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We develop a C++ package of the STOchastic LAttice Simulation (STOLAS) of cosmic inflation. It performs the numerical lattice simulation in the application of the stochastic-$\delta N$ formalism. STOLAS can directly compute the three-dimensional map of the observable curvature perturbation without estimating its statistical properties. In its application to two toy models of inflation, chaotic inflation and Starobinsky's linear-potential inflation, we confirm that STOLAS is well-consistent with the standard perturbation theory. Furthermore, by introducing the importance sampling technique, we have success in numerically sampling the current abundance of primordial black holes in a non-perturbative way. The package is available at https://github.com/STOchasticLAtticeSimulation/STOLAS_dist., Comment: 31 pages, 10 figures

We revisit the hybrid inflation model within the framework of the Grand Unified Theory (GUT), focusing on cases where the waterfall phase transition extends over several e-foldings to dilute monopoles. Considering the stochastic effects of quantum fluctuations, we demonstrate that the waterfall fields (i.e., GUT Higgs) maintain a nonzero vacuum expectation value around the waterfall phase transition. By accurately accounting for the number of degrees of freedom of the GUT Higgs field, we establish that these fluctuations can produce observable gravitational waves without leading to an overproduction of primordial black holes. The amplitude of these gravitational waves is inversely proportional to the degrees of freedom of the waterfall fields, thereby providing a unique method to probe the representation of the GUT Higgs., Comment: 8 pages, 1 figure

Supposing the Laser Interferometer Space Antenna (LISA) gravitational wave (GW) detector, we exhibit the detectability of a hypothetical smooth crossover in the early universe beyond the Standard Model of particle physics through the scalar-induced gravitational wave (SIGW) in terms of the Fisher forecast. A crossover at $\sim100\,\mathrm{TeV}$ can leave a signal on the GW spectrum in the $\sim\mathrm{mHz}$ frequency range, the sweet spot of the LISA sensitivity. These possibilities are also interesting in the primordial black hole (PBH) context as the associated PBH mass $\sim10^{22}\,\mathrm{g}$ lies at the window to explain the whole dark matter. We found that the properties of the crossover can be well determined if the power spectrum of primordial scalar perturbations are as large as $\sim5\times10^{-4}$ on the corresponding scale $\sim10^{12}\,\mathrm{Mpc^{-1}}$., Comment: 8 pages, 6 figures

The recent result of Dark Energy Spectroscopic Instrument (DESI) in combination with other cosmological data shows evidence of the evolving dark energy parameterized by $w_0w_a$CDM model. We interpret this result in terms of a quintessential scalar field and demonstrate that it can explain the DESI result even though it becomes eventually phantom in the past. Relaxing the assumption on the functional form of the equation-of-state parameter $w=w(a)$, we also discuss a more realistic quintessential model. The implications of the DESI result for Swampland conjectures, cosmic birefringence, and the fate of the Universe are discussed as well., Comment: 8 pages, 6 figures; v2: references and discussions added; v3 matches the accepted version in PRD letter; v4: references added

The subsolar mass primordial black hole (PBH) attracts attention as robust evidence of its primordial origin against the astrophysical black hole. Not only with themselves, PBHs can also form binaries with ordinary astrophysical objects, catching them by gravitational wave (GW) bremsstrahlung. We discuss the detectability of the inspiral GWs from binaries consisting of a PBH and a white dwarf (WD) by using space-borne gravitational wave interferometers like DECIGO. The conservative assessment shows the expected event number in three years by DECIGO is $\mathcal{O}(10^{-6})$ for $M_\mathrm{PBH} \sim 0.1M_\odot$. Possible enhancement mechanisms of WD-PBH binary formation may amplify this event rate. We discuss how large enhancement associated with WDs is required to detect WD-PBH merger events without violating the existing constraints on the PBH-PBH merger by the ground-based detector., Comment: 13 pages, 10 figures

Gravitational waves (GWs) induced by primordial fluctuations can be affected by the modification of the sound speed $c^2_{\rm s}$ and the equation of state parameter $w$ once the curvature fluctuations reenter the cosmological horizon. That softening can also significantly boost the production of Primordial Black Holes (PBHs) at the mass scale where the softening arises. In this work, we consider a hypothetical softening of $w$ and $c^2_{\rm s}$ caused by a smooth crossover beyond Standard Model theories, for what we numerically compute the secondary induced GW considering the case of a flat scale-invariant power spectrum. We find that if the amplitude of the power spectrum is sufficiently large, the characteristic feature of the GW signal caused by the smooth crossover can be detected by future space-based gravitational wave interferometers and differentiated from the pure radiation case. At the same time, depending on the mass scale where the crossover occurs, such a scenario can have compatibility with PBHs being all the dark matter when $\mathcal{A} \sim \mathcal{O}(10^{-3})$, with a mass function very sharply peaked around the horizon mass scale of the minimum of the sound speed. Our results show that the GW signal can be used to resolve the existing degeneracy of sharply peaked mass function caused by peaked power spectrums and broad ones in the presence of softenings of $w$ and $c^2_{\rm s}$., Comment: 15 pages, 8 figures. v4: figures updated with a new case of smooth crossover. Accepted for publication in PRD. Code for the numerical computation of the induced GWs is available at https://github.com/albert-escriva/IGWsfSC.git

We study the cancellation of quantum corrections on the superhorizon curvature perturbations from subhorizon physics beyond the single-clock inflation from the viewpoint of the cosmological soft theorem. As an example, we focus on the transient ultra-slow-roll inflation scenario and compute the one-loop quantum corrections to the power spectrum of curvature perturbations taking into account nontrivial surface terms in the action. We find that Maldacena's consistency relation is satisfied and guarantees the cancellation of contributions from the short-scale modes. As a corollary, primordial black hole production in single-field inflation scenarios is not excluded by perturbativity breakdown even for the sharp transition case in contrast to some recent claims in the literature. We also comment on the relation between the tadpole diagram in the in-in formalism and the shift of the elapsed time in the stochastic-$\delta N$ formalism. We find our argument is not directly generalisable to the tensor perturbations., Comment: 23 pages, 8 figures; v2 matches the accepted version in JHEP

The evidence of the nano-Hertz stochastic gravitational wave (GW) background is reported by multiple pulsar timing array collaborations. While a prominent candidate of the origin is astrophysical from supermassive black hole binaries, alternative models involving GWs induced by primordial curvature perturbations can explain the inferred GW spectrum. Serendipitously, the nano-Hertz range coincides with the Hubble scale during the cosmological quantum chromodynamics (QCD) phase transition. The influence of the QCD phase transition can modify the spectrum of induced GWs within the nano-Hertz frequency range, necessitating careful analysis. We estimate GWs induced by power-law power spectra of primordial curvature perturbations taking account of the QCD phase transition. Then we translate the implication of the NANOGrav data into the constraint on the power spectrum of the primordial curvature perturbation, which suggests one would underestimate the amplitude by about $25\%$ and the spectral index by up to $10\%$ if neglecting the QCD effect., Comment: 8 pages, 7 figures; v3 matches the published version in PRD Letter, v2 updates the main figure (Fig. 7)

We show that a hybrid inflation model with multiple waterfall fields can result in the formation of primordial black hole (PBH) with an astrophysical size, by using an advanced algorithm to follow the stochastic dynamics of the waterfall fields. This is in contrast to the case with a single waterfall field, where the wavelength of density perturbations is usually too short to form PBHs of the astrophysical scale (or otherwise PBH are overproduced and the model is ruled out) unless the inflaton potential is tuned. In particular, we demonstrate that PBHs with masses of order $10^{20}\, {\rm g}$ can form after hybrid inflation consistently with other cosmological observations if the number of waterfall fields is about 5 for the case of instantaneous reheating. Observable gravitational waves are produced from the second-order effect of large curvature perturbations as well as from the dynamics of texture or global defects that form after the waterfall phase transition., Comment: 23 pages, 5 figures

We revisit the scenario of primordial black hole (PBH) formation from large curvature perturbations generated during the waterfall phase transition in hybrid inflation models. In a minimal setup considered in the literature, the mass and abundance of PBHs are correlated and astrophysical size PBHs tend to be overproduced. This is because a longer length scale for curvature perturbations (or a larger PBH mass) requires a longer waterfall regime with a flatter potential, which results in overproduction of curvature perturbations. However, in this paper, we discuss that the higher-dimensional terms for the inflaton potential affect the dynamics during the waterfall phase transition and show that astrophysical size PHBs of order $10^{17\text{--}23} \, {\rm g}$ (which can explain the whole dark matter) can form in some parameter space consistently with any existing constraints. The scenario can be tested by observing the induced gravitational waves from scalar perturbations by future gravitational wave experiments, such as LISA., Comment: 14 pages, 8 figures; v2: minor corrections, figures updated, conclusions unchanged; v3: accepted version, minor corrections

In canonical single-field inflation, the production of primordial black holes (PBH) requires a transient violation of the slow-roll condition. The transient ultra slow-roll inflation is an example of such scenarios, and more generally, one can consider the transient constant-roll inflation. We investigate the squeezed bispectrum in the transient constant-roll inflation and find that Maldacena's consistency relation holds for a sufficiently long-wavelength mode, whereas it is violated for modes around the peak scale for the non-attractor case. We also demonstrate how the one-loop corrections are modified compared to the case of the transient ultra slow-roll inflation, focusing on representative one-loop terms originating from a time derivative of the second slow-roll parameter in the cubic action. We find that the perturbativity requirement on those terms does not rule out the production of PBH from the transient constant-roll inflation. Therefore, it is a simple counterexample of the recently claimed no-go theorem of PBH production from single-field inflation., Comment: 29 pages, 15 figures; v2 matches the published version in JCAP

Aspects of primordial black holes, i.e. black holes formed in the early Universe, are reviewed. Special emphasis is put on their formation, their r{\^o}le as dark matter candidates and their manifold signatures, particularly through gravitational waves., Comment: 246 pages, 62 figures, 824 references; v4: major extension and revision to match published version; to appear as invited book chapter in "Listening to the dark Universe: black holes in the era of gravitational-wave astronomy"

Primordial black holes (PBHs) whose masses are in $\sim[10^{-15}M_\odot,10^{-11}M_{\odot}]$ have been extensively studied as a candidate of whole dark matter (DM). One of the probes to test such a PBH-DM scenario is scalar-induced stochastic gravitational waves (GWs) accompanied with the enhanced primordial fluctuations to form the PBHs with frequency peaked in the mHz band being targeted by the LISA mission. In order to utilize the stochastic GWs for checking the PBH-DM scenario, it needs to exactly relate the PBH abundance and the amplitude of the GWs spectrum. Recently in Kitajima et al., the impact of the non-Gaussianity of the enhanced primordial curvature perturbations on the PBH abundance has been investigated based on the peak theory, and they found that a specific non-Gaussian feature called the exponential tail significantly increases the PBH abundance compared with the Gaussian case. In this work, we investigate the spectrum of the induced stochastic GWs associated with PBH DM in the exponential-tail case. In order to take into account the non-Gaussianity properly, we employ the diagrammatic approach for the calculation of the spectrum. We find that the amplitude of the stochastic GW spectrum is slightly lower than the one for the Gaussian case, but it can still be detectable with the LISA sensitivity. We also find that the non-Gaussian contribution can appear on the high-frequency side through their complicated momentum configurations. Although this feature emerges under the LISA sensitivity, it might be possible to obtain information about the non-Gaussianity from GW observation with a deeper sensitivity such as the DECIGO mission., Comment: 33 pages, 19 figures

We propose an extension of the Higgs inflation to the hybrid metric-Palatini gravity, where we introduce non-minimal couplings between Higgs and both the metric-type and the Palatini-type Ricci scalars. We study the inflationary phenomenology of our model and find that slow-roll inflation can be realized in the large-field regime, giving the observationally favored predictions. In particular, the scalar spectral index exhibits an attractor behavior to $n_{\mathrm{s}}\sim 0.964$, while the tensor-to-scalar ratio can take an arbitrary value depending on the non-minimal coupling parameters, with the metric-Higgs limit $r\sim10^{-3}$ being the maximum. We also investigate the unitarity property of our model. As the ultraviolet (UV) cutoff as a low-energy effective field theory (EFT) of this model is significantly lower than the Planck scale due to a strong curvature of field-space, we consider a possible candidate of UV-extended theories with an additional scalar field introduced so as to flatten the field-space in five-dimension. While the field-space can be flatten completely and this approach can lead to a weakly-coupled EFT, we gain an implication that Planck-scale EFT can be only realized in the limit of metric-Higgs inflation. We also discuss generalizations of the model up to mass-dimension four., Comment: 18 pages, 1 figure; v2 matches the published version in JCAP

We investigate the probability distribution of the effective inspiral spin, the mass ratio, and the chirp mass of primordial black hole (PBH) binaries, incorporating the effect of the critical phenomena of gravitational collapse. As a leading order estimation, each binary is assumed to be formed from two PBHs that are randomly chosen according to the probability distribution of single PBHs. We find that, although the critical phenomena can lead to large spins on the low-mass tail, the effective inspiral spin of the binary is statistically very small, $\sqrt{\langle\chi_{\mathrm{eff}}^2\rangle}=8.41\times10^{-4}$. We also see that there is almost no anti-correlation between the effective inspiral spin and the mass ratio, which can be inferred from observations., Comment: 13 pages, 5 figures

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 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

In this work, we have performed numerical simulations of primordial black hole (PBH) formation in the Friedman-Lema\^itre-Robertson-Walker universe filled by radiation fluid, introducing the local-type non-Gaussianity to the primordial curvature fluctuation. We have compared the numerical results from simulations with previous analytical estimations on the threshold value for PBH formation done in the previous paper arXiv:2109.00791, particularly for negative values of the non-linearity parameter $f_{\rm NL}$. Our numerical results show the existence of PBH formation of (the so-called) type I also in the case $f_{\rm NL} \lesssim -0.336$, which was not found in the previous analytical expectations using the critical averaged compaction function. In particular, although the universal value for the averaged critical compaction function $\bar{\mathcal{C}}_{c}=2/5$ found previously in the literature is not satisfied for all the profiles considered in this work, an alternative direct analytical estimate has been found to be roughly accurate to estimate the thresholds, which gives the value of the critical averaged density with a few $\%$ deviation from the numerical one for $f_{\rm NL}\gtrsim -1$., Comment: 20 pages, 9 figures. v2: minor changes. Accepted for publication in JCAP

We present a generic framework to compute the one-point statistics of cosmological perturbations, when coarse-grained at an arbitrary scale $R$, in the presence of quantum diffusion. Making use of the stochastic-$\delta N$ formalism, we show how it can be related to the statistics of the amount of expansion realised until the scale $R$ crosses out the Hubble radius. This leads us to explicit formulae for the probability density function (PDF) of the curvature perturbation, the comoving density contrast, and the compaction function. We then apply our formalism to the calculation of the mass distribution of primordial black holes produced in a single-field model containing a "quantum well" (i.e. an exactly flat region in the potential). We confirm that the PDFs feature heavy, exponential tails, with an additional cubic suppression in the case of the curvature perturbation. The large-mass end of the mass distribution is shown to be mostly driven by stochastic-contamination effects, which produce black holes more massive than those naively expected. This work bridges the final gap between the stochastic-inflation formalism and the calculation of the mass distribution of astrophysical objects such as primordial black holes, and opens up various prospects that we finally discuss., Comment: 39 pages, 6 figures; v2 matches the published version in JCAP; v3 corrects typos; v4 corrects typos

We investigate the UV-completion of the Higgs inflation in the metric and the Palatini formalisms. It is known that the cutoff scales for the perturbative unitarity of these inflation models become much smaller than the Planck scale to be consistent with observations. Expecting that the low cutoff scale originates in the curvature of a field-space spanned by the Higgs fields, we consider embedding the curved field-space into a higher dimensional flat space and apply this procedure to the metric-Higgs and the Palatini-Higgs scenarios. The new field introduced in this way successfully flattens the field-space and UV-completes the Higgs inflation in the metric formalism. However, in the Palatini formalism, the new field cannot uplift the cutoff up to the Planck scale. We also discuss the unavoidable low cutoff in the Palatini formalism in the context of the local conformal symmetry., Comment: 22 pages; v2 matches the published version in JCAP

In this paper, we update the peak theory for the estimation of the primordial black hole (PBH) abundance, particularly by implementing the critical behavior in the estimation of the PBH mass and employing the averaged compaction function for the PBH formation criterion to relax the profile dependence. We apply our peak theory to a specific non-Gaussian feature called the exponential tail, which is characteristic in ultra slow-roll models of inflation. With this type of non-Gaussianity, the probability of a large perturbation is not suppressed by the Gaussian factor but decays only exponentially, so the PBH abundance is expected to be much enhanced. Not only do we confirm this enhancement even compared to the case of the corresponding nonlinearity parameter $f_\mathrm{NL}=5/2$, but also we find that the resultant PBH mass spectrum has a characteristic maximal mass which is not seen in the simple Press--Schechter approach., Comment: 25 pages, 9 figures; v2: published version

We motivate a minimal realization of slow-roll $k$-inflation by incorporating the local conformal symmetry and the broken global $\mathrm{SO}(1,1)$ symmetry in the metric-affine geometry. With use of the metric-affine geometry where both the metric and the affine connection are treated as independent variables, the local conformal symmetry can be preserved in each term of the Lagrangian and thus higher derivatives of scalar fields can be easily added in a conformally invariant way. Predictions of this minimal slow-roll $k$-inflation, $n_\mathrm{s}\sim 0.96$, $r\sim 0.005$, and $c_\mathrm{s}\sim 0.03$, are not only consistent with current observational data but also have a prospect to be tested by forthcoming observations., Comment: 8 pages, 1 figure, v2:published version, references added, v3:reference added

We revisit the squeezed-limit non-Gaussianity in the single-field non-attractor inflation models from the viewpoint of the cosmological soft theorem. In the single-field attractor models, inflaton's trajectories with different initial conditions effectively converge into a single trajectory in the phase space, and hence there is only one \emph{clock} degree of freedom (DoF) in the scalar part. Its long-wavelength perturbations can be absorbed into the local coordinate renormalization and lead to the so-called \emph{consistency relation} between $n$- and $(n+1)$-point functions. On the other hand, if the inflaton dynamics deviates from the attractor behavior, its long-wavelength perturbations cannot necessarily be absorbed and the consistency relation is expected not to hold any longer. In this work, we derive a formula for the squeezed bispectrum including the explicit correction to the consistency relation, as a proof of its violation in the non-attractor cases. First one must recall that non-attractor inflation needs to be followed by attractor inflation in a realistic case. Then, even if a specific non-attractor phase is effectively governed by a single DoF of phase space (represented by the exact ultra-slow-roll limit) and followed by a single-DoF attractor phase, its transition phase necessarily involves two DoF in dynamics and hence its long-wavelength perturbations cannot be absorbed into the local coordinate renormalization. Thus, it can affect local physics, even taking account of the so-called \emph{local observer effect}, as shown by the fact that the bispectrum in the squeezed limit can go beyond the consistency relation. More concretely, the observed squeezed bispectrum does not vanish in general for long-wavelength perturbations exiting the horizon during a non-attractor phase., Comment: 19 pages, 2 figures; v2: Eq. (80) and references added; v3: acknowledgments added; v4: published version

The standard model of particle physics is known to be intriguingly successful. However their rich phenomena represented by the phase transitions (PTs) have not been completely understood yet, including the possibility of the existence of unknown dark sectors. In this Letter, we investigate the measurement of the equation of state parameter $w$ and the sound speed $c_{\rm s}$ of the PT plasma with use of the gravitational waves (GWs) of the universe. Though the propagation of GW is insensitive to $c_{\rm s}$ in itself, the sound speed value affects the dynamics of primordial density (or scalar curvature) perturbations and the induced GW by their horizon reentry can then be an indirect probe both $w$ and $c_{\rm s}$. We numerically reveal the concrete spectrum of the predicted induced GW with two simple examples of the scalar perturbation spectrum: the monochromatic and scale-invariant spectra. In the monochromatic case, we see that the resonant amplification and cancellation scales of the induced GW depend on the $c_{\rm s}$ values at different time respectively. The scale-invariant case gives a more realistic spectrum and its specific shape will be compared with observations. In particular, the QCD phase transition corresponds with the frequency range of the pulsar timing array (PTA) observations. If the amplitude of primordial scalar power is in the range of $10^{-4}\lesssim A_\zeta\lesssim10^{-2}$, the induced GW is consistent with current observational constraints and detectable in the future observation in Square Kilometer Array. Futhermore the recent possible detection of stochastic GWs by NANOGrav 12.5 yr analysis~[1] can be explained by the induced GW if $A_\zeta\sim\sqrt{7}\times10^{-3}$., Comment: 9 pages, 5 figures

Non-Gaussianities of primordial perturbations in the soft limit provide the important information about the light degrees of freedom during inflation. The soft modes of the curvature perturbations, unobservable for a local observer, act as rescaling the spatial coordinates. We determine how the trispectrum in the collapsed limit is shifted by the rescaling due to the soft modes. We find the form of the inequality between $f_{\rm NL}$ and $\tau_{\rm NL}$ parameters is not affected by the rescaling, demonstrating that the role of the inequality as an indicator of the light degrees of freedom remains intact. We also comment on the local observer effect on the consistency relation for ultra slow-roll inflation., Comment: 6 pages, matches published version

Stochastic inflation is an effective theory describing the super-Hubble, coarse-grained, scalar fields driving inflation, by a set of Langevin equations. We previously highlighted the difficulty of deriving a theory of stochastic inflation that is invariant under field redefinitions, and the link with the ambiguity of discretisation schemes defining stochastic differential equations. In this paper, we solve the issue of these "inflationary stochastic anomalies" by using the Stratonovich discretisation satisfying general covariance, and identifying that the quantum nature of the fluctuating fields entails the existence of a preferred frame defining independent stochastic noises. Moreover, we derive physically equivalent It\^o-Langevin equations that are manifestly covariant and well suited for numerical computations. These equations are formulated in the general context of multifield inflation with curved field space, taking into account the coupling to gravity as well as the full phase space in the Hamiltonian language, but this resolution is also relevant in simpler single-field setups. We also develop a path-integral derivation of these equations, which solves conceptual issues of the heuristic approach made at the level of the classical equations of motion, and allows in principle to compute corrections to the stochastic formalism. Using the Schwinger-Keldysh formalism, we integrate out small-scale fluctuations, derive the influence action that describes their effects on the coarse-grained fields, and show how the resulting coarse-grained effective Hamiltonian action can be interpreted to derive Langevin equations with manifestly real noises. Although the corresponding dynamics is not rigorously Markovian, we show the covariant, phase-space Fokker-Planck equation for the Probability Density Function of fields and momenta when the Markovian approximation is relevant [...], Comment: 55 pages + appendices, 3 figures. Except updated title, same as v2: version published in JCAP with minor modifications compared to v1

Systematic understanding for classes of inflationary models is investigated from the viewpoint of the local conformal symmetry and the slightly broken global symmetry in the framework of the metric-affine geometry. In the metric-affine geometry, which is a generalisation of the Riemannian one adopted in the ordinary General Relativity, the affine connection is an independent variable of the metric rather than given e.g. by the Levi-Civita connection as its function. Thanks to this independency, the metric-affine geometry can preserve the local conformal symmetry in each term of the Lagrangian contrary to the Riemannian geometry, and then the local conformal invariance can be compatible with much more kinds of global symmetries. As simple examples, we consider the two-scalar models with the broken $\mathrm{SO}(1,1)$ or $\mathrm{O}(2)$, leading to the well-known $\alpha$-attractor or natural inflation, respectively. The inflaton can be understood as their pseudo Nambu-Goldstone boson., Comment: 6 pages, v2: published version, EPL Editor's Choice, v3: references added

In the context of string theory, several conjectural conditions have been proposed for low energy effective field theories not to be in swampland, the UV-incomplete class. The recent ones represented by the de Sitter and trans-Planckian censorship conjectures in particular seem to conflict with the inflation paradigm of the early universe. We first point out that scenarios where inflation is repeated several times (multi-phase inflation) can be easily compatible with these conjectures. In other words, we relax the constraint on the single inflation for the large scale perturbations to only continue at least around 10 e-folds. In this context, we then investigate if a spectator field can be a source of the almost scale-invariant primordial perturbations on the large scale. As a consequence of such an isocurvature contribution, the resultant perturbations exhibit the non-vanishing non-Gaussianity in general. Also the perturbation amplitude on smaller scales can be completely different from that on the large scale due to the multiplicity of inflationary phases. These signatures will be a smoking gun of this scenario by the future observations., Comment: 10 pages, 4 figures; v2: published version

We propose a class of single-field, slow-roll inflation models in which a typical number of $e$-folds can be extremely large. The key point is to introduce a very shallow local minimum near the top of the potential in a hilltop inflation model. In particular, a typical number of $e$-folds is enhanced if classical behavior dominates around the local minimum such that the inflaton probability distribution is drifted to the local minimum as a whole. After the inflaton escapes from the local minimum due to the stochastic dynamics, the ordinary slow-roll inflation follows and it can generate the primordial density perturbation consistent with observation. Interestingly, our scenario inherits the advantages of the old and new inflation: the typical $e$-folds can be extremely large as in the old inflation, and slow-roll inflation naturally follows after the stochastic regime as in the new inflation. In our numerical example, the typical number of $e$-folds can be as large as $10^{10^{10}}$, which is large enough for various light scalars such the QCD axion to reach the Bunch-Davies distribution., Comment: 6 pages, 3 figures; v2: published version, Fig. 1 added, Figs. 2 & 3 revised

We investigate a possibility of primordial black hole (PBH) formation with a hierarchical mass spectrum in multiple phases of inflation. As an example, we find that one can simultaneously realize a mass spectrum which has recently attracted a lot of attention: stellar-mass PBHs ($\sim\mathcal{O}(10)M_\odot$) as a possible source of binary black holes detected by LIGO/Virgo collaboration, asteroid-mass ($\sim\mathcal{O}(10^{-12})M_\odot$) as a main component of dark matter, and earth-mass ($\sim\mathcal{O}(10^{-5})M_\odot$) as a source of ultrashort-timescale events in Optical Gravitational Lensing Experiment microlensing data. The recent refined de Sitter swampland conjecture may support such a multi-phase inflationary scenario with hierarchical mass PBHs as a transition signal of each inflationary phase., Comment: 12 pages, 4 figures; v2: published version

The stochastic approach aims at describing the long-wavelength part of quantum fields during inflation by a classical stochastic theory. It is usually formulated in terms of Langevin equations, giving rise to a Fokker-Planck equation for the probability distribution function of the fields, and possibly their momenta. The link between these two descriptions is ambiguous in general, as it depends on an implicit discretisation procedure, the two prominent ones being the It\^o and Stratonovich prescriptions. Here we show that the requirement of general covariance under field redefinitions is verified only in the latter case, however at the expense of introducing spurious `frame' dependences. This stochastic anomaly disappears when there is only one source of stochasticity, like in slow-roll single-field inflation, but manifests itself when taking into account the full phase space, or in the presence of multiple fields. Despite these difficulties, we use physical arguments to write down a covariant Fokker-Planck equation that describes the diffusion of light scalar fields in non-linear sigma models in the overdamped limit. We apply it to test scalar fields in de Sitter space and show that some statistical properties of a class of two-field models with derivative interactions can be reproduced by using a correspondence with a single-field model endowed with an effective potential. We also present explicit results in a simple extension of the single-field $\lambda \phi^4$ theory to a hyperbolic field space geometry. The difficulties we describe seem to be the stochastic counterparts of the notoriously difficult problem of maintaining general covariance in quantum theories, and the related choices of operator ordering and path-integral constructions. Our work thus opens new avenues of research at the crossroad between cosmology, statistical physics, and quantum field theory., Comment: 9 pages, 2 figures, additional numerical results, version published as a Letter in Classical and Quantum Gravity

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 show that a detectable tensor-to-scalar ratio $(r\ge 10^{-3})$ on the CMB scale can be generated even during extremely low energy inflation which saturates the BBN bound $\rho_{\rm inf}\approx (30 {\rm MeV})^4$. The source of the gravitational waves is not quantum fluctuations of graviton but those of $SU(2)$ gauge fields, energetically supported by coupled axion fields. The curvature perturbation, the backreaction effect and the validity of perturbative treatment are carefully checked. Our result indicates that measuring $r$ alone does not immediately fix the inflationary energy scale., Comment: 6 pages, 3 figures

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

Primordial black holes (PBHs) are one of the candidates to explain the gravitational wave (GW) signals observed by the LIGO detectors. Among several phenomena in the early Universe, cosmic inflation is a major example to generate PBHs from large primordial density perturbations. In this paper, we discuss the possibility to interpret the observed GW events as mergers of PBHs which are produced by cosmic inflation. The primordial curvature perturbation should be large enough to produce a sizable amount of PBHs and thus we have several other probes to test this scenario. We point out that the current pulsar timing array (PTA) experiments already put severe constraints on GWs generated via the second-order effects, and that the observation of the cosmic microwave background (CMB) puts severe restriction on its $\mu$ distortion. In particular, it is found that the scalar power spectrum should have a very sharp peak at $k \sim 10^{6}$ Mpc$^{-1}$ to fulfill the required abundance of PBHs while evading constraints from the PTA experiments together with the $\mu$ distortion. We propose a mechanism which can realize such a sharp peak. In the future, simple inflation models that generate PBHs via almost Gaussian fluctuations could be probed/excluded., Comment: 15 pages, 5 figures; v2: several discussions clarified, published version

The prospects of future galaxy surveys for non-Gaussianity measurements call for the development of robust techniques for computing the bispectrum of primordial cosmological perturbations. In this paper, we propose a novel approach to the calculation of the squeezed bispectrum in multiple-field inflation. With use of the $\delta N$ formalism, our framework sheds new light on the recently pointed out difference between the squeezed bispectrum for global observers and that for local observers, while allowing one to calculate both. For local observers in particular, the squeezed bispectrum is found to vanish in single-field inflation. Furthermore, our framework allows one to go beyond the near-equilateral ("small hierarchy") limit, and to automatically include intrinsic non-Gaussianities that do not need to be calculated separately. The explicit computational programme of our method is given and illustrated with a few examples., Comment: 1+33 pages, 6 figures, matches published version in JCAP