We systematically investigate the preheating behavior of single field inflation with an oscillon-supporting potential. We compute the properties of the emitted gravitational waves (GWs) and the number density and characteristics of the produced oscillons. By performing numerical simulations for a variety of potential types, we divide the analyzed potentials in two families, each of them containing potentials with varying large- or small-field dependence. We find that the shape and amplitude of the emitted GW spectrum have a universal feature, with the peak around the physical wavenumber $k/a \sim m$ at the inflaton oscillation period, irrespective of the exact potential shape. This can be used as a smoking-gun for deducing the existence of a violent preheating phase and possible oscillon formation after inflation. Despite this apparent universality, we find differences in the shape of the emitted GW spectra between the two potential families, leading to discriminating features between them. In particular, all potentials show the emergence of a two-peak structure in the GW spectrum, arising at the time of oscillon formation. However, potentials exhibiting efficient parametric resonance tend to smear out this structure and by the end of the simulation the GW spectrum exhibits a single broad peak. We further compute the properties of the produced oscillons for each potential, finding differences in the number density and size distribution of stable oscillons and transient overdensities. We perform a linear fluctuation analysis and use Floquet charts to relate the results of our simulations to the structure of parametric resonance. We find that the growth rate of scalar perturbations and the associated oscillon formation time are sensitive to the small-field potential shape while the macroscopic physical properties of oscillons (e.g. total number) depend on the large-field potential shape.
We examine the oscillon formation in a recently proposed inflation model of the pure natural inflation, where the inflaton is an axion that couples to a strongly-coupled pure Yang-Mills theory. The plateau of the inflaton potential, which is favored by recent observations, drives the fragmentation of the inflaton and can produce spatially localized oscillons. We find that the oscillons are formed for F<~ O(0.1) M_{Pl}, with F the effective decay constant of the model. We also comment on observational implications of the oscillons.
We investigate the emergence of large, localized, pseudo-stable configurations (oscillons) from inflaton fragmentation at the end of inflation. We predict the number density of large oscillons, and the conditions necessary for their emergence in a class of inflationary models. Analytic estimates are provided for a 3+1 and 1+1-dimensional universe. We test our predictions with detailed numerical simulations in 1+1-dimensions. We see a zoo of oscillons emerging from the simulations, including the usual small amplitude "sech" oscillons as well as large "flat-topped" oscillons. The emergent oscill…
Oscillons are spatially localized and relatively stable field fluctuations which can form after inflation under suitable conditions. In order to reheat the universe, the fields which dominate the energy density after inflation have to couple to other degrees of freedom and finally produce the matter particles present in the universe today. In this study, we use lattice simulations in 2+1 dimensions to investigate how such couplings can affect the formation and stability of oscillons. We focus on models of hilltop inflation, where we have recently shown that hill crossing oscillons generically …
Oscillons are massive, long-lived, localized excitations of a scalar field. We show that in a large class of well-motivated single-field models, inflation is followed by self-resonance, leading to copious oscillon generation and a lengthy period of oscillon domination. These models are characterized by an inflaton potential which has a quadratic minimum and is shallower than quadratic away from the minimum. This set includes both string monodromy models and a class of supergravity inspired scenarios, and is in good agreement with the current central values of the concordance cosmology paramete…
We investigate the production of gravitational waves during preheating after inflation in the common case of field potentials that are asymmetric around the minimum. In particular, we study the impact of oscillons, comparatively long lived and spatially localized regions where a scalar field (e.g. the inflaton) oscillates with large amplitude. Contrary to a previous study, which considered a symmetric potential, we find that oscillons in asymmetric potentials associated with a phase transition can generate a pronounced peak in the spectrum of gravitational waves, that largely exceeds the linea…
Analytical arguments suggest that a large class of scalar field potentials permit the existence of oscillons -- pseudo-stable, non-topological solitons -- in three spatial dimensions. In this paper we numerically explore oscillon solutions in three dimensions. We confirm the existence of these field configurations as solutions to the Klein-Gorden equation in an expanding background, and verify the predictions of Amin and Shirokoff for the characteristics of individual oscillons for their model. Further, we demonstrate that significant numbers of oscillons can be generated via fragmentation of …
Oscillons are long-lived, localized excitations of nonlinear scalar fields which may be copiously produced during preheating after inflation, leading to a possible oscillon-dominated phase in the early Universe. For example, this can happen after axion monodromy inflation, on which we run our simulations. We investigate the stochastic gravitational wave background associated with an oscillon-dominated phase. An isolated oscillon is spherically symmetric and does not radiate gravitational waves, and we show that the flux of gravitational radiation generated between oscillons is also small. Howe…
We study the production of gravitational waves during oscillations of the inflaton around the minimum of a cuspy potential after inflation. We find that a cusp in the potential can trigger copious oscillon formation, which sources a characteristic energy spectrum of gravitational waves with double peaks. The discovery of such a double-peak spectrum could test the underlying inflationary physics.
A generic feature of string compactifications is the presence of many scalar fields, called moduli. Moduli are usually displaced from their post-inflationary minimum during inflation. Their relaxation to the minimum could lead to the production of oscillons: localised, long-lived, non-linear excitations of the scalar fields. Here we discuss under which conditions oscillons can be produced in string cosmology and illustrate their production and potential phenomenology with two explicit examples: the case of an initially displaced volume modulus in the KKLT scenario and the case of a displaced b…
The dynamics at the end of inflation can generate an asymmetry between particles and anti-particles of the inflaton field. This asymmetry can be transferred to baryons via decays, generating a baryon asymmetry in our Universe. We explore this idea in detail for a complex inflaton governed by an observationally consistent -"flatter than quadratic"- potential with a weakly broken global U(1) symmetry. We find that most of the inflaton asymmetry is locked in non-topological soliton like configurations (oscillons) produced copiously at the end of inflation. These solitons eventually decay into bar…
Formation and Decay of Oscillons in Einstein-Cartan Higgs Inflation
Departamento de Física Teórica and Instituto de Física de Partículas y del Cosmos (IPARCOS-UCM), Universidad Complutense de Madrid（马德里康普顿斯大学理论物理系与粒子与宇宙物理研究所(IPARCOS-UCM)）
Axion monodromy is a generic phenomenon in string compactifications. We investigate the production of gravitational-wave background from axion monodromy inflation during preheating. By performing lattice simulations using pseudo-spectral methods, we find that significant single-peak stochastic gravitational-wave backgrounds are generated during preheating for asymptotic linear $|ϕ|$ and $ϕ^{2/3}$ potentials in axion monodromy inflation and cuspy potentials. This may allow us to explore string compactifications through gravitational waves.
Oscillons are long-lived, localized, oscillating nonlinear excitations of a real scalar field which can be abundantly produced during preheating after inflation. We give the first $(3+1)$-dimensional simulation for the oscillon formation during preheating with noncanonical kinetic terms, e.g. the Dirac-Born-Infeld form, and find that the formation of oscillons is significantly influenced by the noncanonical effect.
Many scalar field theories with attractive self-interactions support exceptionally long-lived, spatially localized and time-periodic field configurations called oscillons. A detailed study of their longevity is important for understanding their applications in cosmology. In this paper, we study gravitational effects on the decay rate and lifetime of dense oscillons, where self-interactions are more or at least equally important compared with gravitational interactions. As examples, we consider the $α$-attractor T-model of inflation and the axion monodromy model, where the potentials become fla…
Oscillons are spatially localised strong fluctuations of a scalar field. They can e.g. form after inflation when the scalar field potential is shallower than quadratic away from the minimum. Although oscillons are not protected by topology, they can be remarkably stable and have a significant impact on the (p)reheating phase. In this work we investigate the properties of oscillons in hilltop-shaped potentials, in particular the typical energies, shapes and lifetimes. In the first part of the paper, we simulate oscillon creation and stabilization with (3+1)-dimensional classical lattice simulat…
The stochastic gravitational wave (GW) background provides a fascinating window to the physics of the very early universe. Beyond the nearly scale-invariant primordial GW spectrum produced during inflation, a spectrum with a much richer structure is typically generated during the preheating phase after inflation (or after some other phase transition at lower energies). This raises the question of what one can learn from a future observation of the stochastic gravitational wave background spectrum about the underlying physics during preheating. Recently, it has been shown that during preheating…
In string theory, the simultaneous existence of many Axion-Like Particles (ALPs) are suggested over a vast mass range, and a variety of potentials have been developed in the context of inflation. In such potentials shallower than quadratic, the prominent instability can produce localized dense objects, oscillons. Because of the approximate conservation of their adiabatic invariant, oscillons generally survive quite long, maybe up to the current age of the universe in the case of ultra-light ALPs with $m \sim 10^{-22}\ {\rm eV}$. Such oscillons can have significant effects on the evolution of t…
Using numerical relativity simulations we study the dynamics of pseudo-topological objects called oscillons for a class of models inspired by axion-monodromy. Starting from free field solutions supported by gravitational attractions, we investigate the effect of adding self-interactions, and contrast this with the effect of adding self-interactions whilst removing gravitational support. We map out regions of the parameter space where the initial conditions rapidly collapse to black holes, and other regions where they remain pseudo-stable or disperse.
Constraining the inflaton potential with gravitational waves from oscillons
Technical University of Sofia（索菲亚理工大学）；Asia Pacific Center for Theoretical Physics (APCTP)（亚太理论物理中心）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo（东京大学宇宙物质量子数学研究所（ Kavli WPI ））；Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理中心引力物理与量子信息）；Leung Center for Cosmology and Particle Astrophysics, National Taiwan University（台湾大学梁林宇宙学与粒子天体物理学中心）；Institute for Theoretical Physics, Leibniz University Hannover（汉诺威莱布尼茨大学理论物理研究所）
Decay and lifetime of oscillons coupled to an external scalar field: Insights from instability band analysis
Institute of Science Tokyo（东京科学大学）；Center for Theoretical Physics of the Universe, Institute for Basic Science（基础科学研究院宇宙理论物理中心）；Yonsei University（延世大学）；Tongji University（同济大学）；Institute for Advanced Study of Tongji University（同济大学高等研究院）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo（东京大学前沿研究机构理化学宇宙物质研究所（WPI））；Yangzhou University（扬州大学）
In the Einstein frame picture of Starobinky's $R^2$ inflation model, cosmic inflation is driven by a slowly rolling inflaton field, called scalaron, and followed by a coherently oscillating scalaron phase. Since the scalaron oscillates excessively many times in its potential, which has a quadratic minimum and is a little shallower than quadratic on the positive side, it may fragment into long-living localized objects, called oscillons or I-balls, due to nonlinear growth of fluctuations before reheating of the universe. We show that while parametric self-resonances amplify scalaron fluctuations…
We investigate the effect of the cuspiness of scalar potentials on the production of gravitational waves during oscillon formation after inflation. We consider a more general form of potentials with a mass parameter $M$, which repoduce cuspy potentials for fields much larger than $M$, and smooth potentials in the opposite limit. For cuspy potentials, nonsmooth oscillations of the inflaton induce an amplification of the inflaton fluctuations at the bottom of the potential, so that oscillons copiously form, which leads to a significant stochastic gravitational wave background with a double-peak …
In 'hilltop inflation', inflation takes place when the inflaton field slowly rolls from close to a maximum of its potential (i.e. the 'hilltop') towards its minimum. When the inflaton potential is associated with a phase transition, possible topological defects produced during this phase transition, such as domain walls, are efficiently diluted during inflation. It is typically assumed that they also do not reform after inflation, i.e. that the inflaton field stays on its side of the 'hill', finally performing damped oscillations around the minimum of the potential. In this paper we study the …
The scale of small-field inflation cannot be constrained via primordial gravitational waves through measurement of tensor-to-scalar ratio $r$. In this study, I show that if cosmic strings are produced after symmetry breaking at the end of hilltop supernatural inflation, this small-field inflation model can be tested through the production of gravitational waves from cosmic strings. Future experiments of gravitational wave detectors will determine or further constrain the parameter space in the model.
We compute the gravitational leptogenesis generated from the parity-violating gravitational waves sourced by an abelian gauge field coupled to a pseudo-scalar inflation. We show that, once the CMB bound on the tensor-to-scalar ratio is enforced, the lepton asymmetry produced by this mechanism during inflation is too small to account for the observed baryon asymmetry of the universe, irrespectively of the inflaton potential, the strength of its coupling to the gauge field, and the details of reheating.
We provide a detailed study of gravitational reheating in quintessential inflation generalizing previous analyses only available for the standard case when inflation is followed by an era dominated by the energy density of radiation. Quintessential inflation assumes a common origin for inflation and the dark energy of the Universe. In this scenario reheating can occur through gravitational particle production during the inflation-kination transition. We calculate numerically the amount of the radiation energy density, and determine the temperature $T_*$ at which radiation starts dominating ove…
We revisit the gravitational production of massive Dirac fermions in inflationary cosmology with a focus on clarifying the analytic computation of the particle number density in both the large and the small mass regimes. For the case in which the masses of the gravitationally produced fermions are small compared to the Hubble expansion rate at the end of inflation, we obtain a universal result for the number density that is nearly independent of the details of the inflationary model. The result is identical to the case of conformally coupled scalars up to an overall multiplicative factor of or…
In the axion monodromy inflation, the inflation is driven by the axion with super-Planckian field values in a monomial potential with superimposed sinusoidal modulations. The coupling of the axion to massless gauge fields can induce copious particle production during inflation, resulting in large non-Gaussian curvature perturbation that leads to the formation of primordial black holes. In this paper, we explore the parameter space in the axion monodromy inflation model that favors the formation of primordial black holes with masses ranging from $10^8$ grams to $20$ solar masses. We also study …
We consider Supersymmetric (SUSY) and non-SUSY models of chaotic inflation based on the simplest power-law potential with exponents n=2 and 4. We propose a convenient non-minimal coupling to gravity and a non-minimal kinetic term which ensure, mainly for n=4, inflationary observables favored by the BICEP2/Keck Array and Planck results. Inflation can be attained for subplanckian inflaton values with the corresponding effective theories retaining the perturbative unitarity up to the Planck scale.
The general potential of power-law inflation is as $ V(ϕ)\propto ϕ^{n} $ with scalar field $ϕ$. The behavior of inflation is often known as power-law expansion like $S(η)\propto η^{1+β}$ with $1+β<0$. In this paper, the theoretical spectra of relic gravitational waves are compared with the measured strain sensitivity of Advanced LIGO and VIRGO, corresponding to the latest detected events of gravitational waves. The results show tight constraints on $β$ and $n$. Also, the obtained constraints indicate that special types of the potential of inflation, prototype, and KKLTI models, which are origi…
Nonthermal leptogenesis via cosmological gravitational particle production is tested by inflationary gravitational waves
University of Manitoba（曼尼托巴大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；The University of Chicago（芝加哥大学）；Rice University（莱斯大学）；University of Winnipeg（温尼伯大学）
We consider gravitational wave production during inflation in type IIB string theory, and the possibility of observable gravitational waves in small field inflation. We show that the gauge field excitations on a set of coincident D7 branes, itself critical for moduli stabilization and hence intrinsic to inflation in string theory, coupled with axion fields from bulk fluxes, can act as a spectator sector during inflation. This results in a large production of chiral gravitational waves, even for relatively small values of the axion-gauge field coupling. We extend this to include a monodromy for…
Motivated by recent progress in our understanding of the $B$-mode polarization of cosmic microwave background (CMB), which provides important information about the inflationary gravitational waves (IGWs), we study the possibility to acquire information about the early universe using future space-based gravitational wave (GW) detectors. We perform a detailed statistical analysis to estimate how well we can determine the reheating temperature after inflation as well as the amplitude, the tensor spectral index, and the running of the inflationary gravitational waves. We discuss how the accuracies…
We reveal the universality of short-term anisotropic inflation. As a demonstration, we study inflation with an exponential type gauge kinetic function which is ubiquitous in models obtained by dimensional reduction from higher dimensional fundamental theory. It turns out that an anisotropic inflation universally takes place in the later stage of conventional inflation. Remarkably, we find that primordial gravitational waves with a peak amplitude around $10^{-26}$ ~ $10^{-27}$ are copiously produced in high-frequency bands 10MHz~100MHz. If we could detect such gravitational waves in future, we …
We study the potential impact of detecting the inflationary gravitational wave background by the future space-based gravitational wave detectors, such as DECIGO and BBO. The signal-to-noise ratio of each experiment is calculated for chaotic/natural/hybrid inflation models by using the precise predictions of the gravitational wave spectrum based on numerical calculations. We investigate the dependence of each inflation model on the reheating temperature which influences the amplitude and shape of the spectrum, and find that the gravitational waves could be detected for chaotic/natural inflation…
Inflationary cosmology is successful in explaining a number of outstanding cosmological issues including the flatness, the horizon and the relic issues. More spectacular is the experimental confirmation of the structure as arose from the inflationary quantum fluctuations. However, the physics in the inflationary era is unclear. Polarization observations of Cosmic Microwave Background (CMB) missions may detect the tensor mode effects of inflationary gravitational waves (GWs) and give an energy scale of inflation. To probe the inflationary physics, direct observation of gravitational waves gener…
It is often said that detecting a spectrum of primordial gravitational waves via observing B-mode polarization of the Cosmic Microwave Background is the "Holy Grail" of inflation. The purpose of this short note is to point out that it is indeed of immense scientific interest to search for a signal of gravitational waves in B-mode polarization. However, rather than proving that inflation is the right paradigm of early universe cosmology, a positive signal of direct primordial B-mode polarization might well be due to other sources than inflation. In fact, a careful characterization of the spectr…
We study inflation driven by a dilaton and an axion, both of which are coupled to a SU(2) gauge field. We find that the inflation driven by the dilaton occurs in the early stage of inflation during which the gauge field grows due to the gauge kinetic function. When the energy density of magnetic fields catches up with that of electric fields, chromo-natural inflation takes over in the late stage of inflation, which we call delayed chromo-natural inflation. Thus, the delayed chromo-natural inflation driven by the axion and the gauge field is induced by the dilaton. The interesting outcome of th…
The search for the curl component (B mode) in the cosmic microwave background (CMB) polarization induced by inflationary gravitational waves is described. The canonical single-field slow-roll model of inflation is presented, and we explain the quantum production of primordial density perturbations and gravitational waves. It is shown how these gravitational waves then give rise to polarization in the CMB. We then describe the geometric decomposition of the CMB polarization pattern into a curl-free component (E mode) and curl component (B mode) and show explicitly that gravitational waves induc…
Thermal history of the Universe between inflation and big-bang nucleosynthesis has not yet been revealed observationally. It will be probed by the detection of primordial gravitational waves generated during inflation, which contain information on the reheating temperature as well as the equation of state of the Universe after inflation. Based on Fisher information formalism, we examine how accurately the tensor-to-scalar ratio and reheating temperature after inflation can be simultaneously determined with space-based gravitational wave detectors such as the DECI-hertz Interferometer Gravitati…
We consider inflation driven by an axion-like particle coupled to an SU(2) gauge sector via a Chern-Simons term. Known as chromo-natural inflation, this scenario is in tension with CMB observations. In order to remedy this fact and preserve both the symmetries and the intriguing gravitational wave phenomenology exhibited by the model, we explore the non-minimal coupling of the axion-inflaton to the Einstein tensor. We identify regions of parameter space corresponding to a viable cosmology at CMB scales. We also highlight the possibility of a large and chiral gravitational wave signal at small …
Thermal inflation is an attractive solution to the cosmological moduli problem. However, domain walls may be formed after thermal inflation and some mechanisms are needed to eliminate the domain wall before it dominates the Universe. We point out that gravitational waves produced by the dynamics of domain walls may be observed by the pulsar timing experiments and future space-borne gravitational wave detectors, which provides a probe into the period of thermal inflation. We also show that the QCD instanton effect can effectively eliminate the domain walls with producing observable amount of gr…
In the context of the Palatini formalism of gravity with an $R^{2}$ term, a $ϕ^{2}$ potential can be consistent with the observed bound on $r$ whilst retaining the successful prediction for $n_{s}$. Here we show that the Palatini $ϕ^{2} R^2$ inflation model can also solve the super-Planckian inflaton problem of $ϕ^{2}$ chaotic inflation, and that the model can be consistent with Planck scale-suppressed potential corrections. If $α\gtrsim 10^{12}$, where $α$ is the coefficient of the $R^2$ term, the inflaton in the Einstein frame, $σ$, remains sub-Planckian throughout inflation. In addition, if…
According to the famous Lyth bound, one can confirm large field inflation by finding tensor modes with sufficiently large tensor-to-scalar ratio $r$. Here we will try to answer two related questions: Is it possible to rule out all large field inflationary models by not finding tensor modes with $r$ above some critical value, and what can we say about the scale of inflation by measuring $r$? However, in order to answer these questions one should distinguish between two different definitions of the large field inflation and three different definitions of the scale of inflation. We will examine t…
A direct detection of primordial gravitational waves is the ultimate probe for any inflation model. While current CMB bounds predict the generic scale-invariant gravitational wave spectrum from slow-roll inflation to be below the reach of upcoming gravitational wave interferometers, this prospect may dramatically change if the inflaton is a pseudoscalar. In this case, a coupling to any abelian gauge field leads to a tachyonic instability for the latter and hence to a new source of gravitational waves, directly related to the dynamics of inflation. In this contribution we discuss how this setup…
In this article we provide a new closed relationship between cosmic abundance of primordial gravitational waves and primordial blackholes originated from initial inflationary perturbations for inflection-point models of inflation where inflation occurs below the Planck scale. The current Planck constraint on tensor-to-scalar ratio, running of the spectral tilt, and from the abundance of dark matter content in the universe, we can deduce a strict bound on the current abundance of primordial blackholes to be within a range, $9.99712\times 10^{-3}<Ω_{PBH}h^{2}<9.99736\times 10^{-3}$.
We completely clarify the feature of primordial non-Gaussianities of tensor perturbations in generalized G-inflation, i.e., the most general single-field inflation model with second order field equations. It is shown that the most general cubic action for the tensor perturbation (gravitational wave) $h_{ij}$ is composed only of two contributions, one with two spacial derivatives and the other with one time derivative on each $h_{ij}$. The former is essentially identical to the cubic term that appears in Einstein gravity and predicts a squeezed shape, while the latter newly appears in the prese…
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 $ρ_{\rm inf}\approx (30 {\rm MeV})^4$. 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.
We study the effects of various phenomena which may have happened in the early universe on the spectrum of inflationary gravitational waves. The phenomena include phase transitions, entropy productions from non-relativistic matter, the production of dark radiation, and decoupling of dark matter/radiation from thermal bath. These events can create several characteristic signatures in the inflationary gravitational wave spectrum, which may be direct probes of the history of the early universe and the nature of high-energy physics.
