitude., Comment: 9 pages, 2 figures

Particle production in strong electromagnetic fields is a recurring theme in solid state physics, heavy ion collisions, early universe cosmology and formal quantum field theory. In this paper we discuss the Dirac equation in a background of parallel electric and magnetic fields. We review the Schwinger particle production rate, clarify the emergence of the chiral anomaly equation and compute the induced current of charged fermions. We distinguish the contributions from non-perturbative particle production, from the running of the gauge coupling constant and from non-linearities in the effective QED Lagrangian, and clarify how these contributions arise within a single framework. We apply these results to axion inflation. A Chern-Simons coupling between the pseudoscalar particle driving cosmic inflaton and an abelian gauge group induces a dual production of gauge fields and charged fermions. We show that the resulting scalar and gravitational wave power spectra strongly depend on the fermion mass., Comment: 45 pages, 9 figures; v2: typos fixed, published version

The coupling of an axion-like particle driving inflation to the Standard Model particle content through a Chern-Simons term generically sources a dual production of massless helical gauge fields and chiral fermions. We demonstrate that the interplay of these two components results in a highly predictive baryogenesis model, which requires no further ingredients beyond the Standard Model. If the helicity stored in the hyper magnetic field and the effective chemical potential induced by the chiral fermion production are large enough to avoid magnetic diffusion from the thermal plasma but small enough to sufficiently delay the chiral plasma instability, then the non-vanishing helicity survives until the electroweak phase transition and sources a net baryon asymmetry which is in excellent agreement with the observed value. If any of these two conditions is violated, the final baryon asymmetry vanishes. The observed baryon asymmetry can be reproduced if the energy scale of inflation is around $H_\text{inf} \sim 10^{10}$ - $10^{12}$ GeV with a moderate dependence on inflation model parameters., Comment: 19 pages, 6 figures; v2: published version

We revisit the non-thermal dark matter (DM) production during the thermalization and reheating era after inflation. The decay of inflaton produces high-energy particles that are thermalized to complete the reheating of the Universe. Before the thermalization is completed, DM can be produced from a collision between the high-energy particles and/or the ambient plasma. We calculate the DM abundance produced from these processes for the case where the cross section of the DM production is proportional to the $n$-th power of the center of mass energy. We find that the collision between the high-energy particles is almost always dominant for $n \gtrsim 4$ while it is subdominant for $n \lesssim 2$. The production from the ambient plasma is dominant when $n \lesssim 3$ and the reheating temperature is of the order of or larger than the DM mass. The production from a collision between the high-energy particle and the ambient plasma is important for $n \lesssim 2$ and the reheating temperature is much lower than the DM mass., Comment: 11 pages, 3 figures; v2: footnote added, error in Eq. (28) corrected, conclusions unchanged

We study the production of chiral fermions in a background of a strong non-abelian gauge field with a non-vanishing Chern-Pontryagin density. We discuss both pair production analogous to the Schwinger effect as well as asymmetric production through the chiral anomaly, sourced by the Chern-Pontryagin density. In abelian gauge theories one may nicely understand these processes by considering that the fermion dispersion relation forms discrete Landau levels. Here we extend this analysis to a non-abelian gauge theory, considering an intrinsically non-abelian isotropic and homogeneous SU(2) gauge field background with a non-vanishing Chern-Pontryagin density. We show that the asymmetric fermion production, together with a non-trivial vacuum contribution, correctly reproduces the chiral anomaly. This indicates that the usual vacuum subtraction scheme, imposing normal ordering, fails in this case. As a concrete example of this gauge field background, we consider chromo-natural inflation. Applying our analysis to this particular model, we compute the backreaction of the generated fermions on the gauge field background. This backreaction receives contributions both from the vacuum through a Coleman-Weinberg-type correction and from the fermion excitations through an induced current., Comment: 27 pages + appendices, 2 figures; v2: published version

Traditional computations of the dark matter (DM) relic abundance, for models where attractive self-interactions are mediated by light force-carriers and bound states exist, rely on the solution of a coupled system of classical on-shell Boltzmann equations. This idealized description misses important thermal effects caused by the tight coupling among force-carriers and other charged relativistic species. We develop for the first time a comprehensive ab-initio derivation for the description of DM long-range interactions in the presence of a hot and dense plasma background directly from non-equilibrium quantum field theory. Most importantly, the scattering and bound states get strongly mixed in the thermal plasma environment, representing a characteristic difference from a pure vacuum theory computation. The main result of this work is a novel differential equation for the DM number density, written down in a form which is manifestly independent under the choice of what one would interpret as a bound or a scattering state at finite temperature. The collision term, unifying the description of annihilation and bound state decay, turns out to have in general a non-quadratic dependence on the DM number density. This generalizes the form of the conventional Lee-Weinberg equation which is typically adopted to describe the freeze-out process. We prove that our general number density equation is consistent with previous literature results under certain limits., Comment: 46 pages, 10 figures

Coherent oscillation of axions or axion-like particles may give rise to long-lived clumps, called axion stars, because of the attractive gravitational force or its self-interaction. Such a kind of configuration has been extensively studied in the context of oscillons without the effect of gravity, and its stability can be understood by an approximate conservation of particle number in a non-relativistic effective field theory (EFT). We extend this analysis to the case with gravity to discuss the longevity of axion stars and clarify the EFT expansion scheme in terms of gradient energy and Newton's constant. Our EFT is useful to calculate the axion star configuration and its classical lifetime without any ad hoc assumption. In addition, we derive a simple stability condition against small perturbations. Finally, we discuss the consistency of other non-relativistic effective field theories proposed in the literature., Comment: 37 pages, 3 figures

We study the dual production of helical Abelian gauge fields and chiral fermions through the Chern-Simons (CS) coupling with a pseudo-scalar inflaton in the presence of a chiral anomaly. Through the CS term, the motion of the inflaton induces a tachyonic instability for one of the two helicities of the gauge field. We show that the resulting helical gauge field necessarily leads to the production of chiral fermions by deforming their Fermi sphere into discrete Landau levels. The population of the lowest Landau level leads to a chiral asymmetry as inferred from the chiral anomaly, while the higher levels are populated symmetrically through pair production. From the backreaction of the fermions on the gauge field production we derive a conservative but stringent upper bound on the magnitude of the gauge fields. Consequently, we find that the scalar perturbations sourced by these helical gauge fields, responsible for enhanced structure formation on small scales, get reduced significantly. We also discuss the fate of the primordial chiral asymmetry and of the helical gauge fields after inflation, and show that the instability in the chiral plasma tends to erase these primordial asymmetries. This result may impact scenarios where the baryon asymmetry of the Universe is connected to primordial magnetic fields., Comment: 46 pages, 11 figures; v2: reference added, published version

We revise primordial black hole (PBH) formation in the axion-like curvaton model and investigate whether PBHs formed in this model can be the origin of the gravtitational wave (GW) signals detected by the Advanced LIGO. In this model, small-scale curvature perturbations with large amplitude are generated, which is essential for PBH formation. On the other hand, large curvature perturbations also become a source of primordial GWs by their second-order effects. Severe constraints are imposed on such GWs by pulsar timing array (PTA) experiments. We also check the consistency of the model with these constraints. In this analysis, it is important to take into account the effect of non-Gaussianity, which is generated easily in the curvaton model. We see that, if there are non-Gaussianities, the fixed amount of PBHs can be produced with a smaller amplitude of the primordial power spectrum., Comment: 25 pages, 8 figures

Primordial Black Hole (PBH) is one of the leading non-particle candidates for dark matter (DM). Although several observations severely constrain the amount of PBHs, it is recently pointed out that there is an uncertainty on the microlensing constraints below $\sim 10^{-10} M_\odot$ which was ignored originally but may weaken the constraints significantly. In this paper, facing this uncertainty, we investigate the possibility that PBHs can make up all DM in a broad mass spectrum. Moreover, we propose a concrete inflation model which can simultaneously produce PBHs for all DM in a broad mass spectrum around $\mathcal O(10^{-13}) M_\odot$ and PBHs for LIGO events in a sharp mass spectrum at $\mathcal O(10) M_\odot$., Comment: 11 pages, 5 figures, v2: published version

LIGO-Virgo collaboration has found black holes as heavy as $M \sim 30M_\odot$ through the detections of the gravitational waves emitted during their mergers. Primordial black holes (PBHs) produced by inflation could be an origin of such events. While it is tempting to presume that these PBHs constitute all Dark Matter (DM), there exists a number of constraints for PBHs with $\mathcal{O} (10) M_\odot$ which contradict with the idea of PBHs as all DM. Also, it is known that weakly interacting massive particle (WIMP) that is a common DM candidate is almost impossible to coexist with PBHs. These observations motivate us to pursue another candidate of DM. In this paper, we assume that the string axion solving the strong CP problem makes up all DM, and discuss the coexistence of string axion DM and inflationary PBHs for LIGO events., Comment: 12 pages, 8 figures; v2: published version

We study the stability of the electroweak vacuum in low-scale inflation models whose Hubble parameter is much smaller than the instability scale of the Higgs potential. In general, couplings between the inflaton and Higgs are present, and hence we study effects of these couplings during and after inflation. We derive constraints on the couplings between the inflaton and Higgs by requiring that they do not lead to catastrophic electroweak vacuum decay, in particular, via resonant production of the Higgs particles., Comment: 11 pages, 4 figures

False vacuum states are metastable in quantum field theories, and true vacuum bubbles can be nucleated due to the quantum tunneling effect. It was recently suggested that an evaporating black hole (BH) can be a catalyst of bubble nucleations and dramatically shortens the lifetime of the false vacuum. In particular, in the context of the Standard Model valid up to a certain energy scale, even a single evaporating BH may spoil the successful cosmology by inducing the decay of our electroweak vacuum. In this paper, we reinterpret catalyzed vacuum decay by BHs, using an effective action for a thin-wall bubble around a BH to clarify the meaning of bounce solutions. We calculate bounce solutions in the limit of a flat spacetime and in the limit of negligible backreaction to the metric, where it is much easier to understand the physical meaning, and compare these results with the full calculations done in the literature. As a result, we give a physical interpretation of the enhancement factor: it is nothing but the probability of producing states with a finite energy. This makes it clear that all the other states such as plasma should also be generated through the same mechanism, and calls for finite-density corrections to the tunneling rate which tend to stabilize the false vacuum. We also clarify that the dominant process is always consistent with the periodicity indicated by the BH Hawking temperature after summing over all possible remnant BH masses or bubble energies, although the periodicity of each bounce solution as a function of a remnant BH can be completely different from the inverse temperature of the system as mentioned in the previous literature., Comment: 34 pages, 13 figures (v2: published version, minor revisions of the text, conclusions remain unchanged)

We study non-thermal gravitino production in the minimal supergravity inflation. In this minimal model utilizing orthogonal nilpotent superfields, the particle spectrum includes only graviton, gravitino, inflaton, and goldstino. We find that a substantial fraction of the cosmic energy density can be transferred to the longitudinal gravitino due to non-trivial change of its sound speed. This implies either a breakdown of the effective theory during reheating or a serious gravitino problem., Comment: 18 pages; published version, references added, minor corrections

Following a new microlensing constraint on primordial black holes (PBHs) with $\sim10^{20}$--$10^{28}\,\mathrm{g}$~[1], we revisit the idea of PBH as all Dark Matter (DM). We have shown that the updated observational constraints suggest the viable mass function for PBHs as all DM to have a peak at $\simeq 10^{20}\,\mathrm{g}$ with a small width $\sigma \lesssim 0.1$, by imposing observational constraints on an extended mass function in a proper way. We have also provided an inflation model that successfully generates PBHs as all DM fulfilling this requirement., Comment: 7 pages, 3 figures