Seeding primordial black holes in multifield inflation
Gonzalo A. Palma, Spyros Sypsas, Cristobal Zenteno
备注：
7 pages, 1 figure; v2: added clarifications around the analytic solution and references. Version accepted in PRL; v3: typo corrected, matches published version
The inflationary origin of primordial black holes (PBHs) relies on a large enhancement of the power spectrum $Δ_ζ$ of the curvature fluctuation $ζ$ at wavelengths much shorter than those of the cosmic microwave background anisotropies. This is typically achieved in models where $ζ$ evolves without interacting significantly with additional (isocurvature) scalar degrees of freedom. However, quantum gravity inspired models are characterized by moduli spaces with highly curved geometries and a large number of scalar fields that could vigorously interact with $ζ$ (as in the cosmological collider picture). Here we show that isocurvature fluctuations can mix with $ζ$ inducing large enhancements of its amplitude. This occurs whenever the inflationary trajectory experiences rapid turns in the field space of the model leading to amplifications that are exponentially sensitive to the total angle swept by the turn, which induce characteristic observable signatures on $Δ_ζ$. We derive accurate analytical predictions and show that the large enhancements required for PBHs demand non-canonical kinetic terms in the action of the multifield system.
We investigate the primordial trispectra of the general multifield DBI inflationary model. In contrast with the single field model, the entropic modes can source the curvature perturbations on the super horizon scales, so we calculate the contributions from the interaction of four entropic modes mediating one adiabatic mode to the trispectra, at the large transfer limit ($T_{RS}\gg1$). We obtained the general form of the 4-point correlation functions, plotted the shape diagrams in two specific momenta configurations, "equilateral configuration" and "specialized configuration". Our figures show…
We explain the motivation and main idea of our work in reference arXiv:0907.2476 [hep-th]. We present a simple model of multifield Dirac-Born-Infeld inflation whose bispectrum exhibits a linear combination of the equilateral and local shapes, which are usually considered as separate possibilities. We also point out the presence of a particularly interesting component of the primordial trispectrum.
Realistic models of high-energy physics include multiple scalar fields. Renormalization requires that the fields have nonminimal couplings to the spacetime Ricci curvature scalar, and the couplings can be large at the energy scales of early-universe inflation. The nonminimal couplings induce a nontrivial field-space manifold in the Einstein frame, and they also yield an effective potential in the Einstein frame with nontrivial curvature. The ridges or bumps in the Einstein-frame potential can lead to primordial non-Gaussianities of observable magnitude. We develop a covariant formalism to stud…
If forthcoming measurements of cosmic photon polarization restrict the primordial tensor-to-scalar ratio to $r < 0.01$, small field inflation will be a principal candidate for the origin of the universe. Here we show that small multifield inflation, without the hybrid mechanism, typically results in large squeezed nongaussianity. Small multifield potentials contain multiple flat field directions, often identified with the gauge invariant field directions in supersymmetric potentials. We find that unless these field directions have equal slopes, large nongaussianity arises. After identifying re…
Future galaxy surveys promise to probe local primordial non-Gaussianity at unprecedented precision, $σ(f_{\rm NL}) \lesssim 1$. We study the implications for multifield inflation by considering spectator models, where inflation is driven by the inflaton field, but the primordial perturbations are (partially) generated by a second, spectator field. We perform an MCMC likelihood analysis using Planck data to study quantitative predictions for $f_{\rm NL}$ and other observables for a range of such spectator models. We show that models where the primordial perturbations are dominated by the specta…
Primordial black holes (PBHs) provide an exciting prospect for accounting for dark matter. In this paper, we consider inflationary models that incorporate realistic features from high-energy physics -- including multiple interacting scalar fields and nonminimal couplings to the spacetime Ricci scalar -- that could produce PBHs with masses in the range required to address the present-day dark matter abundance. Such models are consistent with supersymmetric constructions, and only incorporate operators in the effective action that would be expected from generic effective field theory considerati…
Realistic models of particle physics include many scalar fields. These fields generically have nonminimal couplings to the Ricci curvature scalar, either as part of a generalized Einstein theory or as necessary counterterms for renormalization in curved background spacetimes. We develop a gauge-invariant formalism for calculating primordial perturbations in models with multiple nonminimally coupled fields. We work in the Jordan frame (in which the nonminimal couplings remain explicit) and identify two distinct sources of entropy perturbations for such models. One set of entropy perturbations a…
We study a cosmological scenario in which the DBI action governing the motion of a D3-brane in a higher-dimensional spacetime is supplemented with an induced gravity term. The latter reduces to the quartic Galileon Lagrangian when the motion of the brane is non-relativistic and we show that it tends to violate the null energy condition and to render cosmological fluctuations ghosts. There nonetheless exists an interesting parameter space in which a stable phase of quasi-exponential expansion can be achieved while the induced gravity leaves non trivial imprints. We derive the exact second-order…
We study the post-inflation dynamics of multifield models involving nonminimal couplings using lattice simulations to capture significant nonlinear effects like backreaction and rescattering. We measure the effective equation of state and typical time-scales for the onset of thermalization, which could affect the usual mapping between predictions for primordial perturbation spectra and measurements of anisotropies in the cosmic microwave background radiation. For large values of the nonminimal coupling constants, we find efficient particle production that gives rise to nearly instantaneous pre…
It is becoming increasingly clear that large but rare fluctuations of the primordial curvature field, controlled by the tail of its probability distribution, could have dramatic effects on the current structure of the universe -- {\it e.g.} via primordial black-holes. However, the use of standard perturbation theory to study the evolution of fluctuations during inflation fails in providing a reliable description of how non-linear interactions induce non-Gaussian tails. Here, we use the stochastic inflation formalism to study the non-perturbative effects from multi-field fluctuations on the sta…
We study the multifield inflationary models where the cosmological perturbation is sourced by light scalar fields other than the inflaton. We exploit the operator product expansion and partly the symmetries present during the de Sitter epoch to characterize the non-Gaussian four-point correlator in the squeezed limit. We point out that the contribution to it from the intrinsic non-Gaussianity of the light fields at horizon crossing can be larger than the usually studied contribution arising on superhorizon scales and it comes with a different shape. Our findings indicate that particular attent…
Connected $N$-point amplitudes in quantum field theory are enhanced by a factor of $N!$ in appropriate regimes of kinematics and couplings, but the non-perturbative analysis of this for collider physics applications is subtle. We resolve this question for $N$-point correlation functions of cosmological perturbations in multifield inflation, and comment on its application to primordial non-Gaussianity. We find that they are calculably $N!$-enhanced using a simple model for the mixing of the field sectors which leads to a convolution of their probability distributions. This effect leads to model…
We compute the super-Hubble evolution of non-Gaussianity of primordial curvature perturbations in two-field inflation models by employing two formalisms: delta N and covariant formalisms. Although two formalisms treat the evolution of fluctuations radically different, we show that the formulas of f_{NL} parameter agree quantitatively with each other within 1 % accuracy. We analytically find that the amplitude of f_{NL} decays no faster than a^{-3} as the inflationary trajectory reaches to the adiabatic limit for generic potentials.
We study the structure of two-point correlators of the inflationary field fluctuations in order to improve the accuracy and efficiency of the existing methods to calculate primordial spectra. We present a description motivated by the separation of the fast and slow evolving components of the spectrum which is based on Cholesky decomposition of the field correlator matrix. Our purpose is to rewrite all the relevant equations of motion in terms of slowly varying quantities. This is important in order to consider the contribution from high-frequency modes to the spectrum without affecting computa…
Multifield models of inflation with nonminimal couplings are in excellent agreement with the recent results from {\it Planck}. Across a broad range of couplings and initial conditions, such models evolve along an effectively single-field attractor solution and predict values of the primordial spectral index and its running, the tensor-to-scalar ratio, and non-Gaussianities squarely in the observationally most-favored region. Such models also can amplify isocurvature perturbations, which could account for the low power recently observed in the CMB power spectrum at low multipoles. Future measur…
We study the effects of perturbative reheating on the evolution of the curvature perturbation ζ, in two-field inflation models. We use numerical methods to explore the sensitivity of f_NL, n_s and r to the reheating process, and present simple qualitative arguments to explain our results. In general, if a large non-Gaussian signal exists at the start of reheating, it will remain non zero at the end of reheating. Unless all isocurvature modes have completely decayed before the start of reheating, we find that the non-linearity parameter, f_NL, can be sensitive to the reheating timescale, and th…
Light Scalar Fields Foster Production of Primordial Black Holes
University of Manitoba（曼尼托巴大学）；University of Winnipeg（温尼伯大学）；Santa Cruz Institute for Particle Physics（圣克鲁兹粒子物理研究所）；University of California, Santa Cruz（加利福尼亚大学圣克鲁兹分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of Toronto（多伦多大学）；Massachusetts Institute of Technology（麻省理工学院）
Higgs inflation is a simple and elegant model in which early-universe inflation is driven by the Higgs sector of the Standard Model. The Higgs sector can support early-universe inflation if it has a large nonminimal coupling to the Ricci spacetime curvature scalar. At energies relevant to such an inflationary epoch, the Goldstone modes of the Higgs sector remain in the spectrum in renormalizable gauges, and hence their effects should be included in the model's dynamics. We analyze the multifield dynamics of Higgs inflation and find that the multifield effects damp out rapidly after the onset o…
We study multifield contributions to the scalar power spectrum in an ensemble of six-field inflationary models obtained in string theory. We identify examples in which inflation occurs by chance, near an approximate inflection point, and we compute the primordial perturbations numerically, both exactly and using an array of truncated models. The scalar mass spectrum and the number of fluctuating fields are accurately described by a simple random matrix model. During the approach to the inflection point, bending trajectories and violations of slow roll are commonplace, and 'many-field' effects,…
Primordial black holes (PBHs) that form in the early Universe in the modified Affleck-Dine (AD) mechanism of baryogenesis should have intrinsic log-normal mass distribution of PBHs. We show that the parameters of this distribution adjusted to provide the required spatial density of massive seeds ($\ge 10^4 M_\odot$) for early galaxy formation and not violating the dark matter density constraints, predict the existence of the population of intermediate-mass PBHs with a number density of $\sim 1000$~Mpc$^{-3}$. We argue that the population of intermediate-mass AD PBHs can also seed the formation…
We show that a scalar excited state with large occupation numbers during inflation leads to an enhancement of tensor modes and a characteristic pattern of order-one oscillations in the associated stochastic gravitational wave background (SGWB) sourced during inflation. An effective excited state, i.e. a departure from the Bunch-Davies vacuum, can emerge dynamically as the result of a transient non-adiabatic evolution, e.g. a sharp feature along the inflationary history. We provide an explicit example in a multifield context where the sharp feature triggering the excited state is identified wit…
Recent studies of inflation with multiple scalar fields have highlighted the importance of non-canonical kinetic terms in novel types of inflationary solutions. This motivates a thorough analysis of non-Gaussianities in this context, which we revisit here by studying the primordial bispectrum in a general two-field model. Our main result is the complete cubic action for inflationary fluctuations written in comoving gauge, i.e. in terms of the curvature perturbation and the entropic mode. Although full expressions for the cubic action have already been derived in terms of fields fluctuations in…
We consider a two-dimensional model of inflation, where the inflationary trajectory is "deformed" by a grazing encounter with an Extra Species/Symmetry Point (ESP) after the observable cosmological scales have left the Hubble radius. The encounter entails a sudden production of particles, whose backreaction causes a bending of the trajectory and a temporary decrease in speed, both of which are sensitive to initial conditions. This "modulated" effect leads to an additional contribution to the curvature perturbation, which can be dominant if the encounter is close. We compute associated non-Gaus…
We study the background dynamics and primordial perturbation in $α$-attractor-type double inflation. The model is composed of two minimally coupled scalar fields, where each of the fields has a potential of the $α$-attractor type. We find that the background trajectory in this double inflation model is given by two almost straight lines connected with a turn in the field space. With this simple background, we can classify the property of the perturbations generated in this double inflation model just depending on whether the turn occurs before the horizon exit for the mode corresponding to the…
Recent measurements by the {\it Planck} experiment of the power spectrum of temperature anisotropies in the cosmic microwave background radiation (CMB) reveal a deficit of power in low multipoles compared to the predictions from best-fit $Λ$CDM cosmology. The low-$\ell$ anomaly may be explained by the presence of primordial isocurvature perturbations in addition to the usual adiabatic spectrum, and hence may provide the first robust evidence that early-universe inflation involved more than one scalar field. In this paper we explore the production of isocurvature perturbations in nonminimally c…
We have conducted extensive lattice simulations to study the post-inflation dynamics of multifield models involving nonminimal couplings. We explore the parameter dependence of preheating in these models and describe the various time-scales that control such nonlinear processes as energy transfer, re-scattering, and the approach to radiation-domination and thermalization. In the limit of large nonminimal couplings ($ξ_I \sim 100$), we find that efficient transfer of energy from the inflaton condensate to radiative degrees of freedom, emergence of a radiation-dominated equation of state, and th…
We show that the prediction for the primordial tensor power spectrum cannot be modified at leading order in derivatives. Indeed, one can always set to unity the speed of propagation of gravitational waves during inflation by a suitable disformal transformation of the metric, while a conformal one can make the Planck mass time-independent. Therefore, the tensor amplitude unambiguously fixes the energy scale of inflation. Using the Effective Field Theory of Inflation, we check that predictions are independent of the choice of frame, as expected. The first corrections to the standard prediction c…
While cosmological inflation can erase primordial inhomogeneities, it is possible that inflation may not begin in a significantly inhomogeneous universe. This issue is particularly pressing in multifield scenarios, where even the homogeneous dynamics may depend sensitively on the initial configuration. This paper presents an initial survey of the onset of inflation in multifield models, via qualitative lattice-based simulations that do not include local gravitational backreaction. Using hybrid inflation as a test model, our results suggest that small subhorizon inhomogeneities do play a key ro…
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 study the formation of primordial black holes and the generation of gravitational waves in a class of cosmological models that are direct supersymmetric analogs of the observationally favored nonminimally coupled Higgs inflation model. It is known that this type of model naturally includes multiple scalar fields which may be regarded as the inflaton. For the sake of simplicity we focus on the case where the inflaton field space is two dimensional. We analyze the multifield dynamics and find the region of parameters that gives copious production of primordial black holes that may comprise a …
The origin of the seeds which develop into the observed super-massive black holes at high redshifts may be hard to interpret in the context of the standard $ΛCDM$ of early universe cosmology based on Gaussian primordial perturbations. Here we consider the modification of the halo mass function obtained by introducing skewness and kurtosis of the primordial fluctuations. We show that such primordial non-Gaussianities constrained by the current observational bounds on the nonlinearity parameters of $f_{NL}$ and $g_{NL}$ are not effective at greatly increasing the number density of seeds which co…
We prove that, in a generic single-field model, the consistency relation for the 3-point function in the squeezed limit receives corrections that vanish quadratically in the ratio of the momenta, i.e. as (k_L/k_S)^2. This implies that a detection of a bispectrum signal going as 1/k_L^2 in the squeezed limit, that is suppressed only by one power of k_L compared with the local shape, would rule out all single-field models. The absence of this kind of terms in the bispectrum holds also for multifield models, but only if all the fields have a mass much smaller than H. The detection of any scale de…
The hypermagnetic helicity density at the electroweak phase transition (EWPT) exceeds many orders of magnitude the galactic magnetic helicity density. Together with previous magnetic helicity evolution calculations after the EWPT and hypermagnetic helicity conversion to the magnetic one at the EWPT, the present calculation completes the description of the evolution of this important topological feature of cosmological magnetic fields. It suggests that if the magnetic field seeding the galactic dynamo has a primordial origin, it should be substantially helical. This should be taken into account…
We report first study of complex field inflation. Although understood as a specific two-field inflation, a complex field inflation is able to make more robust model predictions on primordial curvature perturbation. Explicitly we discuss the model realizations of complex chaotic and exponential inflation in various large-field contexts. Both complex field models contain a single complex scalar together with only two free parameters. Using numerical handles aimed to calculate primordial curvature perturbation from multifield inflation, we show that both models are compatible with current Planck …
One-loop renormalization of the effective field theory of inflationary fluctuations from gravitational interactions
New York University（纽约大学）；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）
Using the most recent data from the WMAP, ACT and SPT experiments, we update the constraints on models with oscillatory features in the primordial power spectrum of scalar perturbations. This kind of features can appear in models of inflation where slow-roll is interrupted, like multifield models. We also derive constraints for the case in which, in addition to cosmic microwave observations, we also consider the data on the spectrum of luminous red galaxies from the 7th SDSS catalog, and the SNIa Union Compilation 2 data. We have found that: (i) considering a model with features in the primord…
We study the cosmology of the multifield relativistic Galileon model in which an induced gravity term is added to the Dirac-Born-Infeld action. We highlight the physical insight that is gained by employing a bimetric perspective in which the induced gravity and Einstein-Hilbert action are treated on equal footing. We derive the conditions under which a phase of quasi exponential inflation can be sustained and demonstrate the existence of a critical background energy density above which cosmological fluctuations become ghosts. At the non-linear level, this scenario provides the first concrete e…
