Intermediate Inflation Research Articles

Intermediate inflation in a generalized non-minimal derivative coupling model

In this work, we consider intermediate inflation in the context of the generalized non-minimal derivative coupling (GNMDC) model. In the GNMDC model, inflation is driven by a canonical scalar field that is coupled not only to gravity but also to the derivative of the scalar field. The model introduces new dynamics and features during the inflationary epoch. We find inflationary solutions with a power law scalar field for the power law coupling function. Additionally, we determine the inflaton potential that generates intermediate expansion of the scale factor. We also discuss the background equations in the high friction limit and derive constraints on the parameters of our model. Furthermore, we investigate the cosmological perturbations in the slow roll approximation within the GNMDC model, and we calculate the scalar and tensor spectral index and the tensor-to-scalar ratio during intermediate inflation. We compare the results of this model with observational data that can be used to test the model using cosmic microwave background radiation data. Overall, we establish conditions for the inflaton potential that ensure the continuation of accelerated expansion during slow roll inflation. We numerically analyze the power spectrum and spectral index for scalar and tensor modes in intermediate inflation in the high friction limit, and we use Planck 2018 data to obtain constraints on the parameters of the model. We demonstrate that intermediate inflation in the GNMDC model is successful in evaluation and explanation of background and perturbation quantities using observational data.

Intermediate inflation through Nojiri–Odintsov holographic dark fluid with the cosmological settings of Kaniadakis

This study is inspired by the generalized holographic cut-off proposed by Nojiri and Odintsov (S. I. Nojiri and S. D. Odintsov, Unifying phantom inflation with late-time acceleration: Scalar phantom–non-phantom transition model and generalized holographic dark energy, Gen. Relativ. Gravit. 38 (2006) 1285–1304) as it aims to have an understanding of the Kaniadakis holographic dark fluid, a particular representative of Nojiri–Odintsov holographic dark energy. To realize inflation and late time acceleration of the universe, we have considered this generalized form of holographic fluid as the fluid for realization of inflationary scenario. Here, inflation has a holographic origin, namely that its source is the Kaniadakis holographic energy density. The inflationary cosmology of Kaniadakis holographic dark fluid has been have explored by assuming that the scale factor is an intermediate scale factor. Several constraints have been derived throughout the study in relation to late time acceleration and early inflation. To study the warm inflation with this holographic origin, we have computed tensor-to-scalar ratio for different values of the number of e-fold and warm inflation has been realized in a high dissipative regime.

Scalar warm inflation in holographic cosmology

We consider warm inflation in the context of holographic cosmology. The weak and the strong dissipative regime are analysed in the slow-roll approximation and within what is known as intermediate inflation. For an appropriate choice of the equation of state, the intermediate inflation is not only an exact solution in general relativity, but also in the holographic setup considered in this paper. Within this approach several dissipative and physically relevant functions are considered. We constrain our model using the latest Planck data. We conclude that three of the models analysed are consistent with Planck data for some ranges of the model parameters. However, one of them is ruled out by the observations.

Viable intermediate inflation in the mimetic DBI model

We study the intermediate inflation in the mimetic Dirac–Born–Infeld model. By considering the scale factor as a=a_{0}exp (bt^{beta }), we show that in some ranges of the intermediate parameters b and beta , the model is free of the ghost and gradient instabilities. We study the scalar spectral index, tensor spectral index, and the tensor-to-scalar ratio in this model and compare the results with Planck2018 TT, TE, EE + lowE + lensing + BAO + BK14 data at 68% and 95% CL. In this regard, we find some constraints on the intermediate parameters that lead to the observationally viable values of the perturbation parameters. We also seek the non-Gaussian features of the primordial perturbations in the equilateral configuration. By performing the numerical analysis on the nonlinearity parameter in this configuration, we show that the amplitude of the non-Gaussianity in the intermediate mimetic DBI model is predicted to be in the range -16.7<f^{equil}<-12.5. We show that, with 0<ble 10 and 0.345<beta <0.387, we have an instabilities-free intermediate mimetic DBI model that gives the observationally viable perturbation and non-Gaussianity parameters.

Analysis and design of covariance inflation methods using inflation functions. Part 2: adaptive inflation

AbstractPart 1 of this study shows the existence of a unifying theory that encompasses all exiting covariance inflation (CI) methods under a framework of inflation functions operating on the eigenvalues of the ensemble transform matrix. Given a vast space of potential inflation functions, a natural question is how to choose the optimal one. This part 2 shows how adaptive inflation can be implemented in the context of inflation functions to estimate inflation functions on‐the‐fly from observations. Estimation of prior inflation functions (PIF) is equivalent to estimation of background error covariances G in observation space. However, the conventional CI methods confront a difficult problem of how to convert G back to model space to calculate analysis increments and perturbations, which is possible in very limited cases such as multiplicative inflation. The solution here is to exploit the equivalence between PIFs and inflation functions to transplant the estimated PIF into its equivalent inflation function. Analysis increments and perturbations can be calculated using this intermediate inflation function. Maximum likelihood (ML) estimations of three families of PIFs with two data assimilation systems show that this approach works well and that the adaptive methods can even beat a well‐tuned CI method. Estimation of the inflation functions that do not have equivalent PIFs is more difficult since we lack a theoretical guidance, such as Bayesian inference as in the case of PIFs. Those inflation functions are proposed to be estimated from posterior innovation statistics. There are two supporting facts for this estimation: (a) ML estimation of nonparametric PIFs leads back to the prior innovation statistics, and (b) posterior innovation statistics is an effective diagnostic tool for assessing performance of inflation functions. It is interesting to find that ML estimates of inflation functions yield analyses and forecasts better than ML estimates of PIFs.

Warm intermediate and logamediate cosmic inflation with a constant ‎dissipation coefficient in loop quantum gravity

Warm inflationary model in the context of loop quantum cosmology is investigated. To this aim we consider two cases intermediate inflation and logamediate inflation. In both the cases, assuming a constant dissipation coefficient, we study the model under consideration in weak dissipation regime and also in strong dissipation regime. In each of these cases, we obtain various parameters such as potential function of inflationary scalar field and slow-roll parameters. Perturbation theory and also finding relations between perturbative parameters is studied.

An intermediate inflation of the early Universe from f(R) gravity

In this work, we study on the inflationary era of the Universe in the context of f(R) gravity. For this purpose, we consider the f(R) gravity and its scalar perturbation equations. We start with an equation symmetry approach, a notation, which characterizes both the field equations of the gravity and evolution of the scalar perturbations. Throughout the study, to realize inflation we assume that the first slow-roll parameter $$\epsilon _{1}$$ takes a small value with the number of e-folds which has nearly a constant value as $$N\sim 60$$ . An intermediate inflation, which has an initial condition (the Bunch–Davies vacuum state), is obtained. Here, the resulting solution eventually causes the universe enters to the radiation era. Viability of this inflation scenario is investigated by calculating the power spectrum of the primordial curvature perturbations which is observed nearly scale-invariant with some parameters of the intermediate scale factor. Then, the two observable parameters (i.e., the scalar spectral index parameter and the tensor-to-scalar ratio) are obtained. The findings are compared with latest observational data, and we have observed that this inflation scenario for the early universe is possible.

Cosmological parameters of f(R) gravity with kinetic scalar curvature

We study modified f(R) gravity theory with kinetic scalar curvature reducible to chiral cosmological model of a special type. New method of cosmological parameters calculation based on reduction of two-fields model to standard one with single scalar field is proposed. Parametric correspondence to observational data is shown for massive scalar field, power-law and intermediate inflation.

Intermediate inflation with non-canonical scalar field in the low anisotropy Universe

The behavior of a non-canonical scalar field within an anisotropic Bianchi type I, spatially homogeneous Universe in the framework of the intermediate inflation will be studied. It will be examined on the condition that both the anisotropy and non-canonical sources come together if there is any improvement in compatibility with the observational data originated from Planck 2015. Based on this investigation, it can be observed that automatically a steep potential which can manage inflation in a better way will be obtained. Additionally, as a common procedure for an inflationary study, we shall try to calculate the related inflationary observables such as the amplitude of the scalar perturbations, scalar and tensor spectral indices, tensor-to-scalar ratio, the running spectral index and the number of e-folds. As an exciting part of our results, we will find that our model has a good consistency compared to data resulting from CMB and different Planck results. To justify our claims, the well-known canonical inflationary scenario in an anisotropic Bianchi type I Universe will also be evaluated.

Galileon Intermediate Inflation

Abstract We investigate intermediate inflation in the framework of a Galileon scalar field. To this aim, we first obtain the inflationary observables, including the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index, as well as the non-Gaussianity parameters. Then, we examine the observational viability of the intermediate inflation within the framework of a Galileon scenario. Our results show that although the prediction of intermediate inflation in the standard framework is completely ruled out by the Planck 2015 observations, it can be put inside the allowed regions of the Planck 2015 TT,TE,EE+lowP data in the Galileon setting. Moreover, we determine the parameter space of the Galileon intermediate inflation for which the model is consistent with the Planck 2015 data. Besides, we derive the consistency relation in the Galileon scenario, and find that it differs from the standard inflation. We also estimate the running of the scalar spectral index and find that it is in well agreement with the 95% CL constraint of the Planck 2015 results. Finally, we evaluate the local, equilateral, orthogonal, and enfolded non-Gaussianity parameters, and conclude that not only is the shape of non-Gaussianity approximately close to the equilateral one, but that it also satisfies the 68% CL bound from the Planck 2015 data.

Loop quantum cosmology scalar field models

In this work, we use the Loop Quantum Cosmology (LQC) modified scalar–tensor reconstruction techniques in order to investigate how bouncing and inflationary cosmologies can be realized. With regard to the inflationary cosmologies, we shall be interested in realizing the intermediate inflation and the Type IV singular inflation, while with regard to bouncing cosmologies, we shall realize the superbounce and the symmetric bounce. In all the cases, we shall find the kinetic term of the LQC holonomy corrected scalar–tensor theory and the corresponding scalar potential. In addition, we shall include a study of the effective Equation of State (EoS), emphasizing at the early- and late-time eras. As we demonstrate, in some cases it is possible to have a nearly de Sitter EoS at the late-time era, a result that could be interpreted as the description of a late-time acceleration era. Also, in all cases we shall examine the dynamical stability of the LQC holonomy corrected scalar-tensor theory, and we shall confront the results with those coming from the corresponding classical dynamical stability theory. The most appealing cosmological scenario is that of a Type IV singular inflationary scenario, in which the singularity may occur at the late-time era. As we demonstrate, for this model, during the dark energy era, a transition from non-phantom to a phantom dark energy era occurs.

Loop quantum cosmology-corrected Gauss–Bonnet singular cosmology

In this work we investigate which Loop Quantum Cosmology (LQC)-corrected Gauss–Bonnet [Formula: see text] gravity can realize two singular cosmological scenarios, the intermediate inflation and the singular bounce scenarios. The intermediate inflation scenario has a Type III sudden singularity at [Formula: see text], while the singular bounce has a soft Type IV singularity. By using perturbative techniques, we find the holonomy-corrected [Formula: see text] gravities that generate at leading order the aforementioned cosmologies and we also argue that the effect of the holonomy corrections is minor to the power spectrum of the primordial curvature perturbations of the classical theory.

Impact of generalized dissipative coefficient on warm inflationary dynamics in the light of latest Planck data

The warm inflation scenario in view of the modified Chaplygin gas is studied. We consider the inflationary expansion to be driven by a standard scalar field whose decay ratio Gamma has a generic power-law dependence with the scalar field phi and the temperature of the thermal bath T. By assuming an exponential power-law dependence in the cosmic time for the scale factor a(t), corresponding to the intermediate inflation model, we solve the background and perturbative dynamics considering our model to evolve according to (1) weak dissipative regime and (2) strong dissipative regime. Specifically, we find explicit expressions for the dissipative coefficient, scalar potential, and the relevant inflationary observables like the scalar power spectrum, scalar spectral index, and tensor-to-scalar ratio. The free parameters characterizing our model are constrained by considering the essential condition for warm inflation, the conditions for the model evolves according to weak or strong dissipative regime, and the 2015 Planck results through the n_s–r plane.

Intermediate inflation in a generalized induced-gravity scenario

An intermediate inflationary Universe model in the context of non-minimal coupling to the scalar curvature is analyzed. We will conduct our analysis in the slow-roll approximation of the inflationary dynamics and the cosmological perturbations considering a coupling of the form F(varphi )=kappa +xi _nvarphi ^n. Considering the trajectories in the r–n_s plane from the Planck data, we find the constraints on the parameter space in our model.

Inflation and bounce from classical and loop quantum cosmology imperfect fluids

We investigate how various inflationary and bouncing cosmologies can be realized by imperfect fluids with a generalized equation of state, in the context of both classical and loop quantum cosmologies. With regards to the inflationary cosmologies, we study the intermediate inflation scenario, the [Formula: see text] inflation scenario and two constant-roll inflation scenarios, and with regards to the bouncing cosmologies, we study the matter bounce scenario, the singular bounce and the super bounce scenario. Within the context of the classical cosmology, we calculate the spectral index of the power spectrum of primordial curvature perturbations, the scalar-to-tensor ratio and the running of the spectral index and we compare the resulting picture with the Planck data. As we demonstrate, partial compatibility with the observational data is achieved in the imperfect fluid description, however none of the above scenarios is in full agreement with data. This result shows that although it is possible to realize various cosmological scenarios using different theoretical frameworks, it is not guaranteed that all the theoretical descriptions are viable.

Tachyon inflation with steep potentials

Within the framework of tachyon inflation, we consider different steep potentials and check their viability in light of the Planck 2015 data. We see that in this scenario, the inverse power-law potential $V(\phi)=V_{0}(\phi/\phi_{0})^{-n}$ with $n=2$ leads to the power-law inflation with the scale factor $a(t)\propto t^{q}$ where $q>1$, while with $n<2$, it gives rise to the intermediate inflation with the scale factor $a(t)\propto\exp\left(At^{f}\right)$ where $A>0$ and $0<f<1$. We find that, although the inverse power-law potential with $n\leq 2$ is completely ruled out by the Planck 2015 data, the result of this potential for $n>2$ can be compatible with the 95\% CL region of Planck 2015 TT, TE, EE+lowP data. We further conclude that the exponential potential $V(\phi)=V_{0}e^{-\phi/\phi_{0}}$, the inverse $\cosh$ potential $V(\phi)=V_{0}/\cosh(\phi/\phi_{0})$, and the mutated exponential potential $V(\phi)=V_{0}\left[1+(n-1)^{-(n-1)}(\phi/\phi_{0})^{n}\right]e^{-\phi/\phi_{0}}$ with $n=4$, can be consistent with the 95\% CL region of Planck 2015 TT, TE, EE+lowP data. Moreover, using the $r-n_s$ constraints on the model parameters, we also estimate the running of the scalar spectral index $dn_{s}/d\ln k$ and the local non-Gaussianity parameter $f_{{\rm NL}}^{{\rm local}}$. We find that the lower and upper bounds evaluated for these observables are compatible with the Planck 2015 results.

Hyperpolarized gas diffusion MRI of biphasic lung inflation in short- and long-term emphysema models.

During lung inflation, airspace dimensions are affected nonlinearly by both alveolar expansion and recruitment, potentially confounding the identification of emphysematous lung by hyperpolarized helium-3 diffusion magnetic resonance imaging (HP MRI). This study aimed to characterize lung inflation over a broad range of inflation volume and pressure values in two different models of emphysema, as well as in normal lungs. Elastase-treated rats (n = 7) and healthy controls (n = 7) were imaged with HP MRI. Gradual inflation was achieved by incremental changes to both inflation volume and airway pressure. The apparent diffusion coefficient (ADC) was measured at each level of inflation and fitted to the corresponding airway pressures as the second-order response equation, with minimizing residue (χ2 < 0.001). A biphasic ADC response was detected, with an initial ADC increase followed by a decrease at airway pressures >18 cmH2O. Discrimination between treated and control rats was optimal when airway pressure was intermediate (between 10 and 11 cmH2O). Similar findings were confirmed in mice following long-term exposure to cigarette smoke, where optimal discrimination between treated and healthy mice occurred at a similar airway pressure as in the rats. We subsequently explored the evolution of ADC measured at the intermediate inflation level in mice after prolonged smoke exposure and found a significant increase (P < 0.01) in ADC over time. Our results demonstrate that measuring ADC at intermediate inflation enhances the distinction between healthy and diseased lungs, thereby establishing a model that may improve the diagnostic accuracy of future HP gas diffusion studies.

Viability of the intermediate inflation scenario with F(T) gravity

We study the intermediate inflation scenario in the context of $F(T)$ gravity, and we examine it's viability by calculating the power spectrum of the primordial curvature perturbations and the corresponding spectral index. As we demonstrate, it is possible for the resulting spectral index to be compatible with the observational data and we investigate the parameter space in order to see when the compatibility with data is possible.

On the expanding phase of a singular bounce and intermediate inflation: The modified gravity description

We demonstrate that the intermediate inflation scenario is a singular inflation cosmology, with the singularity at the origin t = 0 being a pressure and energy density singularity and particularly a Type III singularity. Also, we show that the expanding phase of a singular bounce can be identical to the intermediate inflation scenario, if the singular bounce has a Type III singularity at the origin. For the intermediate inflation scenario we examine the cosmological implications on the power spectrum in the context of various forms of modified gravity. Particularly, we calculate the power spectrum in the context of F(R), F(G) Gauss–Bonnet gravity and also for F(T) gravity and we discuss the viability of each scenario by comparing the resulting spectral index with the latest observational data.

Warm intermediate inflation in f ( R ) $f(R)$ gravity

Warm intermediate inflation in f ( R ) $f(R)$ gravity