Showing papers on "Scalar potential published in 2016"
TL;DR: In this article, a tight-binding model of 8mmn$ borophene, a two-dimensional boron crystal, was developed and the authors confirmed that the crystal hosts massless Dirac fermions and the Dirac points are protected by symmetry.
Abstract: A tight-binding model of 8-$Pmmn$ borophene, a two-dimensional boron crystal, is developed. We confirm that the crystal hosts massless Dirac fermions and the Dirac points are protected by symmetry. Strain is introduced into the model, and it is shown to induce a pseudomagnetic field vector potential and a scalar potential. The dependence of the potentials on the strain tensor is calculated. The physical effects controlled by the pseudomagnetic field are discussed.
118 citations
TL;DR: In this article, analytical vacuum stability or bounded from below conditions for general scalar potentials of a few fields are discussed. But the authors focus on the general potential of two real scalars, without and with the Higgs boson.
Abstract: We calculate analytical vacuum stability or bounded from below conditions for general scalar potentials of a few fields. After a brief review of copositivity, we show how to find positivity conditions for more complicated potentials. We discuss the vacuum stability conditions of the general potential of two real scalars, without and with the Higgs boson included in the potential. As further examples, we give explicit vacuum stability conditions for the two Higgs doublet model with no explicit CP breaking, and for the $$\mathbb {Z}_{3}$$
scalar dark matter with an inert doublet and a complex singlet. We give a short overview of positivity conditions for tensors of quartic couplings via tensor eigenvalues.
112 citations
TL;DR: In this article, the authors discuss the implications of the weak gravity conjecture for general models of large-field inflation with a large number of axions N. They show that, from a bottom-up perspective, such models admit a variety of different regimes for the enhancement of the effective axion decay constant, depending on the amount of alignment and the number of instanton terms that contribute to the scalar potential.
Abstract: In this note, we discuss the implications of the weak gravity conjecture (WGC) for general models of large-field inflation with a large number of axions N. We first show that, from the bottom-up perspective, such models admit a variety of different regimes for the enhancement of the effective axion decay constant, depending on the amount of alignment and the number of instanton terms that contribute to the scalar potential. This includes regimes of no enhancement, power-law enhancement and exponential enhancement with respect to N. As special cases, we recover the Pythagorean enhancement of N-flation, the N and N
3/2 enhancements derived by Bachlechner, Long and McAllister and the exponential enhancement by Choi, Kim and Yun. We then analyze which top-down constraints are put on such models from the requirement of consistency with quantum gravity. In particular, the WGC appears to imply that the enhancement of the effective axion decay constant must not grow parametrically with N for N ≫ 1. On the other hand, recent works proposed that axions might be able to violate this bound under certain circumstances. Our general expression for the enhancement allows us to translate this possibility into a condition on the number of instantons that couple to the axions. We argue that, at large N , models consistent with quantum gravity must either allow super-Planckian field excursions or have an enormous, possibly even exponentially large, number of dominant instanton terms in the scalar potential.
106 citations
TL;DR: In this paper, the authors consider type II string compactifications on Calabi-Yau orientifolds with fluxes and D-branes, and analyse the F-term scalar potential that simultaneously involves closed and open string modes.
Abstract: We consider type II string compactifications on Calabi-Yau orientifolds with fluxes and D-branes, and analyse the F-term scalar potential that simultaneously involves closed and open string modes. In type IIA models with D6-branes this potential can be directly computed by integrating out Minkowski three-forms. The result shows a multi-branched structure along the space of lifted open string moduli, in which discrete shifts in special Lagrangian and Wilson line deformations are compensated by changes in the RR flux quanta. The same sort of discrete shift symmetries are present in the superpotential and constrain the Kahler potential. As for the latter, inclusion of open string moduli breaks the factorisation between complex structure and Kahler moduli spaces. Nevertheless, the 4d Kahler metrics display a set of interesting relations that allow to rederive the scalar potential analytically. Similar results hold for type IIB flux compactifications with D7-brane Wilson lines.
99 citations
TL;DR: In this article, the authors give analytical vacuum stability or bounded below conditions for general scalar potentials of a few fields, without and with the Higgs boson included in the potential, and give explicit vacuum stability conditions for the two Higgs doublet model with no explicit CP breaking.
Abstract: We find analytical vacuum stability or bounded below conditions for general scalar potentials of a few fields. After a brief review of copositivity we go beyond it. We discuss the vacuum stability conditions of the general potential of two real scalars, without and with the Higgs boson included in the potential. As further examples, we give explicit vacuum stability conditions for the two Higgs doublet model with no explicit CP breaking, and for the $\mathbb{Z}_{3}$ scalar dark matter with an inert doublet and a complex singlet. We give a short overview of positivity conditions for tensors of quartic couplings via tensor eigenvalues. A Mathematica notebook with the conditions is included with the source files.
86 citations
TL;DR: In this article, an extension of the Starobinsky model, whose parameters are functions of an extra scalar field, is considered and the scalar potential has a flat direction with respect to mixing scalaron with another (matter) scalar fields.
Abstract: We consider an extension of the Starobinsky model, whose parameters are functions of an extra scalar field. Our motivation is to test the robustness (or sensitivity) of the Starobinsky inflation against mixing scalaron with another (matter) scalar field. We find that the extended Starobinsky model is (classically) equivalent to the two-field inflation, with the scalar potential having a flat direction. For the sake of fully explicit calculations, we perform a numerical scan of the parameter space. Our findings support the viability of the Starobinsky-like two-field inflation for a certain range of its parameters, which is characterized by the scalar index $$n_s=0.96\pm 0.01$$
, the tensor-to-scalar ratio $$r<0.06$$
, and a small running of the scalar index at $$|\alpha _s|<0.05$$
.
74 citations
TL;DR: In this paper, the energy levels of a massive spinless particle coupled covariantly to a homogeneous magnetic field parallel to the string were computed in the spacetime induced by a rotating cosmic string.
Abstract: In the spacetime induced by a rotating cosmic string we compute the energy levels of a massive spinless particle coupled covariantly to a homogeneous magnetic field parallel to the string. Afterwards, we consider the addition of a scalar potential with a Coulomb-type and a linear confining term and completely solve the Klein–Gordon equations for each configuration. Finally, assuming rigid-wall boundary conditions, we find the Landau levels when the linear defect is itself magnetized. Remarkably, our analysis reveals that the Landau quantization occurs even in the absence of gauge fields provided the string is endowed with spin.
73 citations
TL;DR: In this article, a renormalization group study of the scalar potential in a minimal U(1) B−L extension of the Standard Model involving one extra heavier Higgs and three heavy right-handed neutrinos with family universal B-L charge assignments is presented.
Abstract: We present a renormalization group study of the scalar potential in a minimal U(1)
B−L
extension of the Standard Model involving one extra heavier Higgs and three heavy right-handed neutrinos with family universal B-L charge assignments. We implement a type-I seesaw for the masses of the light neutrinos of the Standard Model. In particular, compared to a previous study, we perform a two-loop extension of the evolution, showing that two-loop effects are essential for the study of the stability of the scalar potential up to the Planck scale. The analysis includes the contribution of the kinetic mixing between the two abelian gauge groups, which is radiatively generated by the evolution, and the one-loop matching conditions at the electroweak scale. By requiring the stability of the potential up to the Planck mass, significant constraints on the masses of the heavy neutrinos, on the gauge couplings and the mixing in the Higgs sector are identified.
55 citations
TL;DR: In this paper, the energy levels of a massive spinless particle coupled covariantly to a homogeneous magnetic field parallel to the string were computed in the spacetime induced by a rotating cosmic string.
Abstract: In the spacetime induced by a rotating cosmic string we compute the energy levels of a massive spinless particle coupled covariantly to a homogeneous magnetic field parallel to the string. Afterwards, we consider the addition of a scalar potential with a Coulomb-type and a linear confining term and completely solve the Klein-Gordon equations for each configuration. Finally, assuming rigid-wall boundary conditions, we find the Landau levels when the linear defect is itself magnetized. Remarkably, our analysis reveals that the Landau quantization occurs even in the absence of gauge fields provided the string is endowed with spin.
54 citations
17 Aug 2016
TL;DR: In this article, the Galerkin method was applied to the Jiles-Atherton Scalar Models to solve the problem of scalar hypersteresis in the precisach's Scalar Model.
Abstract: Statics and Quasi-Statics Electromagnetics - Brief Presentation Introduction The Maxwell Equations The Maxwell Equations: Local Form The Maxwell Equations: Integral Form The Maxwell Equations in Low Frequency The Electrostatics Magnetostatic Fields Magnetic Materials Inductance and Mutual Inductance Magnetodynamic Fields Fields Defined by Potentials Final Considerations References Ferromagnetic Materials and Iron Losses Introduction Basic Concepts Losses Components Iron Losses under Alternating, Rotating and DC Biased Inductions Final Considerations References Scalar Hysteresis Modeling Introduction The Preisach's Scalar Model The Jiles-Atherton Scalar Model Final Considerations References Vector Hysteresis Modeling Introduction Vector Model Obtained with the Superposition of Scalar Models Vector Generalizations of the Jiles-Atherton Scalar Models Some Remarks Concerning the Vector Behavior of Hysteresis Final Considerations References Brief Presentation of the Finite Element Method Introduction The Galerkin Method: Basic Concepts using Real Coordinates Generalization of the FEM: Using Reference Coordinates Numerical Integration Some Finite Elements Using Edge Elements References Using Nodal Elements with Magnetic Vector Potential Introduction Main Equations Applying Galerkin Method Uniqueness of the Solution the Coulomb's Gauge Implementation Example and Comparisons Final Considerations References The Source-Field Method for 3D Magnetostatic Fields Introduction The Magnetostatic Case - Scalar Potential The Magnetostatic Case - Vector Potential Implementation Aspects and Conventions Computational Implementation Example and Results References The Source-Field Method for 3D Magnetodynamic Fields Introduction Formulation Considering Eddy Currents - Time Stepping Formulation Considering Eddy Currents - Complex Formulation Field-Circuit Coupling Computational Implementation The Differential Permeability Method Example and Results References A Matrix-Free Iterative Solution Procedure for Finite Element Problems Introduction The Classical FEM: T-Scheme The Proposed Technique: N-Scheme Implementation Convergence Implementation of N-Scheme with SOR Applying Non-Stationary Iterative Solver to the N-Scheme CG Algorithm Implementation Examples and Results Results and Discussion References
53 citations
TL;DR: In this article, a finite-temperature diagrammatic perturbation theory of third-harmonic generation in doped graphene is presented, which can be easily generalized to other materials and to include many-body effects.
Abstract: We present a finite-temperature diagrammatic perturbation theory of third-harmonic generation in doped graphene. We carry out calculations of the third-order conductivity in the scalar potential gauge, highlighting a subtle cancellation between a Fermi surface contribution, which contains only power laws, and power-law contributions of interband nature. Only logarithms survive in the final result. We conclude by presenting quantitative results for the upconversion efficiency at zero and finite temperature. Our approach can be easily generalized to other materials and to include many-body effects.
TL;DR: In this article, the authors investigated the chiral phase transition in the soft-wall model of AdS/QCD at zero chemical potential for two-flavor and threeflavor cases, respectively.
Abstract: We investigate the chiral phase transition in the soft-wall model of AdS/QCD at zero chemical potential for two-flavor and three-flavor cases, respectively. We show that there is no spontaneous chiral symmetry breaking in the original soft-wall model. After detailed analysis, we find that in order to realize chiral symmetry breaking and restoration, both profiles for the scalar potential and the dilaton field are essential. The scalar potential determines the possible solution structure of the chiral condensate, except the mass term, it takes another quartic term for the two-flavor case, and for the three-flavor case, one has to take into account an extra cubic term due to the t’Hooft determinant interaction. The profile of the dilaton field reflects the gluodynamics, which is negative at a certain ultraviolet scale and approaches positive quadratic behavior at far infrared region. With this set-up, the spontaneous chiral symmetry breaking in the vacuum and its restoration at finite temperature can be realized perfectly. In the two-flavor case, it gives a second order chiral phase transition in the chiral limit, while the transition turns to be a crossover for any finite quark mass. In the case of three-flavor, the phase transition becomes a first order one in the chiral limit, while above sufficient large quark mass it turns to be a crossover again. This scenario agrees exactly with the current understanding on chiral phase transition from lattice QCD and other effective model studies.
TL;DR: In this paper, a half-space containing saturated porous transversely isotropic material under surface tractions is analyzed for boundary value problem in terms of some line integrals that are evaluated numerically.
TL;DR: In this article, a minimally coupled scalar field with arbitrary potential in a FLRW metric is presented, which is made possible due to the existence of a nonlocal integral of motion corresponding to the conformal Killing field of the two-dimensional minisuperspace metric.
Abstract: We present the solution space for the case of a minimally coupled scalar field with arbitrary potential in a FLRW metric. This is made possible due to the existence of a nonlocal integral of motion corresponding to the conformal Killing field of the two-dimensional minisuperspace metric. The case for both spatially flat and non flat are studied first in the presence of only the scalar field and subsequently with the addition of non interacting perfect fluids. It is verified that this addition does not change the general form of the solution, but only the particular expressions of the scalar field and the potential. The results are applied in the case of parametric dark energy models where we derive the scalar field equivalence solution for some proposed models in the literature.
TL;DR: In this article, the authors studied the possibility that the Higgs field experienced a first order phase transition at the high energy scale due to couplings with scalar fields, and estimated the amount of gravitational waves produced by the phase transition.
Abstract: In a wide class of new physics models, there exist scalar fields that obtain vacuum expectation values of high energy scales. We study the possibility that the standard model Higgs field has experienced first order phase transition at the high energy scale due to the couplings with these scalar fields. We estimate the amount of gravitational waves produced by the phase transition, and discuss observational consequences.
TL;DR: In this article, the in-medium behavior of mesons at finite temperature and baryon chemical potential within a soft-wall model of AdS/QCD was investigated.
Abstract: We investigate the in-medium behavior of mesons at finite temperature and baryon chemical potential within a soft-wall model of AdS/QCD. We use a quartic scalar potential to obtain the correct form of chiral symmetry breaking. At zero quark mass, the chiral phase transition is second order, becoming a crossover at physical quark mass. At zero baryon chemical potential, we find a chiral transition temperature of 155 MeV in the chiral limit and a pseudotransition temperature of 151 MeV at physical quark mass, consistent with lattice results. In the low-temperature limit, the second-order transition occurs at a baryon chemical potential of 566 MeV while the rapid crossover occurs at 559 MeV. A new parametrization of the dilaton profile results in improved meson spectra. Meson melting occurs at a lower temperature and chemical potential than the chiral phase transition, so the vector-axial vector mass splitting remains constant until the bound states melt.
TL;DR: In this paper, the scalar potential of the coset representative of a nonlinear sigma model was studied and the integrability conditions of the Killing spinor equations were analyzed.
TL;DR: In this article, the authors consider classically scale-invariant theories with non-minimally coupled scalar fields and show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg potential.
Abstract: We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale invariance is spontaneously broken. In these theories, however, the Planck mass becomes unstable in the presence of explicit sources of scale invariance breaking, such as non-relativistic matter and cosmological constant terms. We quantify the constraints on such classical models from Big Bang Nucleosynthesis that lead to an upper bound on the non-minimal coupling and require trans-Planckian field values. We show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg potential. The time-averaged motion of the evolving fixed point is strongly suppressed, thus the limits on the evolving gravitational constant from Big Bang Nucleosynthesis and other measurements do not presently constrain this class of theories. Field oscillations around the fixed point, if not damped, contribute to the dark matter density of the Universe.
TL;DR: In this article, the authors present fully dynamical solutions to Einstein-scalar theory in asymptotically anti-de Sitter spacetime with a scalar potential containing particularly rich physics.
Abstract: We present fully dynamical solutions to Einstein-scalar theory in asymptotically anti–de Sitter spacetime with a scalar potential containing particularly rich physics. Depending on one parameter in the potential, we find an especially interesting regime, which exhibits a dynamically unstable black brane, already at zero momentum, while nevertheless having positive specific heat. We show this using the nonlinear dynamics and give a clear interpretation in terms of the spectrum of linearized perturbations. Our results translate directly to their dual strongly coupled nonconformal field theories, whereby we in particular provide two mechanisms to obtain equilibration times much larger than the inverse temperature.
TL;DR: In this article, the authors interpret the recently observed excess in the diphoton invariant mass as a new spin-0 resonant particle and numerically solve the renormalization group equations to investigate the fate of the weakly coupled theory.
Abstract: We interpret the recently observed excess in the diphoton invariant mass as a new spin-0 resonant particle. On theoretical grounds, an interesting question is whether this new scalar resonance belongs to a strongly coupled sector or a well-defined weakly coupled theory. A possible UV-completion that has been widely considered in literature is based on the existence of new vector-like fermions whose loop contributions — Yukawa-coupled to the new resonance — explain the observed signal rate. The large total width preliminarily suggested by data seems to favor a large Yukawa coupling, at the border of a healthy perturbative definition. This potential problem can be fixed by introducing multiple vector-like fermions or large electric charges, bringing back the theory to a weakly coupled regime. However, this solution risks to be only a low-energy mirage: large multiplicity or electric charge can dangerously reintroduce the strong regime by modifying the renormalization group running of the dimensionless couplings. This issue is also tightly related to the (in)stability of the scalar potential. First, we study — in the theoretical setup described above — the parametric behavior of the diphoton signal rate, total width, and one-loop β functions. Then, we numerically solve the renormalization group equations, taking into account the observed diphoton signal rate and total width, to investigate the fate of the weakly coupled theory. We find that — with the only exception of few fine-tuned directions — weakly coupled interpretations of the excess are brought back to a strongly coupled regime if the running is taken into account.
TL;DR: In this paper, the authors investigate cosmological models in a recently proposed geometrical theory of gravity, in which the scalar field appears as part of the spacetime geometry.
Abstract: We investigate cosmological models in a recently proposed geometrical theory of gravity, in which the scalar field appears as part of the spacetime geometry. We extend the previous theory to include a scalar potential in the action. We solve the vacuum field equations for different choices of the scalar potential and give a detailed analysis of the solutions. We show that, in some cases, a cosmological scenario is found that seems to suggest the appearance of a geometric phase transition. We build a toy model, in which the accelerated expansion of the early Universe is driven by pure geometry.
TL;DR: In this article, the electromagnetic fields of an ultrashort, tightly focused, linearly polarized laser pulse in vacuum are derived from scalar and vector potentials using a small parameter, which assumes a small bandwidth of the laser pulse.
Abstract: Analytic expressions for the electromagnetic fields of an ultrashort, tightly focused, linearly polarized laser pulse in vacuum are derived from scalar and vector potentials using a small parameter, which assumes a small bandwidth of the laser pulse. The derived fields are compared with those of the Lax series expansion and the complex-source-point approaches and are shown to be well-behaved and accurate even in the subcycle pulse regime. We further demonstrate that terms stemming from the scalar potential and due to a fast varying pulse envelope are non-negligible and may significantly influence laser-matter interactions.
TL;DR: In this paper, the authors investigate cosmological aspects of spontaneous baryogenesis driven by a scalar field, and present general constraints that are independent of the particle physics model.
Abstract: We investigate cosmological aspects of spontaneous baryogenesis driven by a scalar field, and present general constraints that are independent of the particle physics model. The relevant constraints are obtained by studying the backreaction of the produced baryons on the scalar field, the cosmological expansion history after baryogenesis, and the baryon isocurvature perturbations. We show that cosmological considerations alone provide powerful constraints, especially for the minimal scenario with a quadratic scalar potential. Intriguingly, we find that for a given inflation scale, the other parameters including the reheat temperature, decoupling temperature of the baryon violating interactions, and the mass and decay constant of the scalar are restricted to lie within ranges of at most a few orders of magnitude. We also discuss possible extensions to the minimal setup, and propose two ideas for evading constraints on isocurvature perturbations: one is to suppress the baryon isocurvature with nonquadratic scalar potentials, another is to compensate the baryon isocurvature with cold dark matter isocurvature by making the scalar survive until the present.
TL;DR: In this paper, the authors investigate an inflationary model involving a gauge singlet scalar and fermionic dark matter and find that dark matter mass should be around half the mass of either the Higgs boson or the singlet Scalar.
Abstract: We investigate an inflationary model involving a gauge singlet scalar and fermionic dark matter. The mixing between the singlet scalar and the Higgs boson provides a portal to dark matter. The inflaton could either be the Higgs boson or the singlet scalar, and slow roll inflation is realized via its nonminimal coupling to gravity. In this setup, the effective scalar potential is stabilized by the mixing between two scalars and coupling with dark matter. We study constraints from collider searches, relic density and direct detection, and find that dark matter mass should be around half the mass of either the Higgs boson or singlet scalar. Using the renormalization group equation improved scalar potential and putting all the constraints together, we show that the inflationary observables ${n}_{s}\ensuremath{-}r$ are consistent with current Planck data.
TL;DR: In this paper, the authors derive the effective action of scalar field fluctuations with wavelengths larger than the de Sitter curvature radius and generalize Starobinsky's seminal results on stochastic inflation.
Abstract: The infrared dynamics of a light, minimally coupled scalar field in de Sitter spacetime with Ricci curvature R = 12H2, averaged over horizon sized regions of physical volume VH = (4π/3)(1/H)3, can be interpreted as Brownian motion in a medium with de Sitter temperature TDS = H/2π. We demonstrate this by directly deriving the effective action of scalar field fluctuations with wavelengths larger than the de Sitter curvature radius and generalizing Starobinsky's seminal results on stochastic inflation. The effective action describes stochastic dynamics and the fluctuating force drives the field to an equilibrium characterized by a thermal Gibbs distribution at temperature TDS which corresponds to a de Sitter invariant state. Hence, approach towards this state can be interpreted as thermalization. We show that the stochastic kinetic energy of the coarse-grained description corresponds to the norm of ∂μ and takes a well defined value per horizon volume ½(∇)2 = − ½TDS/VH. This approach allows for the non-perturbative computation of the de Sitter invariant stress energy tensor Tμν for an arbitrary scalar potential.
TL;DR: In this article, the authors investigate cosmological aspects of spontaneous baryogenesis driven by a scalar field, and present general constraints that are independent of the particle physics model.
Abstract: We investigate cosmological aspects of spontaneous baryogenesis driven by a scalar field, and present general constraints that are independent of the particle physics model. The relevant constraints are obtained by studying the backreaction of the produced baryons on the scalar field, the cosmological expansion history after baryogenesis, and the baryon isocurvature perturbations. We show that cosmological considerations alone provide powerful constraints, especially for the minimal scenario with a quadratic scalar potential. Intriguingly, we find that for a given inflation scale, the other parameters including the reheat temperature, decoupling temperature of the baryon violating interactions, and the mass and decay constant of the scalar are restricted to lie within ranges of at most a few orders of magnitude. We also discuss possible extensions to the minimal setup, and propose two ideas for evading constraints on isocurvature perturbations: one is to suppress the baryon isocurvature with nonquadratic scalar potentials, another is to compensate the baryon isocurvature with cold dark matter isocurvature by making the scalar survive until the present.
TL;DR: Using the concept of complex non-PT symmetric potential, the authors in this article studied the creation of zero energy states in graphene by a scalar potential and the admissible range of the potential parameter values for which such states exist has been examined.
TL;DR: In this paper, the authors investigated the inverse problem of determining the time independent scalar potential of the dynamic Schrodinger equation in an infinite cylindrical domain, from partial measurement of the solution on the boundary.
TL;DR: In this paper, the authors investigate the parameter space of the Standard Model enhanced by a gauge real scalar, taking into account all the theoretical and experimental constraints, and show the allowed parameter space for two different types of such singlet-enhanced Standard Model.
Abstract: We investigate the parameter space of the Standard Model enhanced by a gauge singlet real scalar $S$. Taking into account all the theoretical and experimental constraints, we show the allowed parameter space for two different types of such singlet-enhanced Standard Model. For the first case, the scalar potential has an explicit $Z_2$-symmetry, and may lead to a dark matter candidate under certain conditions. For the second case, the scalar potential does not respect any $Z_2$. This is again divided into two subcategories: one where the Standard Model vacuum is stable, and one where it is unstable and can decay into a deeper minimum. We show how the parameters in the scalar potential control the range of validity of all these models. Finally, we show the effect of one-loop correction on the positions and depths of the minima of the potential.
TL;DR: In this article, the authors exploit a new numerical technique for evaluating the tree order contributions to the primordial scalar and tensor power spectra for scalar potential models of inflation, and develop a good analytic approximation which goes beyond generalized slow roll expansions in that it is not contaminated by the physically irrelevant phase, its 0th order term is exact for the constant first slow roll parameter, and the correction is multiplicative rather than additive.
Abstract: We exploit a new numerical technique for evaluating the tree order contributions to the primordial scalar and tensor power spectra for scalar potential models of inflation. Among other things we use the formalism to develop a good analytic approximation which goes beyond generalized slow roll expansions in that (1) it is not contaminated by the physically irrelevant phase, (2) its 0th order term is exact for the constant first slow roll parameter, and (3) the correction is multiplicative rather than additive. These features allow our formalism to capture at first order effects which are higher order in other expansions. Although this accuracy is not necessary to compare current data with any specific model, our method has a number of applications owing to the simpler representation it provides for the connection between the power spectra and the expansion history of a general model.