Axion inflation entails a coupling of the inflaton field to gauge fields through the Chern-Simons term. This results in a strong gauge field production during inflation, which backreacts on the inflaton equation of motion. Here we show that this strongly non-linear system generically experiences a resonant enhancement of the gauge field production, resulting in oscillatory features in the inflaton velocity as well as in the gauge field spectrum. The gauge fields source a strongly enhanced scalar power spectrum at small scales, exceeding previous estimates. For appropriate parameter choices, the collapse of these over-dense regions can lead to a large population of (light) primordial black holes with remarkable phenomenological consequences.
$SU(2)$ gauge fields and axions can have a stable, isotropic and homogeneous configuration during inflation. However, couplings to other matter species lead to particle production, which in turn induces backreaction on and destabilization of the non-abelian and axion background. In this paper, we first study the particle production by a $SU(2)$ gauge field coupled to a massive Dirac doublet. To carry out this calculation we have made two technical improvements compared to what has been done in the literature. First, we apply the anti-symmetrization of the operators to treat particles and anti-…
We calculate the interaction potential between D5 and anti-D5 branes wrapping distant but homologous 2-cycles. The interaction potential is logarithmic in the separation radius and does not decouple at infinity. We show that logarithmic backreaction is generic for 5-branes wrapping distant but homologous 2-cycles, and we argue that this destabilises models of axion monodromy inflation involving NS5 brane-antibrane pairs in separate warped throats towards an uncontrolled region.
We perform an analytical study of the stability of the background solution of the model in which an inflaton, through an axionic coupling to a $U(1)$ gauge field, causes an amplification of the gauge field modes that strongly backreact on its dynamics. To this goal, we study the evolution of the gauge field modes coupled to the inflaton zero mode, treating perturbatively the deviation of the inflaton velocity from its mean-field value. As long as the system is in the strong backreaction regime we find that the inflaton velocity performs oscillations of increasing amplitude about the value it w…
Phenomenological success of inflation models with axion and SU(2) gauge fields relies crucially on control of backreaction from particle production. Most of the previous study only demanded the backreaction terms in equations of motion for axion and gauge fields be small on the basis of order-of-magnitude estimation. In this paper, we solve the equations of motion with backreaction for a wide range of parameters of the spectator axion-SU(2) model. First, we find a new slow-roll solution of the axion-SU(2) system in the absence of backreaction. Next, we obtain accurate conditions for stable slo…
We continue the development of axion monodromy inflation, focussing in particular on the backreaction of complex structure moduli. In our setting, the shift symmetry comes from a partial large complex structure limit of the underlying type IIB orientifold or F-theory fourfold. The coefficient of the inflaton term in the superpotential has to be tuned small to avoid conflict with Kahler moduli stabilisation. To allow such a tuning, this coefficient necessarily depends on further complex structure moduli. At large values of the inflaton field, these moduli are then in danger of backreacting too …
We study the backreaction problem in a mechanism of magnetogenesis from inflation. In usual analysis, it has been assumed that the backreaction due to electromagnetic fields spoils inflation once it becomes important. However, there exists no justification for this assumption. Hence, we analyze magnetogenesis from inflation by taking into account the backreaction. On the contrary to the naive expectation, we show that inflation still continues even after the backreaction begins to work. Nevertheless, it turns out that creation of primordial magnetic fields is significantly suppressed due to th…
We emphasize the importance of effects from heavy fields on supergravity models of inflation. We study, in particular, the backreaction of stabilizer fields and geometric moduli in the presence of supersymmetry breaking. Many effects do not decouple even if those fields are much heavier than the inflaton field. We apply our results to successful models of Starobinsky-like inflation and natural inflation. In most scenarios producing a plateau potential it proves difficult to retain the flatness of the potential after backreactions are taken into account. Some of them are incompatible with non-p…
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 study the geometrical instability arising in multi-field models of inflation with negatively-curved field space. We analyse how the homogeneous background evolves in presence of geometrical destabilisation, and show that, in simple models, a kinematical backreaction effect takes place that shuts off the instability. We also follow the evolution of the unstable scalar fluctuations. We show that they assist the kinematical backreaction while remaining in the perturbative regime. We conclude that, in the simplest models of geometrical destabilisation, inflation does not end prematurely, but ra…
Within a genuinely gauge invariant approach recently developed for the computation of the cosmological backreaction, we study, in a cosmological inflationary context and with respect to various observers, the impact of scalar fluctuations on the space-time dynamics in the long wavelength limit. We stress that such a quantum backreaction effect is evaluated in a truly gauge independent way using a set of effective equations which describe the dynamics of the averaged geometry. In particular we show under what conditions the free falling (geodetic) observers do not experience any scalar-induced …
Axion Inflation: Perturbative control in the strong backreaction regime
CERN（欧洲核子研究中心）；Instituto de Física Téorica UAM-CSIC（马德里自治大学-西班牙国家科研委员会理论物理研究所）；Dipartimento di Fisica e Astronomia “G. Galilei”, Università degli Studi di Padova（帕多瓦大学伽利略物理与天文学系）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室理论部）
Ultralight scalar fields such as axions can form clouds around rotating black holes (BHs) by the superradiant instability. It is important to consider the evolution of clouds associated with BH binaries for the detectability of the presence of clouds through gravitational wave signals and observations of the mass and spin parameters of BHs. We re-examine the impact on the axion cloud due to the tidal perturbation from the companion in a binary system taking into account the following points. First, we study the influence of higher-multipole moments. Second, we consider the backreaction due to …
Institute for Theoretical Physics, University of Münster（明斯特大学理论物理研究所）；Physics Faculty, Taras Shevchenko National University of Kyiv（基辅塔拉斯舍甫琴科国立大学物理系）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学 Kavli 宇宙起源与结构宇宙学前沿研究中心）
We study string inspired two-field models of large-field inflation based on axion monodromy in the presence of an interacting heavier modulus. This class of models has enough structure to approximate at least part of the backreaction effects known in full string theory, such as kinetic mixing with the axion, and flattening of the scalar potential. Yet, it is simple enough to fully describe the structure of higher-point curvature perturbation interactions driven by the adjusting modulus backreaction dynamics. We find that the presence of the heavy modulus can be described via two equivalent eff…
We investigate how long wavelength inflationary fluctuations can cause the background field to deviate from classical dynamics. For generic potentials, we show that, in the Hartree approximation, the long wavelength dynamics can be encapsulated by a two-field model operating in an effective potential. The latter is given by a simple Gaussian integral transformation of the original inflationary potential. We use this new expression to study backreaction effects in quadratic, hilltop, flattened, and axion monodromy potentials. We find that the net result of the altered dynamics is to slightly mo…
The formalism of stochastic inflation is a powerful tool for analyzing the backreaction of cosmological perturbations, and making precise predictions for inflationary observables. We demonstrate this with the simple $m^2ϕ^2$ model of inflation, wherein we obtain an effective field theory for IR modes of the inflaton, which remains coupled to UV modes through a classical noise. We compute slow-roll corrections to the evolution of UV modes (i.e. quantum fluctuations), and track this effect from the UV theory to the IR theory, where it manifests as a correction to the classical noise. We compute …
We analyze the onset of inflation for a simple single-field model when the system begins with significant inhomogeneities on length-scales shorter than the initial Hubble radius. We incorporate certain nonlinear interactions among the coupled degrees of freedom by using the nonperturbative Hartree approximation. Consistent with recent, more computationally intensive numerical-relativity studies, we find inflation to be robust for large-field models, even when the system begins with significant structure on sub-Hubble scales. We consider the space of initial conditions $(φ(t_0), \dotφ (t_0))$, …
In a general single field inflationary model we consider the effects of long wavelength scalar fluctuations on the effective expansion rate and equation of state seen by a class of free falling observers, using a physical gauge invariant formulation. In a previous work we showed that for a free massive inflaton no backreaction is observed within some constraints. In this paper we extend the validity of our previous results to the case of an arbitrary self-interacting inflation potential, working to second order in cosmological perturbation theory and to all order in slow-roll approximation. Fo…
A systematic analysis of possibilities for realizing single-field F-term axion monodromy inflation via the flux-induced superpotential in type IIB string theory is performed. In this well-defined setting the conditions arising from moduli stabilization are taken into account, where we focus on the complex-structure moduli but ignore the Kaehler moduli sector. Our analysis leads to a no-go theorem, if the inflaton involves the universal axion. We furthermore construct an explicit example of F-term axion monodromy inflation, in which a single axion-like field is hierarchically lighter than all r…
We investigate the interplay between moduli dynamics and inflation, focusing on the KKLT-scenario and cosmological $α$-attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for $α$-attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory, or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there …
We propose a model for inflation consisting of an axionic scalar field coupled to a set of three non-Abelian gauge fields. Our model's novel requirement is that the gauge fields begin inflation with a rotationally invariant vacuum expectation value (VEV) that is preserved through identification of SU(2) gauge invariance with rotations in three dimensions. The gauge VEV interacts with the background value of the axion, leading to an attractor solution that exhibits slow roll inflation even when the axion decay constant has a natural value ($<M_{\rm Pl}$). Assuming a sinusoidal potential for the…
We perform a detailed analytical and numerical analysis of the multi-field evolution of Fibre Inflation and show that, regardless of the microscopic realisation of the model, the mass-squared of one of the two ultra-light axions becomes always negative during inflation. This implies that the corresponding isocurvature perturbations experience a potential geometrical destabilisation which seems to bring the system away from the perturbative regime. Therefore we conclude that a full understanding of the inflationary evolution of Fibre Inflation can be achieved only via a non-perturbative analysi…
We consider the backreaction of the long wavelength tensor modes produced during a slow-roll inflationary regime driven by a single scalar field in a spatially flat Friedmann-Lema\^ıtre-Robertson-Walker background geometry. We investigate the effects on non-local observables such as the effective (averaged) expansion rate and equation of state at second order in cosmological perturbation theory. The coupling between scalar and tensor perturbations induces at second order new tensor backreaction terms beyond the one already present in a de Sitter background. We analyze in detail the effects see…
Models of inflation based on axions, which owe their popularity to the robustness against UV corrections, have also a very distinct class of signatures. The relevant interactions of the axion are a non-perturbative oscillating contribution to the potential and a shift-symmetric coupling to gauge fields. We review how these couplings affect the cosmological perturbations via a unified study based on the in-in formalism. We then note that, when the inflaton coupling to gauge fields is high enough to lead to interesting observational results, the backreaction of the produced gauge quanta on the i…
We review the effects of heavy scalar fields during inflation in the framework of $\mathcal N = 1$ supergravity. Such heavy scalars can be geometric moduli from string compactifications or stabilizer fields from a different sector of the theory. Even when these fields are heavier than the Hubble scale during inflation, they generically cause backreactions which alter the dynamics of the system. Severe problems may arise when the heavy fields break supersymmetry, which is quite generic for Kähler moduli. We illustrate these effects in two examples, chaotic inflation and Starobinsky-like inflati…
We investigate how coherent oscillations backreact on the evolution of the condensate wave function of ultra-light axions in the non-relativistic regime appropriate to cosmic structure formation. The coherent oscillations induce higher harmonics beyond the fundamental mode considered so far when a self-interaction is present, and imprint oscillations in the gravitational potential. We emphasize that the effective self-interaction felt by the slowly-varying envelop of the wave function always differs from the bare Lagrangian interaction potential. We also point out that, in the hydrodynamical f…
We study the inflation scenarios, in the framework of superstring theory, where the inflaton is an axion producing the adiabatic curvature perturbations while there exists another light axion producing the isocurvature perturbations. We discuss how the non-trivial couplings among string axions can generically arise, and calculate the consequent cross-correlations between the adiabatic and isocurvature modes through concrete examples. Based on the Planck analysis on the generally correlated isocurvature perturbations, we show that there is a preference for the existence of the correlated isocur…
An attractive candidate for the inflaton is an axion slowly rolling down a flat potential protected by a perturbative shift symmetry. Realisations of this idea within large field, natural and monomial inflation have been disfavoured by observations and are difficult to embed in string theory. We show that subleading, but significant non-perturbative corrections can superimpose sharp cliffs and gentle plateaus into the potential, whose overall effect is to enhance the number of e-folds of inflation. Sufficient e-folds are therefore achieved for smaller field ranges compared to the potential wit…
We study general class of small-field axion inflations which are the mixture of polynomial and sinusoidal functions suggested by the natural and axion monodromy inflations. The axion decay constants leading to the successful axion inflations are severely constrained in order not to spoil the Big-Bang nucleosynthesis and overproduce the isocurvature perturbation originating from the QCD axion. We in turn find that the cosmologically favorable axion decay constants are typically of order the grand unification scale or the string scale which is consistent with the prediction of closed string axio…
String theory generically predicts the coupling between the Affleck-Dine field and axion field through higher-dimensional operators. We thus explore the Affleck-Dine baryogenesis on an axion background. It turns out that the axion oscillation produces an enough amount of baryon asymmetry of the Universe just after the inflation, even without a soft supersymmetry-breaking $A$-term. This baryogenesis scenario is applicable to the string axion inflation.
It is shown that, when the inflaton field modulates the gauge kinetic function of the gauge fields in supergravity realisations of inflation, the dynamic backreaction leads to a new inflationary attractor solution, in which the inflaton's variation suffers additional impedance. As a result, slow-roll inflation can naturally occur along directions of the scalar potential which would be too steep and curved to support it otherwise. This provides a generic solution to the infamous eta-problem of inflation in supergravity. Moreover, it is shown that, in the new inflationary attractor, the spectral…
We study an axion inflation model recently proposed within the framework of type IIB superstring theory, where we pay a particular attention to a sub-Planckian axion decay constant. Our axion potential can lead to the small field inflation with a small tensor-to-scalar ratio, and a typical reheating temperature can be as low as GeV.
The BICEP2 experiment determined the Hubble parameter during inflation to be about $10^{14}$ GeV. Such high inflation scale is in tension with the QCD axion dark matter if the Peccei-Quinn (PQ) symmetry remains broken during and after inflation, because too large axion isocurvature perturbations would be generated. The axion isocurvature perturbations can be suppressed if the axion acquires a sufficiently heavy mass during inflation. We show that this is realized if the PQ symmetry is explicitly broken down to a discrete symmetry and if the breaking is enhanced during inflation. We also show t…
The QCD axion is the leading solution to the strong-CP problem, a dark matter candidate, and a possible result of string theory compactifications. However, for axions produced before inflation, symmetry-breaking scales of $f_a \gtrsim 10^{12}$ GeV (which are favored in string-theoretic axion models) are ruled out by cosmological constraints unless both the axion misalignment angle $θ_0$ and the inflationary Hubble scale $H_I$ are extremely fine-tuned. We show that attempting to accommodate a high-$f_a$ axion in inflationary cosmology leads to a fine-tuning problem that is worse than the strong…
We propose a landscape of many axions, where the axion potential receives various contributions from shift symmetry breaking effects. We show that the existence of the axion with a super-Planckian decay constant is very common in the axion landscape for a wide range of numbers of axions and shift symmetry breaking terms, because of the accidental alignment of axions. The effective inflation model is either natural or multi-natural inflation in the axion landscape, depending on the number of axions and the shift symmetry breaking terms. The tension between BICEP2 and Planck could be due to smal…
We study the axion monodromy inflation with a non-perturbatively generated sinusoidal term. The potential form is a mixture between the natural inflation and the axion monodromy inflation potentials. The sinusoidal term is subdominant in the potential, but leaves significant effects on the resultant fluctuation generated during inflation. A larger tensor-to-scalar ratio can be obtained in our model. We study two scenarios, single inflation scenario and the double inflation scenario. In the first scenario, the axion monodromy inflation with a sufficient number of e-fold generates a larger tenso…
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 …
Natural (axionic) inflation can accommodate sizeable primordial tensor modes but suffers from the necessity of trans-Planckian variations of the inflaton field. This problem can be solved via the mechanism of aligned axions arXiv:hep-ph/0409138, where the aligned axion spirals down in the potential of other axions. We elaborate on the mechanism in view of the recently reported observations of the BICEP2 collaboration arXiv:1403.3985.
High-frequency gravitational waves from axion inflation in the weak-backreaction regime
Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
The recent BICEP2 result shows that the Universe once has gone through the vacuum with the GUT scale energy density. The implied high scale inflation nullifies the dilution idea of topological defects, strings and domain walls, of the axionic system. In particular, domain walls are disastrous if the domain wall problem with domain-wall number greater than 1 is present. We argue that the model-independent axion in string compactification with the anomalous U(1) gauge symmetry resolves the domain wall problem naturally with a symmetry principle.
We investigate the axion inflation model derived by poly-instanton effects in type II superstring theories. Poly-instanton effects are instanton effects corrected by another instanton and it can generate the modulus-axion potential with the double exponential function. Although the axion has a period of small value, this potential can have a flat region because its derivatives are exponentially suppressed by non-perturbative effects. From the view point of the cosmic inflation, such potential is interesting. In this paper, we numerically study the possibilities for realizing the cosmic inflati…
Motivated by the recently proposed Trans-Planckian Censorship Conjecture (TCC), we propose a gauged $B-L$ model of inflection-point inflation with axion dark matter. The Hubble scale during inflation ($H_{\rm inf}$) satisfies the TCC bound of $H_{\rm inf} \lesssim 1$ GeV, the axion dark matter scenario is free from the axion domain wall and isocurvature problems, and the axion decay constant can be larger than $10^{12}$ GeV. The seesaw mechanism is automatically incorporated in the model and the observed baryon asymmetry of the universe can be reproduced via resonant leptogenesis.
We propose a new type of axion inflation with complex structure moduli in the framework of type IIB superstring theory compactified on Calabi-Yau manifold. The inflaton is identified as the axion for the complex structure moduli whose potential is originating from instantonic corrections appearing through the period vector of mirror Calabi-Yau manifold. The axionic shift symmetry is broken down to the discrete one by the inclusion of instantonic correction and certain three-from fluxes. Our proposed inflation scenario is compatible with Kähler moduli stabilization. We also study a typical rehe…
We construct a simple explicit local geometry providing a `bifid throat' for 5-brane axion monodromy. A bifid throat is a throat that splits into two daughter throats in the IR, containing a homologous 2-cycle family reaching down into each daughter throat. Our example consists of a deformed $\mathbb{Z}_3\times\mathbb{Z}_2$ orbifold of the conifold, which provides us with an explicit holographic dual of the bifid throat including D3-branes and fractional 5-branes at the toric singularities of our setup. Having the holographic description in terms of the dual gauge theory allows us to address t…
The non-linear dynamics of axion inflation: a detailed lattice study
Instituto de Física Corpuscular (IFIC), Consejo Superior de Investigaciones Científicas (CSIC) and Universitat de València（粒子物理研究所（IFIC），西班牙国家科学研究委员会（CSIC）和瓦伦西亚大学）；Department of Physics, University of the Basque Country, UPV/EHU（巴斯克大学物理系）；EHU Quantum Center, University of the Basque Country UPV/EHU（巴斯克大学量子中心）
