We provide a formula for the scaling behaviour of the inflationary bispectrum in the 'squeezed' limit where one momentum becomes much smaller than the other two. This determines the scaling of the halo bias at low wavenumber and will be an important observable for the next generation of galaxy surveys. Our formula allows it to be predicted for the first time for a generic inflationary model with multiple light, canonically-normalized scalar fields.
Scale-dependent halo bias due to local primordial non-Gaussianity provides a strong test of single-field inflation. While it is universally understood that single-field inflation predicts negligible scale-dependent bias compared to current observational uncertainties, there is still disagreement on the exact level of scale-dependent bias at a level that could strongly impact inferences made from future surveys. In this paper, we clarify this confusion and derive in various ways that there is exactly zero scale-dependent bias in single-field inflation. Much of the current confusion follows from…
Multi-field models of inflation predict an inequality between the amplitude tauNL of the collapsed limit of the four-point correlator of the primordial curvature perturbation and the amplitude fNL of the squeezed limit of its three-point correlator. While a convincing detection of non-Gaussianity through the squeezed limit of the three-point correlator would rule out all single-field models, a robust confirmation or disproval of the inequality between tauNL and fNL would provide crucial information about the validity of multi-field models of inflation. In this paper, we discuss to which extent…
We consider a cosmological model in which the tensor mode becomes massive during inflation, and study the Cosmic Microwave Background (CMB) temperature and polarization bispectra arising from the mixing between the scalar mode and the massive tensor mode during inflation. The model assumes the existence of a preferred spatial frame during inflation. The local Lorentz invariance is already broken in cosmology due to the existence of a preferred rest frame. The existence of a preferred spatial frame further breaks the remaining local SO(3) invariance and in particular gives rise to a mass in the…
We calculate Large Scale Structure observables for non-Gaussianity arising from non-Bunch-Davies initial states in single field inflation. These scenarios can have substantial primordial non-Gaussianity from squeezed (but observable) momentum configurations. They generate a term in the halo bias that may be more strongly scale-dependent than the contribution from the local ansatz. We also discuss theoretical considerations required to generate an observable signature.
In this article, we show that a stochastic form of scale-dependent halo bias arises in multi-source inflationary models, where multiple fields determine the initial curvature perturbation. We derive this effect for general non-Gaussian initial conditions and study various examples, such as curvaton models and quasi-single field inflation. We present a general formula for both the stochastic and the non-stochastic parts of the halo bias, in terms of the N-point cumulants of the curvature perturbation at the end of inflation. At lowest order, the stochasticity arises if the collapsed limit of th…
We consider models of inflection point inflation. The main drawback of such models is that they suffer from the overshoot problem. Namely the initial condition should be fine tuned to be near the inflection point for the universe to inflate. We show that stringy realizations of inflection point inflation are common and offer a natural resolution to the overshoot problem.
The presence of additional particles during inflation leads to non-Gaussianity in late-time correlators of primordial curvature perturbations. The shape and amplitude of this signal depend on the mass and spin of the extra particles. Constraints on this distinct form of primordial non-Gaussianity, therefore, provide a wealth of information on the particle content during inflation. We investigate the potential of upcoming galaxy surveys in constraining such a signature through its impact on the observed galaxy power spectrum. Primordial non-Gaussianity of various shapes induces a scale-dependen…
We propose an extension of the scalaron-Higgs model by a non-minimal coupling of the Standard Model Higgs boson to the quadratic Ricci scalar resulting in a Higgs-dependent scalaron mass. The model predicts a successful stage of effective single-field Starobinsky inflation. It features a multi-field amplification mechanism leading to a peak in the inflationary power spectrum at small wavelengths which enhances the production of primordial black holes. The extended scalaron-Higgs model unifies inflationary cosmology with elementary particle physics and explains the origin of cold dark matter in…
We consider the description of the clustering of halos for physically-motivated types of non-Gaussian initial conditions. In particular we include non-Gaussianity of the type arising from single field slow-roll, multi fields, curvaton (local type), higher-order derivative-type (equilateral), vacuum-state modifications (enfolded-type) and horizon-scale GR corrections type. We show that large-scale halo bias is a very sensitive tool to probe non-Gaussianity, potentially leading, for some planned surveys, to a detection of non-Gaussianity arising from horizon-scale GR corrections. In tandem with …
A model of inflation realization driven by fermions with curvature-dependent mass is studied. Such a term is derived from the Covariant Canonical Gauge Theory of gravity (CCGG) incorporating Dirac fermions. We obtain an initial de Sitter phase followed by a successful exit, and moreover, we acquire the subsequent thermal history, with an effective matter era, followed finally by a dark-energy epoch. This behavior is a result of the effective `weakening' of gravity at early times, due to the decreased curvature-dependent fermion mass. Through the perturbation level, we obtain the scalar spectra…
Through a detailed numerical investigation in three spatial dimensions, we demonstrate that long-lived time-dependent field configurations emerge dynamically during symmetry breaking in an expanding de Sitter spacetime. We investigate two situations: a single scalar field with a double-well potential and the bosonic sector of an SU(2) non-Abelian Higgs model. For the single scalar, we show that large-amplitude oscillon configurations emerge spontaneously and persist to contribute about 1.2% of the energy density of the universe. We also show that for a range of parameters, oscillon lifetimes a…
Many models of inflation predict oscillatory features in the bispectrum of primordial fluctuations. Since it has been shown that primordial non-Gaussianity can lead to a scale-dependent halo bias, we investigate the effect of oscillations in the three-point function on the clustering of dark-matter halos. Interestingly, we find that features in the inflaton potential such as oscillations or sharp steps get imprinted in the mass dependence of the non-Gaussian halo bias. In this paper, we focus on models displaying a sharp feature in the inflaton potential as well as Resonant non-Gaussianity. In…
We consider a quasi-single field inflation model in which the inflaton interacts with a massive scalar field called the isocurvaton. Due to the breaking of time translational invariance by the inflaton background, these interactions induce kinetic mixing between the inflaton and isocurvaton, which is parameterized by a constant $μ$. We derive analytic formulae for the curvature perturbation two-, three-, four-, five-, and six-point functions explicitly in terms of the external wave-vectors in the limit where $μ$ and the mass of the isocurvaton $m$ are both much smaller than $H$. In previous wo…
With the advent of large scale galaxy surveys, constraints on primordial non-Gaussianity (PNG) are expected to reach ${\cal O}(f_\text{NL}) \sim 1$. In order to fully exploit the potential of these future surveys, a deep theoretical understanding of the signatures imprinted by PNG on the large scale structure of the Universe is necessary. In this paper, we explore the effect of a stochastic moving barrier on the amplitude of the non-Gaussian bias induced by local quadratic PNG. We show that, in the peak approach to halo clustering, the amplitude of the non-Gaussian bias will generally differ f…
In conventional model independent approaches, the power spectrum of primordial perturbations is characterized by such free parameters as spectral index, its running, the running of running, and the tensor-to-scalar ratio. In this work we, show that, at least for simple inflationary potentials, one can find the primordial scalar and tensor power spectra exactly by resumming over all the running terms. In this model-dependent method, we expand the power spectra about the pivot scale to find the series terms as functions of the e-folding number for some single field models of inflation. Interesti…
We investigate the phenomenological consequences of a modification of the initial state of a single inflationary field. While single-field inflation with the standard Bunch-Davies initial vacuum state does not generally produce a measurable three-point function (bispectrum) in the squeezed configuration, allowing for a non-standard initial state produces an exception. Here, we calculate the signature of an initial state modification in single-field slow-roll inflation in both the scale-dependent bias of the large-scale structure (LSS) and mu-type distortion in the black-body spectrum of the co…
We calculate the scale dependence of the bispectrum and trispectrum in (quasi) local models of non-Gaussian primordial density perturbations, and characterize this scale dependence in terms of new observable parameters. They can help to discriminate between models of inflation, since they are sensitive to properties of the inflationary physics that are not probed by the standard observables. We find consistency relations between these parameters in certain classes of models. We apply our results to a scenario of modulated reheating, showing that the scale dependence of non-Gaussianity can be s…
We consider a general initial state for inflation as the mechanism for generating scale-dependent hemispherical asymmetry. An observable scale-dependent non-Gaussianity is generated that leads to observable hemispherical asymmetry from the super-horizon long mode modulation. We show that the amplitude of dipole asymmetry falls off exponentially on small angular scales which can address the absence of dipole asymmetry at these scales.In addition, depending on the nature of non-vaccum initial state, the amplitude of the dipole asymmetry has oscillatory features which can be detected in a careful…
We compute analytically the dominant contribution to the tree-level bispectrum in the Starobinsky model of inflation. In this model, the potential is vacuum energy dominated but contains a subdominant linear term which changes the slope abruptly at a point. We show that on large scales compared with the transition scale $k_0$ and in the equilateral limit the analogue of the non-linearity parameter scales as $(k/k_0)^2$, that is its amplitude decays for larger and larger scales until it becomes subdominant with respect to the usual slow-roll suppressed corrections. On small scales we show that …
Oscillations in the frequency profile of the scalar-induced contribution to the stochastic gravitational wave background are a characteristic signal for small-scale features during inflation. We investigate how this oscillatory frequency profile is affected by the expansion history of the post-inflationary universe. Our results are applicable as long as the equation of state of the universe can be taken as constant during the period in which the gravitational waves are produced, and we compute the spectrum of gravitational waves induced by both sharp and resonant features, associated with osci…
A model of inflation is presented where the inflaton field is a complex scalar field coupled to a U(1) gauge field. Due to the axial symmetry of the potential, the inflation is driven by the radial direction while the angular field is gauged by U(1). Due to the coupling of the inflaton to the gauge field, a time dependent mass term for the gauge field is generated dynamically and conformal invariance is broken. We study whether a significant amount of primordial magnetic fields can be generated during inflation by allowing a time-dependent U(1) gauge kinetic coupling.
We study an inflationary model driven by a single minimally coupled standard kinetic term scalar field with a step in its mass modeled by an Heaviside step function. We present an analytical approximation for the mode function of the curvature perturbation, obtain the power spectrum analytically and compare it with the numerical result. We show that, after the scale set by the step, the spectrum contains damped oscillations that are well described by our analytical approximation. We also compute the dominant contribution to the bispectrum in the equilateral and the squeezed limits and find new…
Because the scale of inflation is conformal frame dependent, in order to fully characterize it one should quote its value in terms of all the independent equal-time dimensionless ratios in the theory. We argue that when couplings depend on the inflaton itself, one cannot calculate these ratios in terms of measurable quantities such as the tensor amplitude and the Planck mass at present. This uncertainty also becomes manifest when we try to express the (frame-dependent) inflationary scale in terms of masses that are measurable today. Although we can calculate inflationary scale in the Einstein …
We study the effects of non-trivial initial quantum states for inflationary fluctuations within the context of the effective field theory for inflation constructed by Cheung et al. which allows us to discriminate between different initial states in a model-independent way. We develop a Green's function/path integral based formulation that incorporates initial state effects and use it to address questions such as how state-dependent is the consistency relation for the bispectrum, how many e-folds beyond the minimum required to solve the cosmological fine tunings of the big bang are we allowed s…
For any physical system satisfying the Einstein's equations, the comoving curvature perturbations satisfy an equation involving the momentum-dependent effective sound speed, valid for any system with a well defined energy-stress tensor, including multi-fields models of inflation. We derive a general model-independent formula for the effective sound speed of comoving adiabatic perturbations, valid for a generic field-space metric, without assuming any approximation to integrate out entropy perturbations, but expressing the momentum-dependent effective sound speed in terms of the components of t…
In this work we study the large scale structure bias in models of anisotropic inflation. We use the Peak Background Splitting method in Excursion Set Theory to find the scale-dependent bias. We show that the amplitude of the bias is modified by a direction- dependent factor. In the specific anisotropic inflation model which we study, the scale- dependent bias vanishes at leading order when the long wavelength mode in squeezed limit is aligned with the anisotropic direction in the sky. We also extend the scale-dependent bias formulation to the general situations with primordial anisotropy. We f…
Primordial non-Gaussianity of local type is known to produce a scale-dependent contribution to the galaxy bias. Several classes of multi-field inflationary models predict non-Gaussian bias which is stochastic, in the sense that dark matter and halos don't trace each other perfectly on large scales. In this work, we forecast the ability of next-generation Large Scale Structure surveys to constrain common types of primordial non-Gaussianity like $f_{NL}$, $g_{NL}$ and $τ_{NL}$ using halo bias, including stochastic contributions. We provide fitting functions for statistical errors on these parame…
We consider the running of the spectral index as a probe of both inflation itself, and of the overall evolution of the very early universe. Surveying a collection of simple single field inflationary models, we confirm that the magnitude of the running is relatively consistent, unlike the tensor amplitude, which varies by orders of magnitude. Given this target, we confirm that the running is potentially detectable by future large scale structure or 21 cm observations, but that only the most futuristic measurements can distinguish between these models on the basis of their running. For any speci…
Following the 2015 Planck release, we briefly comment on the status and some ongoing opportunities in the interface between inflationary cosmology, string theory, and CMB data. The constraints in the $r$-$n_s$ plane introduce a new parameter into inflationary cosmology relative to the simplest quadratic inflation model, in a direction which fits well with couplings to heavy fields as occurs in string theory. The precision of the data permits further searches for and constraints on additional model-dependent features, such as oscillatory $N$-spectra, a program requiring specific theoretically m…
We consider a model of inflation consisting a single fluid with a time-dependent equation of state. In this phenomenological picture, two periods of inflation are separated by an intermediate non-inflationary stage which can be either a radiation dominated, matter dominated or kinetic energy dominated universe, respectively, with the equation of state $w=1/3$, 0 or 1. We consider the toy model in which the change in $w$ happens instantaneously. Depending on whether the mode of interest leaves the horizon before or after or between the phase transitions, the curvature power spectrum can have no…
The Hamilton-Jacobi (HJ) approach for exploring inflationary trajectories is employed in the generation of generalised inflationary non-Gaussian signals arising from single field inflation. Scale dependent solutions for $f_{NL}$ are determined via the numerical integration of the three--point function in the curvature perturbation. This allows the full exploration of single field inflationary dynamics in the out-of-slow-roll regime and opens up the possibility of using future observations of non-Gaussianity to constraint the inflationary potential using model-independent methods. The distribut…
Within the framework of inflationary model with field-dependent kinetic term for quartic and natural potentials, we investigate generation of the primordial black holes (PBHs) and induced gravitational waves (GWs). In this setup, we consider a kinetic function as $G(ϕ)=g_I(ϕ)\big(1+g_{II}(ϕ)\big)$ and show that in the presence of first term $g_I(ϕ)$ both quartic and natural potentials, in contrast to the standard model of inflation, can be consistent, with the 68\% CL of Planck observations. Besides, the second term $g_{II}(ϕ)$ can cause a significant enhancement in the primordial curvature pe…
In the primordial universe, oscillations of heavy fields can be considered as standard clocks to measure the expansion or contraction history of the universe. Those standard clocks provide a model-independent way of distinguishing inflation and alternative scenarios. However, the mass of the heavy fields may not be a constant mass, but rather mass dynamically generated by non-minimal coupling to the Ricci scalar, or self-interactions. In the case of dynamically generated mass, the mass of the heavy field is generically of order Hubble, and thus is time-dependent in alternative to inflation sce…
If the entire post-inflationary patch is large compared to our Hubble volume even a small level of non-Gaussianity can cause statistics of the primordial curvature field in our Hubble volume to be biased by mode-coupling. We explicitly compute the variation of locally measured statistics of the primordial curvature $ζ$ from non-Gaussian mode coupling within a specific inflationary scenario: the curvaton model with a quadratic curvaton potential. This "super cosmic variance" is calculated in two ways: (i) as a super observer who has access to the curvature perturbation field across the entire p…
We discuss the generation of primordial magnetic fields during inflation in the dilaton-axion electromagnetism, in which the dilaton and axion dynamics are introduced in terms of two time dependent functions of the cosmic scale factor, $I(a) F^2/4$ and $J(a) F\tilde{F}/4$, respectively, where $F$ is the electromagnetic field strength and $\tilde{F}$ is its dual. We study the form of $J(a)$ that can generate a large seed magnetic field in the weak coupling regime, $I(a)<1$. Although the $J(a)$ function is model dependent, the axion-photon coupling indeed opens up a new window for a successful i…
If cosmic inflation suffered tiny time-dependent deviations from the slow-roll regime, these would induce the existence of small scale-dependent features imprinted in the primordial spectra, with their shapes and sizes revealing information about the physics that produced them. Small sharp features could be suppressed at the level of the two-point correlation function, making them undetectable in the power spectrum, but could be amplified at the level of the three-point correlation function, offering us a window of opportunity to uncover them in the non-Gaussian bispectrum. In this article, we…
It is known that infrared (IR) quantum fluctuations in de Sitter space could break the de Sitter symmetry and generate time dependent observable effects. In this paper, we consider a dilaton-gravity theory. We find that gravitational IR effects lead to a time dependent shift on the vev of the dilaton and results in a screening (temporal) of the cosmological constant/Hubble parameter. In the Einstein frame, the effect is exponentiated and can give rises to a much more notable amount of screening. Taking the dilaton as inflaton, we obtain an inflationary expansion of the slow roll kind. This inf…
We consider whether the non-Gaussian scale-dependent halo bias can be used not only to constrain the local form of non-Gaussianity but also to distinguish among different shapes. In particular, we ask whether it can constrain the behavior of the primordial three-point function in the squeezed limit where one of the momenta is much smaller than the other two. This is potentially interesting since the observation of a three-point function with a squeezed limit that does not go like the local nor equilateral templates would be a signal of non-trivial dynamics during inflation. To this end we use …
We present constraints on how far single field inflation may depart from the familiar slow-roll paradigm. Considering a fast-roll regime while requiring a (near)-scale-invariant power spectrum introduces large self-interactions for the field and consequently large and scale-dependent non-Gaussianities. Employing this signal, we use the requirement of weak-coupling together with WMAP constraints to derive bounds on generic $P(X,ϕ)$ theories of single field inflation.
We revisit the efficiency of Schwinger mechanism in creating charged pairs during inflation. We consider a minimal setup of inflation in which the inflaton field is a complex scalar field charged under a $U(1)$ gauge field. There is a time dependent conformal coupling which pumps energy from the inflaton field to the gauge field to furnish a nearly constant background electric field energy density to drive the Schwinger mechanism. The coupling between the gauge field and the scalar field induces a time dependent effective mass for the inflaton field. The requirement of a long period of slow-ro…
During inflation, massive fields can contribute to the power spectrum of curvature perturbation via a dimension-5 operator. This contribution can be considered as a bias for the program of using $n_s$ and $r$ to select inflation models. Even the dimension-5 operator is suppressed by $Λ= M_p$, there is still a significant shift on the $n_s$-$r$ diagram if the massive fields have $m\sim H$. On the other hand, if the heavy degree of freedom appears only at the same energy scale as the suppression scale of the dimension-5 operator, then significant shift on the $n_s$-$r$ diagram takes place at $m=…
Scale-Dependent Loop Corrections to the Inflationary Power Spectrum
CERN（欧洲核子研究组织）；Imperial College London（伦敦帝国理工学院）；Laboratoire de Physique de l’École Normale Supérieure, ENS, CNRS, Université PSL, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室，ENS，法国国家科学研究中心，巴黎文理研究大学，索邦大学，巴黎西岱大学）
Inflation can be parameterized by means of truncated flow equations. In this "horizon-flow" setup, generic results have been obtained, such as typical values for $r/(1-n_\mathrm{S})$. They are sometimes referred to as intrinsic features of inflation itself. In this paper we first show that the phenomenological class of inflationary potentials sampled by horizon-flow is directly responsible for such predictions. They are therefore anything but generic. Furthermore, the horizon-flow setup is shown to rely on trajectories in phase space that differ from the slow-roll. For a given potential, we de…
We apply the effective field theory approach to quasi-single field inflation, which contains an additional scalar field with Hubble scale mass other than inflaton. Based on the time-dependent spatial diffeomorphism, which is not broken by the time-dependent background evolution, the most generic action of quasi-single field inflation is constructed up to third order fluctuations. Using the obtained action, the effects of the additional massive scalar field on the primordial curvature perturbations are discussed. In particular, we calculate the power spectrum and discuss the momentum-dependence…
We study the scale dependent bias of the halo power spectrum arising from primordial non-Gaussianity. We present an analytic result of the halo bias including up to the trispectrum contributions. We find the scale dependent bias opens a new possibility of probing the relation between the non-linearity parameters $\fnl$ and $\tnl$.
Long-short mode coupling during inflation, encoded in the squeezed bispectrum of curvature perturbations, induces a dependence of the local, small-scale power spectrum on long-wavelength perturbations, leading to a scale-dependent halo bias. While this scale dependence is absent in the large-scale limit for single-field inflation models that satisfy the consistency relation, certain models such as resonant non-Gaussianity show a peculiar behavior on intermediate scales. We reconsider the predictions for the halo bias in this model by working in Conformal Fermi Coordinates, which isolate the ph…
We investigate influences of the curved field-space metric of multi-field inflationary models on the squeezed bispectrum. The reduced bispectrum in squeezed limit is computed using the δN formalism. The calculation is performed under the slow-roll approximation and assumption that field derivative of the field-space metric is sufficiently small such that the contributions from Riemann tensor of the field-space can be approximately ignored. Based on these approximations, We compute the analytic expressions for the reduced bispectrum in squeezed limit, and find that, for such a nearly flat field…
Single field inflationary models predict nearly Gaussian initial conditions and hence a detection of non-Gaussianity would be a signature of the more complex inflationary scenarios. In this paper we study the effect on the cosmic microwave background and on large scale structure from primordial non-Gaussianity in a two-field inflationary model in which both the inflaton and curvaton contribute to the density perturbations. We show that in addition to the previously described enhancement of the galaxy bias on large scales, this setup results in large-scale stochasticity. We provide joint constr…
In the Higgs inflation scenario the Higgs field is strongly coupled to the Ricci scalar in order to drive primordial inflation. However, in its original form in pure metric formulation of gravity, the ultraviolet (UV) cutoff of the Higgs interactions and the Hubble rate are of the same magnitude, and this makes the whole inflationary evolution dependent of the unknown UV completion of the Higgs sector. This problem, the unitarity violation, plagues the Higgs inflation scenario. In this letter we show that, in the Palatini formulation of gravitation, Higgs inflation does not suffer from unitari…
We investigate Natural Inflation with non-minimal coupling to gravity, characterized either by a quadratic or a periodic term, within the Warm Inflation paradigm during the slow roll stage, in both strong and weak dissipation limits, and show that, in the case of $T$-linearly dependent dissipative term, it can accommodate the spectral index $n_s$ and tensor-to-scalar ratio $r$ observables given by Planck 2018 constraints, albeit with a too small value of the e-folding number to solve the horizon problem, providing thus only a partial solution to Natural Inflation issues. Assuming a $T$-cubical…
We propose a novel mechanism for enhancing the primordial gravitational waves without significantly affecting the curvature perturbations produced during inflation. This is achieved due to non-linear sourcing of resonantly amplified scalar field fluctuations. Our result is an explicit scale-dependent counter-example of the famous Lyth bound, which opens up a promising perspective of producing detectable inflationary tensor modes with low-scale inflation and a sub-Planckian field excursion. We explicitly demonstrate the testability of our mechanism with upcoming Cosmic Microwave Background B-mo…
