Sufficient Inflation Research Articles

Chaotic inflationary universe in Rastall gravity

We study Linde’s chaotic inflation in Rastall gravity with a homogeneous scalar field. In Einstein’s general theory of relativity, Linde obtained chaotic scenario, which emerged from chaotic distribution of scalar field satisfying a limiting value of the initial scalar field ϕo > 3 MP that lies in the quantum gravity. The upper limit on the initial scalar field is obtained for a sufficient inflation to encompass the present universe. In the Rastall gravity, the upper limit is reduced depending on the Rastall parameter γ < 1. The upper limit on ϕo is found to increases for [Formula: see text]. In the later case, sufficient inflation is not permitted and the role of curvaton field is explored for an acceptable early chaotic inflation.

Transfer Patterns and Clinical Applications of the Forehead Flaps Based on the Supratrochlear Artery and Supraorbital Artery.

This study aimed to describe the application of transferring preexpanded forehead flaps based on the supratrochlear and supraorbital arteries in 3 patterns for facial reconstruction: Pattern I, interpolated flap; Pattern II, island flap; and Pattern III, propeller flap, which was subdivided into direct propeller flap (Pattern IIIa) and indirect propeller flap (Pattern IIIb). During the first stage, a tissue expander was inserted underneath the forehead. After sufficient inflation of the expander, a forehead flap based on the supratrochlear or supraorbital artery was elevated and transferred to reconstruct the facial defects. Three weeks after the surgery, pedicle division was performed, in which Pattern I and Pattern IIIb flaps were used. Twenty-four patients underwent facial reconstruction. Twenty-three flaps survived without any perfusion-related complications. Venous congestion developed in an island flap. All patients were followed up after surgery, ranging from 2 to 156 (mean, 19) months. The color and texture of the flap matched those of the adjacent skin. The patients and their families were satisfied with the final functional and esthetic outcomes. The forehead flap based on the supratrochlear and supraorbital arteries provides reliable coverage of facial defects. The conventional interpolated flap continues to be the most dependable. Single-stage reconstruction using the island flap and direct propeller flap is applicable to patients who decline the pedicle division procedure. The novel technique of using the indirect propeller flap is safe for cheek reconstruction with minimal donor-site morbidity and esthetically pleasing results.

Sideburn Reconstruction Using a Pre-Expanded Island Scalp Flap Based on the Parietal Branch of Superficial Temporal Vessels.

Sideburns are crucial for head and face esthetics. Absence of sideburns is associated with physical and psychological consequences. Many methods have been described for sideburn reconstruction; however, characteristics of the ideal method include optimal vascularization, ideal hair density, natural hair growth, and facial symmetry with minimum donor-site morbidity. In this study, the authors describe a novel method of sideburn reconstruction using a pre-expanded island scalp flap based on the parietal branch of the superficial temporal artery. Between February 2012 and December 2020, 9 patients underwent sideburn reconstruction surgery that involved 2 stages. During the first stage, an appropriately sized tissue expander was inserted underneath the scalp. After sufficient inflation of the expander, at the second stage, an island scalp flap based on the parietal branch of the superficial temporal vessels was elevated to reconstruct the sideburns. The mean size of the defects was 8 × 4.4 cm (range, 6 × 3-12 × 5 cm), whereas the average flap dimension was 10.22 × 5.67 cm (range, 8 × 4-13 × 8 cm). All flaps survived completely without any perfusion-related complications. Patients were followed up after surgery, ranging from 4 to 34 months (mean, 15.67 months). All patients and/or their parents were satisfied with the final appearance in terms of hair density, hair growth direction, and facial symmetry. Although a 2-stage procedure, this novel technique allows the reconstruction of a new sideburn with natural growth and orientation of the hair and minimal morbidity for patients.

Large and small field inflation from hyperbolic sigma models

Long standing themes in inflation include the issue of large field vs. small field inflation as well as the question what fraction of phase space leads to sufficient inflation and furthermore is compatible with the experimental data. In the present paper, these issues are discussed in the context of modular inflation, a specialization of the framework of automorphic nonlinear $\ensuremath{\sigma}$ models associated to homogeneous spaces $G/K$ in which the continuous shift symmetry group $G$ is weakly broken to discrete subgroups $\mathrm{\ensuremath{\Gamma}}$. The target spaces of these theories inherit a curved structure from the group $G$, which in the case of modular invariant inflation leads to a hyperbolic field space geometry. It is shown that in this class of models the symmetry structure leads to both large and small field inflationary trajectories within a single modular inflation model. The present paper analyzes the concrete model of $j$-inflation, a hyperbolic model with nontrivial inflaton interactions. It describes in some detail the structure of the initial conditions, including a systematic analysis of several phenomenological functions on the target space, leading to constraints on the curvature scalar of the field space by upcoming experiments, as well as a discussion of the scaling behavior of the spectral index, the finite volume fraction of the field space leading to sufficient inflation, the attractor behavior of $j$-inflation, and a comparison of inflaton trajectories vs. target space geodesics. The tensor-ratio analysis shows that $j$-inflation is an interesting target for upcoming ground and satellite experiments.

Inflation in a scalar–vector–tensor theory

In this work, we study inflation in a particular scalar-vector-tensor theory of gravitation without the $U(1)$ gauge symmetry. The model is constructed from the more general action introduced in Heisenberg et al. (Phys Rev D 98:024038, 2018) using certain specific choices for the Lagrangians and the coupling functions. Also, for this model we build the explicit form for the action, and from it, we derive the general equations: the energy-momentum tensor and the equations of motion, and using the flat FLRW background, we have analyzed if it's possible to obtain an inflationary regime with it. Additionally, using particular choices for the potential, the coupling functions, suitable dimensionless coupling constants and initial conditions, it was possible verify numerically that this model of inflation is viable. In this sense, we could verify that the introduction of the coupling function $f(\phi)$ in our model of inflation, allows us to reach a suitable amount of $e$-foldings $N$ for sufficient inflation. This is a remarkable result, since without the coupling function contribution, the amount of $e$-foldings is smaller at the end of inflation, as has been demonstrated in Heisenberg et al. (2018). Also, the no-ghosts and stability conditions that the model during inflation must satisfy, i.e., absence of ghosts and Laplacian instabilities of linear cosmological perturbations were obtained, furthermore these conditions were verified numerically too.

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.

Finite measure for the initial conditions of inflation

We investigate whether inflation requires finely tuned initial conditions in order to explain the degree of flatness and homogeneity observed in the Universe. We achieve this by using the Eisenhart lift, which can be used to write any scalar field theory in a purely geometric manner. Using this formalism, we construct a manifold whose points represent all possible initial conditions for an inflationary theory. After equipping this manifold with a natural metric, we show that the total volume of this manifold is finite for a wide class of inflationary potentials. Hence, we identify a natural measure that enables us to distinguish between generic and finely tuned sets of initial conditions without the need for a regulator, in contrast to previous work in the literature. Using this measure, we find that the initial conditions that allow for sufficient inflation are indeed finely tuned. The degree of fine-tuning also depends crucially on the value of the cosmological constant at the time of inflation. Examining the example potential $V=\lambda\varphi^4+\Lambda$, we find that we require percent-level fine tuning if we allow the cosmological constant during inflation to be much larger than it is today. However, if we fix the cosmological constant to its presently observed value, the degree of fine tuning required is of order $10^{-29}$.

Inflation driven by massive vector fields with derivative self-interactions

Inspired by the Generalized Proca Theory, we study a vector–tensor model of inflation with massive vector fields and derivative self-interactions. The action under consideration contains a usual Maxwell-like kinetic term, a general potential term and a term with nonminimal derivative coupling between the vector field and gravity, via the dual Riemann tensor. In this theory, the last term contains a free parameter, [Formula: see text], which quantifies the nonminimal derivative coupling. In this scenario, taking into account a spatially flat Friedmann–Robertson–Walker (FRW) universe and a general vector field, we obtain the general expressions for the equation of motion and the total energy–momentum tensor. Choosing a Proca-type potential, a suitable inflationary regimen driven by massive vector fields is studied. In this model, the isotropy of expansion is guaranteed by considering a triplet of orthogonal vector fields. In order to obtain an inflationary solution with this model, the quasi de Sitter expansion was considered. In this case, the vector field behaves as a constant. Finally, slow-roll analysis is performed and slow-roll conditions are defined for this model, which, for suitable constraints of the model parameters, can give the required number of e-folds for sufficient inflation.

Initial conditions for inflation in an FRW universe

We examine the class of initial conditions which give rise to inflation. Our analysis is carried out for several popular models including: Higgs inflation, Starobinsky inflation, chaotic inflation, axion monodromy inflation and non-canonical inflation. In each case we determine the set of initial conditions which give rise to sufficient inflation, with at least $60$ e-foldings. A phase-space analysis has been performed for each of these models and the effect of the initial inflationary energy scale on inflation has been studied numerically. This paper discusses two scenarios of Higgs inflation: (i) the Higgs is coupled to the scalar curvature, (ii) the Higgs Lagrangian contains a non-canonical kinetic term. In both cases we find Higgs inflation to be very robust since it can arise for a large class of initial conditions. One of the central results of our analysis is that, for plateau-like potentials associated with the Higgs and Starobinsky models, inflation can be realised even for initial scalar field values which lie close to the minimum of the potential. This dispels a misconception relating to plateau potentials prevailing in the literature. We also find that inflation in all models is more robust for larger values of the initial energy scale.

Inflation with an antisymmetric tensor field

We investigate the possibility of inflation with models of antisymmetric tensor field having minimal and nonminimal couplings to gravity. Although the minimal model does not support inflation, the nonminimal models, through the introduction of a nonminimal coupling to gravity, can give rise to stable de-Sitter solutions with a bound on the coupling parameters. The values of field and coupling parameters are sub-planckian. Slow roll analysis is performed and slow-roll parameters are defined which can give the required number of e-folds for sufficient inflation. Stability analysis has been performed for perturbations to antisymmetric field while keeping the metric unperturbed, and it is found that only the sub-horizon modes are free of ghost instability for de-Sitter space.

WKB approximation for a deformed Schrodinger-like equation and its applications to quasinormal modes of black holes and quantum cosmology

In this paper, we use the WKB approximation method to approximately solve a deformed Schrodinger-like differential equation: [−ħ2∂ξ2g2(−iħα∂ξ)−p2(ξ)]ψ(ξ)=0, which are frequently dealt with in various effective models of quantum gravity, where the parameter α characterizes effects of quantum gravity. For an arbitrary function g(x) satisfying several properties proposed in the paper, we find the WKB solutions, the WKB connection formulas through a turning point, the deformed Bohr–Sommerfeld quantization rule, and the deformed tunneling rate formula through a potential barrier. Several examples of applying the WKB approximation to the deformed quantum mechanics are investigated. In particular, we calculate the bound states of the Pöschl–Teller potential and estimate the effects of quantum gravity on the quasinormal modes of a Schwarzschild black hole. Moreover, the area quantum of the black hole is considered via Bohr's correspondence principle. Finally, the WKB solutions of the deformed Wheeler–DeWitt equation for a closed Friedmann universe with a scalar field are obtained, and the effects of quantum gravity on the probability of sufficient inflation is discussed in the context of the tunneling proposal.

Cosmological perturbations in transient phantom inflation scenarios

We present a model of inflation where the inflaton is accommodated as a phantom field which exhibits an initial transient pole behavior and then decays into a quintessence field which is responsible for a radiation era. We must stress that the present unified model only deals with a single field and that the transition between the two eras is achieved in a smooth way, so the model does not suffer from the eternal inflation issue. We explore the conditions for the crossing of the phantom divide line within the inflationary era along with the structural stability of several critical points. We study the behavior of the phantom field within the slow-climb approximation along with the necessary conditions to have sufficient inflation. We also examine the model at the level of classical perturbations within the Newtonian gauge and determine the behavior of the gravitational potential, contrast density and perturbed field near the inflation stage and the subsequent radiation era.

Can Germany save itself from negative rates?

German inflation looks set to rise in response to diminishing slack in the economy. But this will be a mixed blessing for those in Germany hit by negative policy rates and ECB asset purchases. Higher German inflation may eliminate the need for further ECB policy action, but it is unlikely to trigger imminent rate hikes. As a result, the rise in inflation will merely lower real interest rates for German savers. Structural cross‐country differences mean that the ECB is better able to hit its inflation target when the peripheral economies rather than Germany are the region's growth engine. A key reason for this is that the German Phillips curve is flat by Eurozone standards, meaning that policymakers need to work hard to generate sufficient inflation in Germany to offset sustained weakness elsewhere. Despite this, there is evidence to suggest that the tightening labour market is beginning to push German wage growth higher. And if productivity growth remains subdued, this will lead to faster unit labour cost growth. While firms could respond by lowering their margins, the strength of household spending suggests that firms may be more inclined than in the past to pass on higher costs to consumers. In all, we expect German inflation to rise more sharply than elsewhere to around 2% in 2017, meaning that the ECB will not unveil further unconventional policy support. But it would take much sharper rises in German wage growth and inflation than in our baseline forecast to prompt the ECB to bring forward interest rate rises.

Sub-Planckian two-field inflation consistent with the Lyth bound

The BICEP2 observation of a large tensor-to-scalar ratio, r = 0.20+0.07-0.05, implies that the inflaton ϕ in single-field inflation models must satisfy ϕ ∼ 10MPl in order to produce sufficient inflation. This is a problem if interaction terms suppressed by the Planck scale impose a bound ϕ ≲ MPl. Here we consider whether it is possible to have successful sub-Planckian inflation in the case of two-field inflation. The trajectory in field space cannot be radial if the effective single-field inflaton is to satisfy the Lyth bound. By considering a complex field Φ, we show that a near circular but aperiodic modulation of a |Φ|4 potential can reproduce the results of ϕ2 chaotic inflation for ns and r while satisfying |Φ| ≲ 0.01 MPl throughout. More generally, for models based on a |Φ|4 potential, the simplest sub-Planckian models are equivalent to ϕ2 and ϕ4/3 chaotic inflation.

O Mercado de Ações no Brasil antes do Índice Bovespa

O trabalho descreve a disponibilidade de índices de mercado de ações e títulos públicos de renda fixa no período de 1950 a 1967, antes da criação do Ibovespa. Retornos nominais mensais são calculados, levando à determinação do prêmio histórico por risco de mercado, chegando-se à média mensal de 1,86% ao mês, contra 1,69% ao mês no período de janeiro de 1968 a outubro de 2013. Os retornos dos dois segmentos são ajustados pela variação do Índice Geral de Preços – Disponibilidade Interna (IGP-DI), e é constatado que, no período anterior a janeiro de 1968, os dois tipos de ativo não protegeram o investidor contra a inflação. A principal contribuição deste estudo, porém, é o fornecimento de acesso público a arquivo contendo as séries de valores dos dois tipos de índices, acrescentando mais de 17 anos de dados às séries básicas utilizadas na análise do mercado brasileiro de capitais.

No-boundary measure and preference for large e-foldings in multi-field inflation

The no-boundary wavefunction of quantum gravity usually assigns only very small probability to long periods of inflation. This was a reason to doubt about the no-boundary wavefunction to explain the observational universe. We study the no-boundary proposal in the context of multi-field inflation to see whether the number of fields changes the situation. For a simple model, we find that indeed the no-boundary wavefunction can give higher probability for sufficient inflation, but the number of fields involved Nf has to be very high, e.g., Nf ≃ m−2.

Exploring a string-like landscape

We explore inflationary trajectories within randomly-generated two-dimensional potentials, considered as a toy model of the string landscape. Both the background and perturbation equations are solved numerically, the latter using the two-field formalism of Peterson and Tegmark which fully incorporates the effect of isocurvature perturbations. Sufficient inflation is a rare event, occurring for only roughly one in 105 potentials. For models generating sufficient inflation, we find that the majority of runs satisfy current constraints from WMAP. The scalar spectral index is less than 1 in all runs. The tensor-to-scalar ratio is below the current limit, while typically large enough to be detected by next-generation CMB experiments and perhaps also by Planck. In many cases the inflationary consistency equation is broken by the effect of isocurvature modes.

Gauge field back-reaction in Born–Infeld cosmologies

In this paper, we investigate the back-reaction of U(1) gauge fields into a specific class of inflationary settings. To be more precise, we employ a Bianchi-I geometry (taken as an anisotropic perturbation of a flat FRW model) within two types of Born–Infeld (BI) theories. First, we consider pure Born–Infeld electromagnetism. For either a constant or a b(ϕ) coupling, inflationary trajectories are modified but anisotropies increase. In particular, for the former coupling we find that a quadratic inflaton potential, within a constant ratio for the scalar and gauge energy densities, does not induce sufficient inflation, while in the latter, the back-reaction in the cosmology determines (from the tensor–scalar ratio) a narrow range where inflation can occur. A Dirac–Born–Infeld framework is analysed afterwards in both non-relativistic and relativistic regimes. In the former, for different cases of the coupling (richer with respect to mere BI setups) between scalar and gauge sectors, we find that inflationary trajectories are modified, with anisotropy increasing or decreasing. In particular, a tachyonic solution is studied, allowing for a nonstandard ratio between scalar and gauge matter densities, enhancing sufficient inflation, but with the anisotropy increasing. For the relativistic limit, inflationary trajectories are also modified and anisotropies increase faster than in the non-relativistic limit. Finally we discuss how magnetic seed fields could evolve in these settings.

Avoiding the blue spectrum and the fine-tuning of initial conditions in hybrid inflation

Hybrid inflation faces two well-known problems: the blue spectrum of the nonsupersymmetric version of the model and the fine-tuning of the initial conditions of the fields leading to sufficient inflation to account for the standard cosmological problems. They are investigated by studying the exact two-fields dynamics instead of assuming slow-roll. When the field values are restricted to be less than the reduced Planck mass, a non-negligible part of the initial condition space (around 15% depending on potential parameters) leads to successful inflation. Most of it is located outside the usual inflationary valley and organized in continuous patterns instead of being isolated as previously found. Their existence is explained and their properties are studied. This shows that no excessive fine-tuning is required for successful hybrid inflation. Moreover, by extending the initial condition space to Planckian-like or super-Planckian values, inflation becomes generically sufficiently long and can produce a red-tilted scalar power spectrum due to slow-roll violations. The robustness of these properties is confirmed by conducting our analysis on three other models of hybrid-type inflation in various framework: ``smooth'' and ``shifted'' inflation in SUSY and SUGRA, and ``radion assisted'' gauge inflation. A high percentage of successful inflation for smooth hybrid inflation (up to 80%) is observed.

Inflation with hyperbolic potential in the braneworld model

In this paper we study inflationary dynamics with a scalar field in an inverse coshyperbolic potential in the braneworld model. We note that a sufficient inflation may be obtained with the potential considering slow-roll approximation in the high energy limit. We determine the minimum values of the initial inflaton field required to obtain sufficient inflation and also determine the relevant inflationary parameters. The numerical values of spectral index of the scalar perturbation spectrum are determined by varying the number of e-foldings for different initial values of the inflaton field. The result obtained here is in good agreement with the current observational limits.