We present a model of $F(R)$ gravity in the presence of a string theory motivated misalignment axion like particle materialized in terms of a canonical scalar field minimally coupled with gravity, and we study the cosmological phenomenology of the model, emphasizing mainly on the late-time era. The main result of the paper is that inflation and the dark energy era may be realized in a geometric way by an $F(R)$ gravity, while the axion is the dark matter constituent of the Universe. The $F(R)$ gravity model consists of an $R^2$ term, which as we show dominates the evolution during the early time, thus producing a viable inflationary phenomenology, and a power law term $\sim R^δ$ with $δ\ll 1 $ and positive, which eventually controls the late-time era. The axion field remains frozen during the inflationary era, which is an effect known for misalignment axions, but as the Universe expands, the axion starts to oscillate, and its energy density scales eventually as we show, as $ρ_a\sim a^{-3}$. After appropriately rewriting the gravitational equations in terms of the redshift $z$, we study in detail the late-time phenomenology of the model, and we compare the results with the $Λ$CDM model and the latest Planck 2018 data. As we show, the model for small redshifts $0<z<5$ is phenomenologically similar to the $Λ$CDM model, however at large redshifts and deeply in the matter domination era, the results are different from those of the $Λ$CDM model due to the dark energy oscillations. For the late-time study we investigate the behavior of several well-known statefinder quantities, like the deceleration parameter, the jerk and $Om(z)$, and we demonstrate that the statefinders which contain lower derivatives of the Hubble rate have similar behavior for both the $Λ$CDM and the axion $F(R)$ gravity model.
The key to the phenomenological success of inflation models with axion and SU(2) gauge fields is the isotropic background of the SU(2) field. Previous studies showed that this isotropic background is an attractor solution during inflation starting from anisotropic (Bianchi Type I) spacetime; however, not all possible initial anisotropic parameter space was explored. In this paper, we explore more generic initial conditions without assuming the initial slow-roll dynamics. We find some initial anisotropic parameter space which does not lead to the isotropic background, but to violation of slow-r…
A numerical study of a pseudoscalar inflation having an axion-photon-like coupling is performed by solving numerically the coupled differential equations of motion for inflaton and photon mode functions from the onset of inflation to the end of reheating. The backreaction due to particle production is also included self-consistently. We find that this particular inflation model realizes the idea of a warm inflation in which a steady thermal bath is established by the particle production. In most cases this thermal bath exceeds the amount of radiation released in the reheating process. In the s…
In this work we investigate the quantitative effects of the misalignment kinetic axion on $R^2$ inflation. Due to the fact that the kinetic axion possesses a large kinetic energy which dominates its potential energy, during inflation its energy density redshifts as stiff matter fluid and evolves in a constant-roll way, making the second slow-roll index to be non-trivial. At the equations of motion level, the $R^2$ term dominates the evolution, thus the next possible effect of the axion could be found at the cosmological perturbations level, via the second slow-roll index which is non-trivial. …
We study the axionic inflation with a modulated potential and examine if the primordial tensor power spectrum exhibits oscillatory feature, which is testable with future space-based gravitational wave experiments such as DECIGO and BBO. In the case of the single-field axion monodromy inflation, it turns out that it is difficult to detect the oscillation in the spectrum due to suppression of the sub-Planckian decay constant of axion. On the other hand, in the case of aligned chromo-natural inflation where the axion is coupled to a SU(2) gauge field, it turns out that the sizable oscillation in …
It is quite well known for some time that string inspired axionic terms of the form $ν(ϕ)\tilde{R}R$, known also as Chern-Simons terms, do not affect the scalar perturbations and the background evolution for a flat Friedman-Robertson-Walker Universe. In this paper we study and quantify the implications of the presence of the above term in the context of vacuum $f(R)$. Particularly, we assume that axionic dark matter is present during inflation, and we examine in a quantitative way the effects of axionic Chern-Simons terms on the tensor perturbations. The axion field is quantified in terms of a…
We discuss two-stage dilaton-axion inflation models [1] and describe $α$-attractor models with either exponential or polynomial approach to the plateau. We implement one of the models of primordial black hole production proposed in [2] in the $α$-attractor context, and develop its supergravity version. The predictions of this model following from its polynomial attractor properties are: $n_s$ and $r$ are $α$-independent, $r$ depends on the mass parameter $μ$ defining the approach to the plateau. The tachyonic instability at the transition point between the two stages of inflation is proportion…
In this paper, we examine the viability of inflation models with a spectator axion field coupled to both gravitational and SU(2) gauge fields via Chern-Simons couplings. Requiring phenomenological success of the axion-SU(2) sector constrains the coupling strength of the gravitational Chern-Simons term. We find that the impact of this term on the production and propagation of gravitational waves can be as large as fifty percent enhancement for the helicity that is not sourced by the gauge field, if the cut-off scale is as low as $Λ$ = 20H. The effect becomes smaller for a larger value of $Λ$, w…
Warm inflation has been noted previously as a possible way to implement inflationary models compatible with the dS swampland bounds. But often in these discussions the heat bath dynamics is kept largely unspecified. We point out that the recently introduced Minimal Warm Inflation of arXiv:1910.07525, where an axionic coupling of the inflaton leads to an explicit model for the thermal bath, yields models of inflation that can easily fit cosmological observations while satisfying de Sitter swampland bounds, as well as the swampland distance bound and trans-Planckian censorship.
The abundance of the QCD axion is known to be suppressed if the Hubble parameter during inflation, $H_{\rm inf}$, is lower than the QCD scale, and if the inflation lasts sufficiently long. We show that the tight upper bound on the inflation scale can be significantly relaxed if the eternal old inflation is driven by the standard-model Higgs field trapped in a false vacuum at large field values. Specifically, $H_{\rm inf}$ can be larger than $100\,$GeV if the false vacuum is located above the intermediate scale. We also discuss the slow-roll inflation after the tunneling from the false vacuum t…
We revisit the model of axion inflation in the context of stochastic inflation and investigate the effects of the stochastic noises associated to the electromagnetic fields. Because of the parity violating interaction, one polarization of the gauge field is amplified inducing large curvature perturbation power spectrum. Taking into account the stochastic kicks arising from the short modes at the time of horizon crossing we obtain the corresponding Langevin equations for the long modes of the electromagnetic and axion fields. It is shown that a mean-reverting process governs the dynamics of the…
We study the scalar-tensor-tensor non-Gaussian signal in an inflationary model comprising also an axion coupled with SU(2) gauge fields. In this set-up, metric fluctuations are sourced by the gauge fields already at the linear level providing an enhanced chiral gravitational waves spectrum. The same mechanism is at work in generating an amplitude for the three-point function that is parametrically larger than in standard single-field inflation.
In this work we introduce an effective model of $f(R)$ gravity containing a non-minimal coupling to the axion scalar field. The axion field is described by the misalignment model, in which the primordial $U(1)$ Peccei-Quinn symmetry is broken during inflation and the $f(R)$ gravity is described by the $R^2$ model, and in addition, the non-minimal coupling has the form $\sim h(ϕ)R^γ$, with $0<γ<0.75$. By appropriately constraining the non-minimal coupling at early times, the axion field remains frozen in its primordial vacuum expectation value, and the $R^2$ gravity dominates the inflationary e…
We constructed a new class of inflationary model with the higher derivative axion field which obeys constant shift symmetry. In the usual axion (natural) inflation, the axion decay constant is predicted to be in the super-Planckian regime which is believed to be incompatible with an effective field theory framework. With a novel mechanism originating from a higher derivative kinetic gravity braiding (KGB) of an axion field we found that there exist a huge parameter regime in our model where axion decay constant could be naturally sub-Planckian. Thanks to the KGB which effectively reduces the P…
In order to accommodate the QCD axion as the dark matter (DM) in a model in which the Peccei-Quinn (PQ) symmetry is broken before the end of inflation, a relatively low scale of inflation has to be invoked in order to avoid bounds from DM isocurvature fluctuations, $H_* \lesssim \mathcal{O}(10^9)\,$GeV. We construct a simple model in which the Standard Model Higgs field is non-minimally coupled to Palatini gravity and acts as the inflaton, leading to a scale of inflation $H_* \sim 10^8\,$GeV. When the energy scale at which the PQ symmetry breaks is much larger than the scale of inflation, we f…
We successfully embed the Kim-Nilles-Peloso (KNP) alignment mechanism for enhancing the axion decay constant in the context of large volume type IIB orientifolds. The flat direction is generated in the plane of ($C_0$-$C_2$) axions corresponding to the involutively even universal axion $C_0$ and odd axion $C_2$, respectively. The moduli stabilization with large volume scheme has been established as well.
We study the production of primordial circular ("V-mode") polarization in axion inflation coupled to fermions and gauge fields, with special attention paid to (p)reheating. We construct the power spectrum of $V$, and find a blue-tilted spectrum with index $n_V=4$. This is independent of the dominant decay channel of the inflaton (direct fermion vs. direct photon production)
We present an intrinsic leptogenesis mechanism in models of axion inflation with a classical SU(2) gauge field. The gauge field is coupled to the axion with a Chern-Simons interaction and comprises a tiny fraction of the total energy, $\frac{ρ_{_{\rm YM}}}{ρ_{_{\rm tot}}}\lesssimε^2$. However, it has spin-2 fluctuations which breaks the parity and leads to the generation of chiral gravitational waves during inflation. By the gravitational anomaly in SM, it naturally creates a net lepton number density, sufficient to explain the matter asymmetry. We show that this mechanism can generate the obs…
We show that the cosmological abundance of string axions is much smaller than naive estimates if the Hubble scale of inflation, $H_{\rm inf}$, is sufficiently low (but can still be much higher than the axion masses) and if the inflation lasts sufficiently long. The reason is that the initial misalignment angles of the string axions follow the Bunch-Davies distribution peaked at the potential minima. As a result, the cosmological moduli problem induced by the string axions can be significantly relaxed by low-scale inflation, and astrophysical and cosmological bounds are satisfied over a wide ra…
Remarkably, if $CP$ was spontaneously broken in the physics of inflation, fermions would notice and remember it. Based on that, we present a new (non-thermal) mechanism for generating self-interacting dark Dirac fermions prior to the Hot Big Bang. The non-Abelian gauge fields and axions are well-motivated matter contents for the particle physics of inflation. In this background, we analytical study Dirac fermion doublets charged under the $SU(2)$ gauge field and use point-splitting technique to regularize the currents. We show that the non-trivial $CP$-violating vacuum structure of $SU(2)$-axi…
Because of their quantum fluctuations, axion fields had a chance to experience field excursions traversing many minima of their potentials during inflation. We study this situation by analyzing the dynamics of an axion-spectator field $ψ$, present during inflation, with a periodic potential given by $v(ψ) = Λ^4 [1 - \cos (ψ/ f)]$. By assuming that the vacuum expectation value of the field is stabilized at one of its minima, say $ψ= 0$, we compute every $n$-point correlation function of $ψ$ up to first order in $Λ^4$ using the in-in formalism. This computation allows us to identify the distribu…
We study the preheating of gauge fields in a simple axion monodromy model and compute the induced entropy perturbations and their effect on the curvature fluctuations. We find that the correction to the spectrum of curvature perturbations has a blue spectrum with index $n_s = 5/2$. Hence, these induced modes are harmless for the observed structure of the universe. Since the spectrum is blue, there is the danger of overproduction of primordial black holes. However, we show that the observational constraints are easily satisfied.
We look at the possibility of superinflationary behavior in a class of anisotropic Type-IIB superstring cosmologies in the context of Pre-big Bang scenario and find that there exists a rather narrow range of parameters for which these models inflate. We then show that, although in general this behavior is left untouched by the introduction of a Ramond-Ramond axion field through a SL(2,R) rotation, there exists a particular class of axions for which inflation disappears completely. Asymptotic past initial conditions are briefly discussed, and some speculations on the possible extension of Pre-b…
We study an inflationary model developed by Kaloper and Sorbo, in which the inflaton is an axion with a sub-Planckian decay constant, whose potential is generated by mixing with a topological 4-form field strength. This gives a 4d construction of "axion monodromy inflation": the axion winds many times over the course of inflation and draws energy from the 4-form. The classical theory is equivalent to chaotic inflation with a quadratic inflaton potential. Such models can produce "high scale" inflation driven by energy densities of the order of $(10^{16}\ GeV)^4$, which produces primordial gravi…
We study the production and backreaction of massive vector-like fermions in the background of a classical SU(2) gauge field during axion-driven inflation. We demonstrate all ultraviolet divergences due to the interactions with the fermions can be absorbed by renormalization of the axion wavefunction and the gauge coupling. The effects of the fermion-axion interaction vanish in the massless limit as required by symmetry. For very massive fermions, contact interactions are induced between the axion, the gauge field and the gravitational field. In this massive limit, we find the usual axion-gauge…
We present a minimal extension of the Standard Model (SM) providing a consistent picture of particle physics from the electroweak scale to the Planck scale and of cosmology from inflation until today. Three right-handed neutrinos $N_i$, a new color triplet $Q$ and a complex SM-singlet scalar $σ$, whose vacuum expectation value $v_σ\sim 10^{11}$ GeV breaks lepton number and a Peccei-Quinn symmetry simultaneously, are added to the SM. At low energies, the model reduces to the SM, augmented by seesaw generated neutrino masses and mixing, plus the axion. The latter solves the strong CP problem and…
We introduce an axion-inflation model embedded in the Left-Right symmetric extension of the SM in which $W_R$ is coupled to the axion. This model merges three milestones of modern cosmology, i.e., inflation, cold dark matter, and baryon asymmetry. Thus, it can naturally explain the observed coincidences among cosmological parameters, i.e., $η_{B}\approx P_ζ$ and $Ω_{DM} \simeq 5~Ω_{B}$. The source of asymmetry is spontaneous CP violation in the physics of inflation, and the lightest right-handed neutrino is the cold dark matter candidate with mass $m_{N_1}\sim 1~GeV$. The introduced mechanism …
Building on Weinberg's approach to effective field theory for inflation, we construct an effective Lagrangian for a pseudo scalar (axion) inflaton field with shift symmetry. In this Lagrangian we allow the axion field to couple to non-Abelian gauge fields via a Chern-Simons term. We then analyze a class of inflation models driven by kinetic terms. We find that the observational constraints on the amplitudes of curvature perturbations and non-Gaussianity yield a lower bound for the tensor-to-scalar ratio of $r\gtrsim 5\times 10^{-3}$ from the vacuum fluctuation. The sourced gravitational wave f…
Gravitational waves from axion inflation in the gradient expansion formalism. Part II. Fermionic axion inflation
Institute for Theoretical Physics, University of Münster（明斯特大学理论物理研究所）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学 Kavli 宇宙粒子与宇宙学研究所（WPI））；Physics Faculty, Taras Shevchenko National University of Kyiv（基辅塔拉斯·舍甫琴科国立大学物理系）
Under the main assumption that the axion scalar field mainly composes the dark matter in the Universe, in this paper we shall extend the formalism of kinetic axion $R^2$ gravity to include Gauss-Bonnet terms non-minimally coupled to the axion field. As we demonstrate, this non-trivial Gauss-Bonnet term has dramatic effects on the inflationary phenomenology and on the kinetic axion scenario. Specifically, in the context of our formalism, the kinetic axion ceases to be kinetically dominated at the end of the inflationary era, since the condition $\dotϕ\simeq 0$ naturally emerges in the theory. T…
We propose the unified models of cosmological inflation, spontaneous SUSY breaking, and the dark energy (de Sitter vacuum) in $N=1$ supergravity with the dilaton-axion chiral superfield $T$ in the presence of an $N=1$ vector multiplet with the alternative Fayet-Iliopoulos term. By using the Kähler potential as $K=-α\log(T+\bar{T})$ and the superpotential as a sum of a constant and a linear term, we find that viable inflation is possible for $3\leqα\leqα_{\rm max}$ where $α_{\rm max}\approx 7.235$. Observations of the amplitude of primordial scalar perturbations fix the SUSY breaking scale in o…
We study a new model of quintessential inflation which is inspired by supergravity and string theory. The model features a kinetic pole, which gives rise to the inflationary plateau, and a runaway quintessential tail. We envisage a coupling between the inflaton and the Peccei-Quinn (PQ) field which terminates the roll of the runaway inflaton and traps the latter at an enhanced symmetry point (ESP), thereby breaking the PQ symmetry. The kinetic density of the inflaton is transferred to the newly created thermal bath of the hot big bang due to the decay of PQ particles. The model successfully ac…
We consider a mechanism for producing a significant population of primordial black holes (PBHs) and an observable stochastic gravitational wave background (SGWB) within string theory inspired models of inflation. In this framework where inflaton is identified as a non-compact axion-like field, sub-leading non-perturbative effects can superimpose steep cliffs connected by smooth plateaus onto the underlying axion potential. In the presence of coupling to Abelian gauge fields, the motion of axion on the cliff-like region(s) of its potential triggers a localized production of one helicity state o…
A gravitational wave background is expected to emerge from the superposition of numerous gravitational wave sources of both astrophysical and cosmological origin. A number of cosmological models can have a parity violation, resulting in the generation of circularly polarised gravitational waves. We investigate the constraining power of third generation Einstein Telescope and Cosmic Explorer detectors, for a gravitational wave background generated by early universe axion inflation.
We show that the upper bound of the classical QCD axion window can be significantly relaxed for low-scale inflation. If the Gibbons-Hawking temperature during inflation is lower than the QCD scale, the initial QCD axion misalignment angle follows the Bunch-Davies distribution. The distribution is peaked at the strong CP conserving minimum if there is no other light degree of freedom contributing to the strong CP phase. As a result, the axion overproduction problem is significantly relaxed even for an axion decay constant larger than $10^{12}$GeV. We also provide concrete hilltop inflation mode…
Axion Inflation from Heavy-Fermion One-Loop Effects
International Centre for Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences（国际理论物理中心亚太分中心，中国科学院大学）；Taiji Laboratory for Gravitational Wave Universe, University of Chinese Academy of Sciences（太极引力波宇宙实验室，中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences (CAS)（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Department of Physics, Anhui Normal University（安徽师范大学物理系）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院基础物理与数学学院）
We show that inflation with a quadratic potential occurs naturally in theories where an axion-like field mixes with a 4-form. Such an axion is massive, with the mass which arises from the mixing being protected by the axion shift symmetry. The 4-form backgrounds break this symmetry spontaneously and comprise a mini-landscape, where their fluxes can change by emission of membranes. Inflation can begin when the 4-form dominates the energy density. Eventually this energy is reduced by membrane emission and the axion can roll slowly towards its minimum, as in the simplest version of chaotic inflat…
We show that the initial misalignment angle of the QCD axion (or axion-like particles) can be set very close to $π$, if the QCD axion has a mixing with another heavy axion which induces the phase shift $\approx π$ after inflation. In the simplest case, the heavy axion plays the role of the inflaton, and we call such inflation as "$π$nflation." The basic idea was first proposed by Daido and the present authors in Ref. [1702.03284] in 2017 and more recently discussed in Ref. [1903.00462]. We show that the QCD axion with a decay constant $f_a \gtrsim 3 \times 10^9\,$ GeV can explain dark matter b…
High-Quality Axion Dark Matter without Isocurvature Problem
Kavli IPMU (WPI), UTIAS, University of Tokyo（东京大学）；Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）
We examine the theoretical possibility for the heavy QCD axion to induce slow-roll inflation while solving the strong CP problem through the Peccei-Quinn mechanism. If the cancellation between contributions from a small-size instanton and another Peccei-Quinn symmetry breaking occurs with high accuracy, the potential can be flattened enough near its maximum to achieve hilltop inflation. This comes at the cost of severe fine-tuning of their relative size and phase, but it also allows us to relate the high quality problem of the Peccei-Quinn symmetry to the fine-tuning problem of the hilltop inf…
