Inflationary Parameters Research Articles

Generalized cosmic Chaplygin inflationary model on the brane

The generalized cosmic Chaplygin model in the context of brane-inflationary background is being considered by taking the standard scalar field as matter field. We develop the modified first Friedmann equation and conservation equation under slow-roll approximations. We also discuss the feature of the generalized cosmic Chaplygin gas model in the presence of chaotic potential in the high-energy limit. Various inflationary parameters, such as slow-roll parameters, scalar and tensor power spectra, scalar spectral index and tensor-to-scalar ratio are evaluated. To this end, Planck results are used to constraint new parameters.

Solving dynamical equations in general homogeneous isotropic cosmologies with a scalaron

We study general dynamical equations describing homogeneous isotropic cosmologies coupled to a scalaron $\psi$. For flat cosmologies ($k=0$), we analyze in detail the gauge-independent equation describing the differential, $\chi(\alpha)\equiv\psi^\prime(\alpha)$, of the map of the metric $\alpha$ to the scalaron field $\psi$, which is the main mathematical characteristic locally defining a `portrait' of a cosmology in `$\alpha$-version'. In the `$\psi$-version', a similar equation for the differential of the inverse map, $\bar{\chi}(\psi)\equiv \chi^{-1}(\alpha)$, can be solved asymptotically or for some `integrable' scalaron potentials $v(\psi)$. In the flat case, $\bar{\chi}(\psi)$ and $\chi(\alpha)$ satisfy the first-order differential equations depending only on the logarithmic derivative of the potential. Once we know a general analytic solution for one of these $\chi$-functions, we can explicitly derive all characteristics of the cosmological model. In the $\alpha$-version, the whole dynamical system is integrable for $k\neq 0$ and with any `$\alpha$-potential', $\bar{v}(\alpha)\equiv v[\psi(\alpha)]$, replacing $v(\psi)$. There is no a priori relation between the two potentials before deriving $\chi$ or $\bar{\chi}$, which implicitly depend on the potential itself, but relations between the two pictures can be found by asymptotic expansions or by inflationary perturbation theory. Explicit applications of the results to a more rigorous treatment of the chaotic inflation models and to their comparison with the ekpyrotic-bouncing ones are outlined in the frame of our `$\alpha$-formulation' of isotropic scalaron cosmologies. In particular, we establish an inflationary perturbation expansion for $\chi$. When all the conditions for inflation are satisfied and $\chi$ obeys a certain boundary (initial) condition, we get the standard inflationary parameters, with higher-order corrections.

Braneworld inflation with a complex scalar field from Planck 2015

We study an inflationary model with a single complex scalar field in the framework of braneworld Randall–Sundrum model type 2. From the scalar curvature perturbation constrained by the recent observation values, and for specific choice of parameters, we can reduce the values of the coupling constant to take the natural values, and we found that the phase theta \(\theta \) of the inflation field can take the narrow interval. We have also derived all known inflationary parameters \((n_{s},\)r and \(\frac{dn_{s}}{d\ln (k)})\), which are widely consistent with the recent Planck data for a suitable choice of brane tension value \(\lambda \).

Dynamics of bulk viscous pressure effected inflation in braneworld scenario

The main goal of the present work is to examine the possible realization of warm chaotic inflation and logamediate inflation within the framework of a modified Chaplygin gas brane-world model. In this respect, the slow-roll parameters, number of e-folds, scalar-tensor power spectra, spectral indices, tensor–scalar ratio and running of scalar spectral index is being evaluated. These parameters are being analyzed for variable as well as constant dissipation and bulk viscous coefficients. Further, the trajectories among the inflationary parameters such as ns−ϕ,ns−r,αs−ϕ and ns−αs are also developed to examine their behavior as well as physical cosmology. Some of results of inflationary parameters in all cases are: r < 0.11, ns=0.96±0.025 and αs=−0.019±0.025. It is interesting to mention here that the results of inflationary parameters are consistent with BICEP2, WMAP (7+9) and Planck data.

A new large field inflation constrained by Planck 2015

In this work we propose a new large field inflation model, parametrized by a parameter \( \beta\) sharing the same features with T-Model. We apply the slow-roll approximation to investigate the inflationary parameters, and we found that they depend on some value of \( \beta\) and the e-folds number Ne. In this context, we have computed and discussed the perturbation of the scalar curvature and determined the energy scale \( V_{0}\), which we found to be in the GUT regime. We also showed that, in our scenario, the various inflationary spectrum perturbation parameters, the spectral index \( n_{s}\), the ratio of tensor to scalar perturbations r and the running \( \frac{d ns}{d \ln k}\), perfectly agree with the recent experimental observations in the event \( \beta > 0.5\) and \( Ne\sim 45-60\). As a result we have reproduced successfully the main part, \( n_{s}-r\), consistent with Planck data.

Braneworld Inflation in Supergravity with a Shift Symmetric Kähler Potential

We propose a new solution to the η-problem in supergravity using a shift symmetric Kahler potential in the context of the Randall–Sundrum type II model. We focus on a F-term supergravity inflation with a minimal Kahler potential taking into account the radiative corrections. The slow-roll conditions are ensured by the shift symmetry where a very small value of η(η≪1) is obtained. In this context, we derive all known spectrum inflationary parameters which are widely consistent with Planck 2015 data for a particular choice of brane tension and coupling constant values. A suitable observational central value of ns=0.96 is also obtained in the case of minimal Kahler potential.

Large slow roll parameters in single field inflation

We initially consider two simple situations where inflationary slow roll parameters are large and modes no longer freeze out shortly after exiting the horizon, treating both cases analytically. By modes, we refer to the comoving curvature perturbation R. We then consider applications to transient phases where the slow roll parameters can become large, especially in the context of the common `fast-roll' inflation frequently used as a mechanism to explain the anomalously low scalar power at low l in the CMB. These transient cases we treat numerically. We find when ϵ, the first slow roll parameter, and only ϵ is large, modes decay outside the horizon, and when δ, the second slow roll parameter, is large, modes grow outside the horizon. When multiple slow roll parameters are large the behavior in general is more complicated, but we nevertheless show in the `fast-roll' inflation case, modes grow outside the horizon.

Can monetary policy fully stabilize pure demand shocks in a monetary union with a fiscal leader?

We consider the ability of monetary policy to fully stabilize pure demand shocks in a monetary union with strategically acting fiscal authorities. We show that when one national fiscal authority enjoys a strategic advantage over the other and fiscal policy can directly affect inflation, monetary policy cannot fully stabilize pure demand shocks at the union level, unless they are common. Moreover, we characterize a situation where country-specific fiscal policies diverge, being counter-cyclical for one country and pro-cyclical for the other, for high enough values of the direct effect of fiscal policy on the inflation parameter. The coordination of national fiscal policies becomes desirable for the union central bank.

A latent variable model for analyzing mixed longitudinal (k,l)-inflated count and ordinal responses

ABSTRACTA random effects model for analyzing mixed longitudinal count and ordinal data is presented where the count response is inflated in two points (k and l) and an (k,l)-Inflated Power series distribution is used as its distribution. A full likelihood-based approach is used to obtain maximum likelihood estimates of parameters of the model. For data with non-ignorable missing values models with probit model for missing mechanism are used.The dependence between longitudinal sequences of responses and inflation parameters are investigated using a random effects approach. Also, to investigate the correlation between mixed ordinal and count responses of each individuals at each time, a shared random effect is used. In order to assess the performance of the model, a simulation study is performed for a case that the count response has (k,l)-Inflated Binomial distribution. Performance comparisons of count-ordinal random effect model, Zero-Inflated ordinal random effects model and (k,l)-Inflated ordinal random effects model are also given. The model is applied to a real social data set from the first two waves of the national longitudinal study of adolescent to adult health (Add Health study). In this data set, the joint responses are the number of days in a month that each individual smoked as the count response and the general health condition of each individual as the ordinal response. For the count response there is incidence of excess values of 0 and 30.

Non-parametric reconstruction of an inflaton potential from Einstein–Cartan–Sciama–Kibble gravity with particle production

The coupling between spin and torsion in the Einstein-Cartan-Sciama-Kibble theory of gravity generates gravitational repulsion at very high densities, which prevents a singularity in a black hole and may create there a new universe. We show that quantum particle production in such a universe near the last bounce, which represents the Big Bang gives the dynamics that solves the horizon, flatness, and homogeneity problems in cosmology. For a particular range of the particle production coefficient, we obtain a nearly constant Hubble parameter that gives an exponential expansion of the universe with more than 60 $e$-folds, which lasts about $\sim 10^{-42}$ s. This scenario can thus explain cosmic inflation without requiring a fundamental scalar field and reheating. From the obtained time dependence of the scale factor, we follow the prescription of Ellis and Madsen to reconstruct in a non-parametric way a scalar field potential which gives the same dynamics of the early universe. This potential gives the slow-roll parameters of cosmic inflation, from which we calculate the tensor-to-scalar ratio, the scalar spectral index of density perturbations, and its running as functions of the production coefficient. We find that these quantities do not significantly depend on the scale factor at the Big Bounce. Our predictions for these quantities are consistent with the Planck 2015 observations.

Imprints of massive primordial fields on large-scale structure

Attention has focussed recently on models of inflation that involve a second or more fields with a mass near the inflationary Hubble parameter H, as may occur in supersymmetric theories if the supersymmetry-breaking scale is not far from H. Quasi-single-field (QsF) inflation is a relatively simple family of phenomenological models that serve as a proxy for theories with additional fields with masses m∼ H. Since QsF inflation involves fields in addition to the inflaton, the consistency conditions between correlations that arise in single-clock inflation are not necessarily satisfied. As a result, correlation functions in the squeezed limit may be larger than in single-field inflation. Scalar non-Gaussianities mediated by the massive isocurvature field in QsF have been shown to be potentially observable. These are especially interesting since they would convey information about the mass of the isocurvature field. Here we consider non-Gaussian correlators involving tensor modes and their observational signatures. A physical correlation between a (long-wavelength) tensor mode and two scalar modes (tss), for instance, may give rise to local departures from statistical isotropy or, in other words, a non-trivial four-point function. The presence of the tensor mode may moreover be inferred geometrically from the shape dependence of the four-point function. We compute tss and stt (one soft curvature mode and two hard tensors) bispectra in QsF inflation, identifying the conditions necessary for these to “violate” the consistency relations. We find that while consistency conditions are violated by stt correlations, they are preserved by the tss in the minimal QsF model. Our study of primordial correlators which include gravitons in seeking imprints of additional fields with masses m∼ H during inflation can be seen as complementary to the recent ``cosmological collider physics'' proposal.

Cosmological attractor inflation from the RG-improved Higgs sector of finite gauge theory

The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of finite gauge models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameter values. The inflationary models thus obtained are seen to be in good agreement with the most recent and accurate observational data. More specifically, the values of the relevant inflationary parameters, ns and r, are close to the corresponding ones in the R2 and Higgs-driven inflation scenarios. It is shown that the model here constructed and Higgs-driven inflation belong to the same class of cosmological attractors.

Designing and testing inflationary models with Bayesian networks

Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use Nf-quadratic inflation as an illustrative example, finding that the number of e-folds N* between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters.

Detecting relic gravitational waves by pulsar timing arrays: Effects of cosmic phase transitions and relativistic free-streaming gases

Relic gravitational waves (RGWs) generated in the early Universe form a stochastic GW background, which can be directly probed by measuring the timing residuals of millisecond pulsars. In this paper, we investigate the constraints on the RGWs and on the inflationary parameters by the observations of current and potential future pulsar timing arrays. In particular, we focus on effects of various cosmic phase transitions (e.g. $e^{+}e^{-}$ annihilation, QCD transition and SUSY breaking) and relativistic free-streaming gases (neutrinos and dark fluids) in the general scenario of the early Universe, which have been neglected in the previous works. We find that the phase transitions can significantly damp the RGWs in the sensitive frequency range of pulsar timing arrays, and the upper limits of tensor-to-scalar ratio $r$ increase by a factor $\sim 2$ for both current and future observations. However, the effects of free-steaming neutrinos and dark fluids are all too small to be detected. Meanwhile, we find that, if the effective equation of state $w$ in the early Universe is larger than $1/3$, i.e. deviating from the standard hot big bang scenario, the detection of RGWs by pulsar timing arrays becomes much more promising.

Optimal Investment-Consumption Strategy under Inflation in a Markovian Regime-Switching Market

This paper studies an investment-consumption problem under inflation. The consumption price level, the prices of the available assets, and the coefficient of the power utility are assumed to be sensitive to the states of underlying economy modulated by a continuous-time Markovian chain. The definition of admissible strategies and the verification theory corresponding to this stochastic control problem are presented. The analytical expression of the optimal investment strategy is derived. The existence, boundedness, and feasibility of the optimal consumption are proven. Finally, we analyze in detail by mathematical and numerical analysis how the risk aversion, the correlation coefficient between the inflation and the stock price, the inflation parameters, and the coefficient of utility affect the optimal investment and consumption strategy.

Dynamics of tachyon fields and inflation - comparison of analytical and numerical results with observation

The role tachyon fields may play in evolution of early universe is discussed in this paper. We consider the evolution of a flat and homogeneous universe governed by a tachyon scalar field with the DBI-type action and calculate the slow-roll parameters of inflation, scalar spectral index (n), and tensor-scalar ratio (r) for the given potentials. We pay special attention to the inverse power potential, first of all to V (x) ~ x?4, and compare the available results obtained by analytical and numerical methods with those obtained by observation. It is shown that the computed values of the observational parameters and the observed ones are in a good agreement for the high values of the constant X0. The possibility that influence of the radion field can extend a range of the acceptable values of the constant X0 to the string theory motivated sector of its values is briefly considered.

Linear inflation from quartic potential

We show that if the inflaton has a non-minimal coupling to gravity and the Planck scale is dynamically generated, the results of Coleman-Weinberg inflation are confined in between two attractor solutions: quadratic inflation, which is ruled out by the recent measurements, and linear inflation which, instead, is in the experimental allowed region. The minimal scenario has only one free parameter -- the inflaton's non-minimal coupling to gravity -- that determines all physical parameters such as the tensor-to-scalar ratio and the reheating temperature of the Universe. Should the more precise future measurements of inflationary parameters point towards linear inflation, further interest in scale-invariant scenarios would be motivated.

Kähler potential braneworld inflation in supergravity after Planck 2015

We analyze the slow-roll mechanism in Randall–Sundrum II braneworld with a supersymmetric hybrid inflation model. We are interested in studying various inflationary spectrum perturbation parameters in two cases. The first is the minimal Kähler potential where the inflationary parameters depend on the number of [Formula: see text]-foldings [Formula: see text] as well as the brane tension [Formula: see text], such that we produce the central value of the spectral index [Formula: see text]. The second case concerns the nonminimal Kähler potential, where the inflationary parameters depend only on the brane tension. Also, the [Formula: see text]-problem is solved for natural coupling parameter values which is not realized in the standard case. In addition, for a suitable choice of brane tension value [Formula: see text], the perturbation spectrum is widely consistent with Planck data.

Effects of quantum fluctuations of metric on the universe

In general, one can propose a modified gravity by replacing the Einstein-Hilbert Lagrangian with different functions of the Ricci scalar, known as ƒ ( R ) theory. We consider a model of modified gravity from the nonperturbative quantization of a metric, namely decomposing the metric operator into a sum of a classical metric and a fluctuating part. We obtain the modified gravitational field equations and the modified conservational equations. We apply it to the Friedmann-Lemaitre-Robertson-Walker spacetime, obtain the modified Friedmann equations. We find that due to the quantum fluctuations a bounce universe can be obtained and a decelerated expansion can also possibly be obtained even in a dark energy dominated epoch, we also constrain the related parameters according to the physical conditions. We not only analyze the effects of quantum fluctuations on the evolutions of the radiation and dust, but also present the its modifications on inflation parameters, such as slow-roll parameters, spectral index, and the spectrum of the primordial curvature perturbation.

Origin of inflation in CFT driven cosmology: $$R^2$$ R 2 -gravity and non-minimally coupled inflaton models

We present a detailed derivation of the recently suggested new type of hill-top inflation [arXiv:1509.07270] originating from the microcanonical density matrix initial conditions in cosmology driven by conformal field theory (CFT). The cosmological instantons of topology $S^1\times S^3$, which set up these initial conditions, have the shape of a garland with multiple periodic oscillations of the scale factor of the spatial $S^3$-section. They describe underbarrier oscillations of the inflaton and scale factor in the vicinity of the inflaton potential maximum, which gives a sufficient amount of inflation required by the known CMB data. We build the approximation of two coupled harmonic oscillators for these garland instantons and show that they can generate inflation consistent with the parameters of the CMB primordial power spectrum in the non-minimal Higgs inflation model and in $R^2$ gravity. In particular, the instanton solutions provide smallness of inflationary slow-roll parameters $\epsilon$ and $\eta<0$ and their relation $\epsilon\sim\eta^2$ characteristic of these two models. We present the mechanism of formation of hill-like inflaton potentials, which is based on logarithmic loop corrections to the asymptotically shift-invariant tree level potentials of these models in the Einstein frame. We also discuss the role of $R^2$-gravity as an indispensable finite renormalization tool in the CFT driven cosmology, which guarantees the non-dynamical (ghost free) nature of its scale factor and special properties of its cosmological garland type instantons. Finally, as a solution to the problem of hierarchy between the Planckian scale and the inflation scale we discuss the concept of a hidden sector of conformal higher spin fields.