Single-field Models Research Articles

Constant roll inflation in multifield models

Constant roll inflation is analyzed in the presence of multi scalar fields which are assumed to be described by a constant roll rate each. The different cases are studied and the corresponding potentials are reconstructed. The exact solutions are obtained, which show a similar behaviour to the single scalar field model. For one of the cases analyzed in the paper, the so-called adiabatic field also constant rolls while entropy perturbations become null, while the second case may lead to non-adiabatic perturbations. Both cases can fit well the Planck data by assuming the appropriate values for the free parameters of the models.

Crystal field model simulations of magnetic response of pairs, triplets and quartets of Mn3+ ions in GaN

A ferromagnetic coupling between localized Mn spins was predicted in a series of ab initio and tight binding calculations and experimentally verified for the dilute magnetic semiconductor Ga1−x Mn x N. In the limit of small Mn concentrations, x ≲ 0.01, the paramagnetic properties of this material were successfully described using a single ion crystal field model approach. In order to obtain the description of magnetization in (Ga,Mn)N in the presence of interacting magnetic centers, we extend the previous model of a single substitutional Mn3+ ion in GaN by considering pairs, triplets and quartets of Mn3+ ions coupled by a ferromagnetic superexchange interaction. Using this approach we investigate how the magnetic properties, particularly the magnitude of the uniaxial anisotropy field, change as the number of magnetic Mn3+ ions in a given cluster increases from 1 to 4. Our simulations are then exploited in explaining experimental magnetic properties of Ga1−x Mn x N with x ≅ 0.03, where the presence of small magnetic clusters gains in significance. As a result the approximate lower and upper limits for the values of exchange couplings between Mn3+ ions in GaN, being in nearest neighbors (nns) J nn and next nns J nnn positions, respectively, are established.

Small-scale primordial fluctuations in the 21 cm Dark Ages signal

ABSTRACT Primordial black hole production in the mass range $10\!-\!10^4 \, {\rm M_\odot}$ is motivated respectively by interpretations of the LIGO/Virgo observations of binary black hole mergers and by their ability to seed intermediate black holes that would account for the presence of supermassive black holes at very high redshift. Their existence would imply a boost in the primordial power spectrum if they were produced by overdensities reentering the horizon and collapsing after single-field inflation. This, together with their associated Poisson fluctuations would cause a boost in the matter power spectrum on small scales. The extra power could become potentially observable in the 21 cm power spectrum on scales around $k\sim 0.1\!-\!50\, {\rm Mpc^{-1}}$ with the new generation of filled low-frequency interferometers. We explicitly include the contribution from primordial fluctuations in our prediction of the 21 cm signal that has been previously neglected, by constructing primordial power spectra motivated by single-field models of inflation that would produce extra power on small scales. We find that depending on the mass and abundance of primordial black holes, it is important to include this contribution from the primordial fluctuations, so as not to underestimate the 21 cm signal. Evidently our predictions of detectability, which lack any modelling of foregrounds, are unrealistic, but we hope that they will motivate improved cleaning algorithms that can enable us to access this intriguing corner of primordial black hole-motivated parameter space.

Swampland, trans-Planckian censorship and fine-tuning problem for inflation: tunnelling wavefunction to the rescue

The trans-Planckian censorship conjecture implies that single-field models of inflation require an extreme fine-tuning of the initial conditions due to the very low-scale of inflation. In this work, we show how a quantum cosmological proposal—namely the tunneling wavefunction—naturally provides the necessary initial conditions without requiring such fine-tunings. More generally, we show how the tunneling wavefunction can provide suitable initial conditions for hilltop inflation models, the latter being typically preferred by the swampland constraints.

Evaluation of the Impact of Rainfall Inputs on Urban Rainfall Models: A Systematic Review

Over the past several decades, urban flooding and other water-related disasters have become increasingly prominent and serious. Although the urban rain flood model’s benefits for urban flood simulation have been extensively documented, the impact of rainfall input to model simulation accuracy remains unclear. This systematic review aims to provide structured research on how rain inputs impact urban rain flood model’s simulation accuracy. The selected 48 peer-reviewed journal articles published between 2015 and 2019 on the Web of Science™ database were analyzed by key factors, including rainfall input type, calibration times and verification times. The results from meta-analysis reveal that when a traditional rain measurement was used as the rainfall input, model simulation accuracy was higher, i.e., the Nash–Sutcliffe efficiency coefficient (NSE) of traditional technology for rain measurement was higher than the 0.18 for the new technology rain measurement with respect to flow simulation. In addition, the single-field sub-flood calibration model was better than the multi-field sub-flood calibration model. NSE was higher than 0.14. The precision was better for the verification period; NSE of the calibration value showed a 0.07 higher verification value on average in flow simulation. These findings have certain significance for the development of future urban rain flood models and propose the development direction of the future urban rain flood model. Finally, in view of the rainfall input problem of the urban storm flood model, we propose the future development direction of the urban storm flood model.

Planck2018 results

We analyse thePlanckfull-mission cosmic microwave background (CMB) temperature andE-mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and optimal modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following final results:fNLlocal= −0.9 ± 5.1;fNLequil= −26 ± 47; andfNLortho= −38 ± 24 (68% CL, statistical). These results include low-multipole (4 ≤ ℓ < 40) polarization data that are not included in our previous analysis. The results also pass an extensive battery of tests (with additional tests regarding foreground residuals compared to 2015), and they are stable with respect to our 2015 measurements (with small fluctuations, at the level of a fraction of a standard deviation, which is consistent with changes in data processing). Polarization-only bispectra display a significant improvement in robustness; they can now be used independently to set primordial NG constraints with a sensitivity comparable to WMAP temperature-based results and they give excellent agreement. In addition to the analysis of the standard local, equilateral, and orthogonal bispectrum shapes, we consider a large number of additional cases, such as scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The non-primordial lensing bispectrum is, however, detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5σ. Beyond estimates of individual shape amplitudes, we also present model-independent reconstructions and analyses of thePlanckCMB bispectrum. Our final constraint on the local primordial trispectrum shape isgNLlocal= (−5.8 ± 6.5) × 104(68% CL, statistical), while constraints for other trispectrum shapes are also determined. Exploiting the tight limits on various bispectrum and trispectrum shapes, we constrain the parameter space of different early-Universe scenarios that generate primordial NG, including general single-field models of inflation, multi-field models (e.g. curvaton models), models of inflation with axion fields producing parity-violation bispectra in the tensor sector, and inflationary models involving vector-like fields with directionally-dependent bispectra. Our results provide a high-precision test for structure-formation scenarios, showing complete agreement with the basic picture of the ΛCDM cosmology regarding the statistics of the initial conditions, with cosmic structures arising from adiabatic, passive, Gaussian, and primordial seed perturbations.

Generating primordial features at large scales in two field models of inflation

We investigate the generation of features at large scales in the primordial power spectrum (PPS) when inflation is driven by two scalar fields. In canonical single field models of inflation, these features are often generated due to deviations from the slow-roll regime. While deviations from slow-roll can be naturally achieved in two field models due to a sharp turn in the trajectory in the field space, features at the largest scales of the types suggested by CMB temperature anisotropies are more difficult to achieve in models involving two canonical scalar fields due to the presence of isocurvature fluctuations. We show instead that a coupling between the kinetic terms of the scalar fields can easily produce such features. We discuss models whose theoretical predictions are consistent with current observations and highlight the implications of our results.

Primordial black holes as dark matter and gravitational waves from single-field polynomial inflation

We consider the possibility that the majority of dark matter in our Universe consists of black holes of primordial origin. We determine the conditions under which such black holes may have originated from a single-field model of inflation characterized by a quartic polynomial potential. We also explore the effect of higher-dimensional operators. The large power spectrum of curvature perturbations that is needed for a large black hole abundance sources sizable second order tensor perturbations. The resulting stochastic background of primordial gravitational waves could be detected by the future space-based observatories LISA and DECIGO or—as long as we give up on the dark matter connection—by the ground-based Advanced LIGO-Virgo detector network.

Inflationary equilibrium configurations of scalar-tensor theories of gravity

In this paper we investigate the asymptotic dynamics of inflationary cosmological models that are based in scalar-tensor theories of gravity. Our main aim is to explore the global structure of the phase space in the framework of single-field inflation models. For this purpose we make emphasis in the adequate choice of the variables of the phase space. Our results indicate that, although single-field inflation is generic in the sense that the corresponding critical point in the phase space exists for a wide class of potentials, along given phase space orbits -- representing potential cosmic histories -- the occurrence of the inflationary stage is rather dependent on the initial conditions. We have been able to give quantitative estimates of the relative probability (RP) for initial conditions leading to slow-roll inflation. For the non-minimal coupling model with the $\phi^2$-potential our rough estimates yield to an almost vanishing relative probability: $10^{-13}\,\%\lesssim RP\ll 10^{-8}\,\%$. These bonds are greatly improved in the scalar-tensor models, including the Brans-Dicke theory, where the relative probability $1\,\%\lesssim RP\leq 100\,\%$. Hence slow-roll inflation is indeed a natural stage of the cosmic expansion in Brans-Dicke models of inflation. It is confirmed as well that the dynamics of vacuum Brans-Dicke theories with arbitrary potentials are non-chaotic.

Scalaron-Higgs inflation

In scalaron-Higgs inflation the Standard Model Higgs boson is non-minimally coupled to gravity and the Einstein-Hilbert action is supplemented by the quadratic scalar curvature invariant. For the quartic Higgs self-coupling λ fixed at the electroweak scale, we find that the resulting inflationary two-field model effectively reduces to a single field model with the same predictions as in Higgs inflation or Starobinsky inflation, including the limit of a vanishing non-minimal coupling. For the same model, but with the scalar field a priori not identified with the Standard Model Higgs boson, we study the inflationary consequences of an extremely small λ. Depending on the initial conditions for the inflationary background trajectories, we find that the two-field dynamics either again reduces to an effective single-field model with a larger tensor-to-scalar ratio than predicted in Higgs inflation and Starobinsky inflation, or involves the full two-field dynamics and leads to oscillatory features in the inflationary power spectrum. Finally, we investigate under which conditions the inflationary scenario with extremely small λ can be realized dynamically by the Standard Model renormalization group flow and discuss how the scalaron-Higgs model can provide a natural way to stabilize the electroweak vacuum.

Simple supergravity model of inflation constrained with Planck 2018 data

We study a model of inflation based on $\mathcal{N}=1$ supergravity essentially depending on one effective parameter. Under a field transformation we show that this model turns out to be equivalent to a previously studied supergravity model known to be ruled out with the original choice of the parameter. Such parameter measures the slope of the potential at observable scales. Through a Bayesian parameter estimation, it is shown how this model is compatible with recent CMB temperature measurements by {\it Planck 2018} giving rise to a simple, viable, single field model of inflation. The tensor to scalar ratio constraint is found to be $r_{0.002}<0.065$ with negative running. We discuss how observables are invariant under the field transformation which leaves unaltered the slow-roll parameters. As a consequence the use of one presentation of the model or its field-transformed version is purely a matter of convenience.

Reheating after swampland conjecture

The evolution of the universe started from a hot and dense Big Bang point. Temperature fluctuation map of cosmic microwave background (CMB) radiation and initial seeds of large scale structures (LSS) are explained by an inflationary period in a very early time. Inflaton as quanta of the inflation field is responsible for the accelerated expansion of the universe. Potentials of the self-interacting single field models are constrained by observational data as well as quantum gravity. Some forms of the potential are rolled out by data of Planck satellite and some of them by quantum gravity constraints. In the standard model of inflation or cold inflation firstly universe expands where the inflaton rolls the nearly flat part of the potential and in the second part, the universe reheats where the inflaton oscillates around the minimum of the potential which leads to thermalized radiation dominated universe. String theory as the best model of quantum gravity forbids the oscillation around the minimum of the potential during the thermalized epoch of the reheating. But in the warm model of inflation thermalization happens during the accelerated expansion of the universe where the inflaton rolls nearly steep potential and the universe will be radiation dominated without any separated reheating epoch.

Primordial black holes from the preheating instability in single-field inflation

After the end of inflation, the inflaton field oscillates around a local minimum of its potential and decays into ordinary matter. These oscillations trigger a resonant instability for cosmological perturbations with wavelengths that exit the Hubble radius close to the end of inflation. In this paper, we study the formation of Primordial Black Holes (PBHs) at these enhanced scales. We find that the production mechanism can be so efficient that PBHs subsequently dominate the content of the universe and reheating proceeds from their evaporation. Observational constraints on the PBH abundance also restrict the duration of the resonant instability phase, leading to tight limits on the reheating temperature that we derive. We conclude that the production of PBHs during reheating is a generic and inevitable property of the simplest inflationary single-field models, and does not require any fine tuning of the inflationary potential.

Measuring bias via the consistency relations of the large scale structure

Consistency Relations (CR) for the Large Scale Structure are exact equalities between correlation functions of different order. These relations descend from the equivalence principle and hold for primordial perturbations generated by single-field models of inflation. They are not affected by nonlinearities and hold also for biased tracers and in redshift space. We show that Baryonic Acoustic Oscillations (BAO) in the bispectrum (BS) in the squeezed limit are suppressed with respect to those in the power spectrum (PS) by a coefficient that depends on the BS configuration and on the bias parameter (and, in redshift space, also on the growth rate). We test these relations using large volume N-body simulations and show that they provide a novel way to measure large scale halo bias and, potentially, the growth rate. Since bias is obtained by comparing two directly observable quantities, the method is free from theoretical uncertainties both on the computational scheme and on the underlying cosmological model.

Are primordial black holes produced by entropy perturbations in single field inflationary models?

We show that in single field inflationary models the super-horizon evolution of curvature perturbations on comoving slices ℛ, which can cause the production of primordial black holes (PBH), is not due to entropy perturbations, but to the background evolution effect on the conversion between entropy and curvature perturbations. We derive a general relation between the time derivative of comoving curvature perturbations and entropy perturbations, in terms of a conversion factor depending on the background evolution. Contrary to previous results derived in the uniform density gauge assuming the gradient term can be neglected on super-horizon scales, the relation is valid on any scale for any minimally coupled single scalar field model, also on sub-horizon scales where gradient terms are large. We apply it to the case of quasi-inflection inflation, showing that while entropy perturbations are decreasing, ℛ can grow on super-horizon scales, due to a large increase of the conversion factor. This happens in the time interval during which a sufficiently fast decrease of the equation of state w transforms into a growing mode what in slow-roll models would be a decaying mode. The same mechanism also explains the super-horizon evolution of ℛ in globally adiabatic systems, for which entropy perturbations vanish on any scale, such as ultra slow roll inflation and its generalizations.

From Minkowski to de Sitter in multifield no-scale models

ABSTRACTWe show the uniqueness of superpotentials leading to Minkowski vacua of single-field no-scale supergravity models, and the construction of dS/AdS solutions using pairs of these single-field Minkowski superpotentials. We then extend the construction to two- and multifield no-scale supergravity models, providing also a geometrical interpretation. We also consider scenarios with additional twisted or untwisted moduli fields, and discuss how inflationary models can be constructed in this framework.

Superpotential method for chiral cosmological models connected with modified gravity

We consider the Chiral Cosmological Models (CCMs) and modified gravity theories associated with them. Generalization of the superpotential method for a general CCM with several scalar fields is performed, and the method of construction CCMs admitting exact solutions is developed. New classes of exact solutions in the two-component CCM connected with an $f(R)$ gravity model with an additional scalar field have been constructed. We construct new cosmological solutions for a diagonal metric of the target space, including modified power-law solutions. In particular, we propose the reconstruction procedure based on the superpotential method and present examples of kinetic part reconstruction for periodic and hyperbolic Hubble parameters. We also focus on a cyclic type of Universe dubbed the Quasi-Steady State (QSS) model, with the aim of constructing single- and double-field potentials for one and the same behaviour of the Hubble parameter using the developed superpotential method for the CCM. The realization of this task includes a new set of solutions for a CCM with a scale factor characterized by the QSS theory. We also propose a method for reducing the two-field CCM to the single scalar field model.

Onset of inflation amid backreaction from inhomogeneities

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 $(\varphi (t_0), \dot{\varphi} (t_0))$, where $\varphi$ is the vacuum expectation value of the quantized field that drives inflation. Although some regions of $(\varphi (t_0), \dot{\varphi} (t_0))$ that would have yielded sufficient inflation in the absence of inhomogeneities fail to do so when backreaction from inhomogeneities is incorporated, an equal volume of such regions succeeds in producing sufficient inflation which did not do so in the absence of inhomogeneities. For large-field models, in other words, the total volume of the space of initial conditions $(\varphi (t_0), \dot{\varphi} (t_0))$ that yields sufficient inflation is {\it conserved} when we incorporate nonlinear backreaction from inhomogeneities, compared to the case in which inhomogeneities are neglected.

Hyperbolic field space and swampland conjecture for DBI scalar

We study a model of two scalar fields with a hyperbolic field space and show that it reduces to a single-field Dirac-Born-Infeld (DBI) model in the limit where the field space becomes infinitely curved. We apply the de Sitter swampland conjecture to the two-field model and take the same limit. It is shown that in the limit, all quantities appearing in the swampland conjecture remain well-defined within the single-field DBI model. Based on a consistency argument, we then speculate that the condition derived in this way can be considered as the de Sitter swampland conjecture for a DBI scalar field by its own. The condition differs from those proposed in the literature and only the one in the present paper passes the consistency argument. As a byproduct, we also point out that one of the inequalities in the swampland conjecture for a multi-field model with linear kinetic terms should involve the lowest mass squared for scalar perturbations and that this quantity can be significantly different from the lowest eigenvalue of the Hessian of the potential in the local orthonormal frame if the field space is highly curved. Finally, we propose an extension of the de Sitter swampland conjecture to a more general scalar field with the Lagrangian of the form P(X,φ), where X=−(∂φ)2/2.

Primordial perturbations and non-gaussianities in Hořava-Lifshitz gravity * * Partly supported by the Chinese National Youth Thou-sand Talents Program (71000-41180003)

We investigate primordial perturbations and non-gaussianities in the Hořava-Lifshitz theory of gravitation. In the UV limit, the scalar perturbation in the Hořava theory is naturally scale-invariant, ignoring the details of the expansion of the Universe. One may thus relax the exponential inflation and the slow-roll conditions for the inflaton field. As a result, it is possible that the primordial non-gaussianities, which are " slow-roll suppressed” in the standard scenarios, become large. We calculate the non-gaussianities from the bispectrum of the perturbation and find that the equilateral-type non-gaussianity is of the order of unity, while the local-type non-gaussianity remains small, as in the usual single-field slow-roll inflation model in general relativity. Our result is a new constraint on Hořava-Lifshitz gravity.