Constant-roll Condition Research Articles

Analytical insights into constant-roll condition: extending the paradigm to non-canonical models

In this work, we explore the prospect of generalizing the constant-roll condition in canonical inflationary model to non-canonical models. To find a natural generalization, we focus on three manifestations of this condition and construct constant-roll models corresponding to each manifestation. These models are not equivalent but reduce to the familiar constant-roll model in canonical limit. To showcase the applicability of our generalized mechanism, we examine a specific class of non-canonical models, which can be viewed as extensions of k/G inflation. In these models sound speed is constant. We conduct a comparative study, and with an analytical examination of the model, specify instances when our constant-roll conditions yield dissimilar outcomes and when they exhibit analogies. We also apply our findings to scrutinize another kinetically driven inflationary model with varying sound speed. We demonstrate that each of our constant-roll conditions leads to a unique set of solutions. Afterward, we construct a four-stage constant-roll kinetically driven inflation that complies with CMB constraints, it sustains for a sufficiently long period of time, and finally gracefully exits. In this model the spectrum of curvature perturbations is enhanced in a brief phase of non-slow-roll inflationary evolution. Employing numerical methods, we analyse this scenario to elucidate how altering the constant-roll condition impacts the power spectrum and the model's dynamics.

Extended constant-roll condition in non-canonical scalar field inflation

In this work, we apply the extended constant-roll condition to non-canonical scalar fields. We use in particular two types of non-canonical fields, namely, the tachyon field and the Dirac–Born–Infeld (DBI) field. We assume, in particular, that the tachyon scalar field satisfies the condition [Formula: see text], while the DBI scalar field satisfies the condition [Formula: see text]. We use the extended constant-roll condition to calculate the inflation indices for each of these non-canonical fields. In order to test the extended constant-roll condition, we use three types of potentials, namely chaotic potential, linear power-law potential and exponential potential, and choose power-law and exponential forms for the smooth function [Formula: see text]. It is then shown that the models under consideration are compatible with the latest Planck 2018 constraints.

Constant-roll and primordial black holes in f(Q,T) gravity

In this study, we investigate the consequence of the constant-roll condition and examine the role of a chosen form of f(Q,T) gravity, given by f(Q,T)=αQ2+σT, in the cosmological inflation process. We analyze the inflationary scenario by calculating modified Friedmann equations and giving an alternative technique that enables relating modified slow-roll parameters to the constant roll parameter β. Considering both chaotic and hilltop models, we calculate the spectral index and the tensor-to-scalar ratio and compare their compatibility with Planck’s data for different choices of the constant roll parameter β. We examine the evolution of primordial black holes in our chosen modified gravity model taking into account the accretion process and the evaporation due to Hawking radiation. We compute the evaporation and accretion masses rate and provide an analytic estimation of the primordial black holes mass and of the radiation in the f(Q,T) gravity model.

Constant-roll inflation in modified f(R,phi ) gravity model using Palatini formalism

In this work, we study a constant-roll inflationary model in the Palatini formalism using modified gravity. Here our action consists a non-minimal coupling of a scalar field phi with Ricci scalar R in a general form of f(R,phi ). Using Palatini approach, we write its equivalent scalar-tensor form in the Einstein frame and then apply the constant-roll condition in the equation of motion for the inflaton field. Later the tensor-to-scalar ratio and the spectral index are calculated using the slow-roll parameters and the results obtained are matched with the Planck 2018 data. We found that the results agree nicely with the observations within the parameter regime under consideration.

Constant-roll inflation field with Tsallis entopic proposal

In this work, we investigate the high-energy era of the universe from the constant-roll condition perspective by taking the Friedmann equation, which is modified by a non-additive Tsallis entropic proposal. In the framework of the observational data, we determine the constant-roll parameter. Under the fixed field condition of the constant-roll parameter, for the wide range of the power-term of the chaotic potentials, sim phi ^{n}, which involves some string-chaotic potential models, n=frac{2}{3}, n=frac{4}{5}, the non-additive (nonextensive) Tsallis parameter is analyzed graphically. The resulting analysis shows that, in addition to a quasi-de Sitter phase, any value of the range 0.5<n<1.2 points to a dynamical form of the dark energy (quintessence) in the early universe. It implies that n values in the range may be included in string-chaotic potential models. The non-additive Tsallis parameter provides this with the help of its negative values in the constant-roll field.

Cosmic Evolution of the Logarithmic f(R) Model and the dS Swampland Conjecture

In this paper, we study the inflationary scenario in logarithmic f(R) gravity, where the rate of inflation roll is constant. On the other hand, our gravitational f(R) model is a polynomial plus a logarithmic term. We take advantage of constant-roll conditions and investigate the cosmic evolution of the logarithmic f(R) gravity. We present a numerical and a graphical study using the model parameters. Additionally, we obtain the corresponding potential by using the constant-roll condition. We obtain the exact value of the potential satisfying the constant-roll conditions. Next, we challenge it with refined swampland conjecture with respect to the Planck data. Finally, we compare our results with the latest observable data.

Anisotropic Constant-roll \(k\)-inflation Model

In this paper, we would like to figure out whether a {\it k}-inflation model admits the Bianchi type I metric as its inflationary solution under a constant-roll condition in the presence of the supergravity motivated coupling between scalar and vector fields, \(f^2(\phi)F_{\mu\nu}F^{\mu\nu}\). As a result, some novel anisotropic inflationary solutions are shown to appear along with a power-law one in this scenario. Furthermore, these solutions are numerically confirmed to be attractive, in contrast to the prediction of the Hawking's cosmic no-hair conjecture.

Constant-roll, cosmic acceleration, and massive neutrinos

We propose a model to describe the late-time cosmic acceleration in the context of the constant-roll model. By considering a coupling between massive neutrinos and the quintessence, the onset of evolution of the quintessence is related to the neutrinos' behavior. When the neutrinos become non-relativistic, the dark energy density increases from zero and results in late-time cosmic acceleration alleviating the coincidence problem. The quintessence potential is such that it evolves under the constant-roll condition giving rise to persistent late-time acceleration.

Inflation with Einstein-Gauss-Bonnet, non-minimal, and non-minimal derivative couplings: the constant-roll condition

In our research, we consider and study the inflation theories of Einstein-Gauss-Bonnet, minimal, non-minimal, and non-minimal derivative coupling with the constant-roll condition. Given the gravitational wave event, GW170817, which produces the speed of gravitational waves that was almost equal to the speed of light in vacuum, we constrain that the speed of the tensor perturbation was nearly equal to unity, . We involve a scalar field potential whose function can be obtained from an equation of motion by choosing the Gauss-Bonnet coupling functions. We use the linear and quadratic coupling functions, which are their simplest functions. The one result obtained are able to produce observed quantities such as the spectral index for scalar perturbation, ns = 0.9642, the spectral index for tensor perturbation, nT = −5.2471 × 10−4, and tensor-scalar ratio, r = 0.0041, which are compatible with the newest Planck data using the slow-roll parameters obtained analytically.

Generalizing the constant-roll condition in scalar inflation

In this work, we generalize the constant-roll condition for minimally coupled canonical scalar field inflation. Particularly, we shall assume that the scalar field satisfies the condition [Formula: see text], and we derive the field equations under this assumption. We call the framework extended constant-roll framework. Accordingly, we calculate the inflationary indices and the corresponding observational indices of inflation. In order to demonstrate the inflationary viability, we choose three potentials that are problematic in the context of slow-roll dynamics, namely, chaotic, linear power-law and exponential inflation, and by choosing a simple power-law form for the smooth function [Formula: see text], we show that in the extended constant-roll framework, the models are compatible with the latest 2018 Planck constraints on inflation. We also justify appropriately why we called this new framework extended constant-roll framework, and we show that the condition [Formula: see text] is equivalent to the condition [Formula: see text], with the latter condition being a simple generalization of the constant-roll condition. Finally, we examine an interesting physical situation, in which a general extended constant-roll scalar field model is required to satisfy the cosmological tracker condition used in quintessence models. In contrast to the slow-roll and ordinary constant-roll cases, in which case the tracker condition is not compatible with neither the slow-roll or the ordinary constant-roll conditions, the extended constant-roll condition can be compatible with the tracker condition. This feature leads to a new inflationary phenomenological framework, the essential features of which we develop in brief. The main feature of the new theoretical framework is that the function [Formula: see text] and the potential [Formula: see text] are no longer free to choose, but these are directly functionally related.

Anisotropic constant-roll inflation for the Dirac\u2013Born\u2013Infeld model

In this paper, we study a non-canonical extension of a supergravity-motivated model acting as a vivid counterexample to the cosmic no-hair conjecture due to its unusual coupling between scalar and electromagnetic fields. In particular, a canonical scalar field is replaced by the string-inspired Dirac–Born–Infeld one in this extension. As a result, exact anisotropic inflationary solutions for this Dirac–Born–Infeld model are figured out under a constant-roll condition. Furthermore, numerical calculations are performed to verify that these anisotropic constant-roll solutions are indeed attractive during their inflationary phase.

Anisotropic constant-roll inflation with noncommutative model and swampland conjectures

In this paper, we study a constant-roll inflationary model in the presence of a noncommutative parameter with a homogeneous scalar field minimally coupled to gravity. The specific noncommutative inflation conditions proposed new consequences. On the other hand, we use anisotropic conditions and find new anisotropic constant-roll solutions with respect to noncommutative parameter. Also, we will plot some figures with respect to the specific values of the corresponding parameter and the swampland criteria which is raised from the exact potential obtained from the constant-roll condition. Finally, different of figures lead us to analyze the corresponding results and also show the effect of above mentioned parameter on the inflationary model.

Non-minimally coupled scalar k-inflation dynamics

In this work, we shall study k-inflation theories with non-minimal coupling of the scalar field to gravity, in the presence of only a higher-order kinetic term of the form $$\sim \hbox {const}\times X^{\mu }$$ , with $$X=\frac{1}{2}\partial _{\mu } \phi \partial ^{\mu }\phi $$ . The study will be focused in the cases where a scalar potential is included or is absent, and the evolution of the scalar field will be assumed to satisfy the slow-roll or the constant-roll condition. In the case of the slow-roll models with scalar potential, we shall calculate the slow-roll indices and the corresponding observational indices of the theory, and we demonstrate that the resulting theory is compatible with the latest Planck data. The same results are obtained in the constant-roll case, at least in the presence of a scalar potential. In the case that models without potential are considered, the results are less appealing since these are strongly model dependent, and at least for a power-law choice of the non-minimal coupling, the theory is non-viable. Finally, due to the fact that the scalar and tensor power spectra are conformal invariant quantities, we argue that the Einstein frame counterpart of the non-minimal k-inflation models with scalar potential can be a viable theory, due to the conformal invariance of the observational indices. The Einstein frame theory is more involved and thus more difficult to work with it analytically, so one implication of our work is that we provide evidence for the viability of another class of k-inflation models.

Non-minimally coupled Einstein–Gauss–Bonnet gravity with massless gravitons: the constant-roll case

In this letter, we study the behavior of non-minimally coupled Einstein–Gauss–Bonnet gravity theories with the constant-roll condition. Recalling the results of the striking GW170817 event, we demand that the velocity of the gravitational waves is equated to unity in natural units, meaning that \(c_T^2=1\). This is a powerful restriction since it leads to a decrease in the degrees of freedom and subsequently reveals a connection between the scalar functions of the theory which presumably have different origins. In this framework, we shall assume that a scalar potential is present and can be extracted easily from the equations of motion by simply designating the scalar coupling functions. Obviously, a different approach is feasible but such choice will prove to be extremely convenient. Afterward, we impose certain approximations in order to facilitate our study. Each assumption is capable of producing different phenomenology so a summary of all the possible configurations for Hubble’s parameter, its derivative and the scalar potential along with the corresponding assumptions are present at the end of the paper. We show that compatibility under the constant-roll assumption can be achieved for a variety of model functions and different approaches, although one must always be aware of the imposed approximations since the possibility of a model producing viable results while simultaneously violating even a single approximation exists. Finally, in the end, a new formalism which leads to a plethora of convenient coupling functions according to the readers choice is presented. Utilizing such formalism may lead to new cases for coupling functions which have not been used yet, but are in fact able of producing viable phenomenology for the inflationary era.

A nearly massless graviton in Einstein-Gauss-Bonnet inflation with linear coupling implies constant-roll for the scalar field

The striking GW170817 event indicated that the graviton is nearly massless, since the gamma rays emitted from the two neutron stars merging arrived almost simultaneously with the gravitational waves. Thus, the graviton must also be massless during the inflationary and post-inflationary era, since there is no obvious reason to believe otherwise. In this letter we shall investigate the theoretical implications of the constraint that the graviton is massless to an Einstein-Gauss-Bonnet theory with linear coupling of the scalar field to the four-dimensional Gauss-Bonnet invariant. As we show, the constraint of having gravitational wave speed of the primordial gravitational waves equal to one severely restricts the dynamics of the scalar field, imposing a direct constant-roll evolution on it. Also, as we show, the spectral index of the primordial scalar perturbations for the GW170817-compatible Einstein-Gauss-Bonnet theory with linear coupling is different in comparison to the same theory with non-linear coupling. Thus the phenomenology of the model is expected to be different, and we briefly discuss this issue too. In addition, the constant-roll condition is always related to non-Gaussianities, thus it is interesting that the imposition of a massless graviton in an Einstein-Gauss-Bonnet theory with linear coupling may lead to non-Gaussianities, so we briefly discuss this issue too.

Ghost-free non-local F(R) gravity cosmology

Abstract In this work we shall study ghost-free non-local F ( R ) gravity models. Firstly we shall demonstrate how the ghost degrees of freedom may occur in the non-local F ( R ) gravity models, and accordingly we shall modify appropriately the gravitational action of non-local F ( R ) gravity models in order to eliminate the ghosts. Also we shall investigate how the (anti-)de Sitter and the Minkowski spacetime cosmological solutions may arise in the theory, and we investigate when these solutions are stable. Moreover, we shall examine the inflationary phenomenology of the Jordan frame ghost-free non-local F ( R ) gravity. We shall study two F ( R ) gravity models, the power law F ( R ) gravity model ∼ R n with 1 n 2 , n ≠ 2 and the R 2 model, assuming that the slow-roll condition holds true for the Hubble rate during the inflationary era H ≪ H 2 and that the general constant-roll condition ϕ = 3 β H ϕ holds true for the evolution of the scalar field, which includes the slow-roll case for β = 0 . As we shall demonstrate, the power-law non-local F ( R ) gravity case can produce a viable inflationary era, compatible with observations, in the constant-roll case, unlike for the R 2 model. It is conceivable that the results are model dependent, as in the ordinary vacuum F ( R ) gravity.

Constant-roll in the Palatini-R2 models

We consider models of a scalar field coupled to quadratic R+R2 gravity in the framework of the Palatini formulation. The resulting Einstein-frame generalized k-inflation effective theory is analyzed assuming that the constant-roll condition holds. We focus on a quartic self-interaction potential, a case of particular appeal modelling Higgs inflation, considering the cases of minimal and non-minimal coupling of the inflaton to gravity. For an appropriate range of the model parameters in the large field domain the obtained values for the inflationary observables are found in agreement with current observations.

Constant-roll k-inflation dynamics

In this work we shall investigate the phenomenological implications of the constant-roll condition on a k-Inflation theory of gravity. The latter theories are particularly promising, since these remained robust to the results of GW170817, since these have a gravitational wave speed cT = 1 in natural units. We shall mainly focus on the phenomenology of the k-Inflation models, with the only assumption being the slow-roll condition imposed on the first and fourth slow-roll parameters, and the constant-roll condition for the evolution of the scalar field. We present in detail the final form of the gravitational equations of motion that control the dynamics of the cosmological system, with the constant-roll condition imposed, and by using a conveniently, from the perspective of analytical manipulations, chosen potential, we express the slow-roll indices and the resulting observational indices of the theory as functions of the e-foldings number. The results of our analysis indicate that the constant-roll k-Inflation theory can be compatible with the Planck 2018 data, for a wide range of the free parameters. Also we examine in a quantitative way the effects of the constant-roll condition on the parameter on which the bispectrum is proportional, in the equilateral momentum approximation, and we demonstrate that the effect of the constant-roll condition is non-trivial. In effect, non-Gaussianities in the theory may be enhanced, a phenomenon which is known to be produced by constant-roll scalar theories of gravity in general.

Constant-roll inflation driven by a scalar field with nonminimal derivative coupling

In this work, we study constant-roll inflation driven by a scalar field with nonminimal derivative coupling to gravity, via the Einstein tensor. This model contains a free parameter, [Formula: see text], which quantifies the nonminimal derivative coupling and a parameter [Formula: see text] which characterizes the constant-roll condition. In this scenario, using the Hamilton–Jacobi-like formalism, an ansatz for the Hubble parameter (as a function of the scalar field) and some restrictions on the model parameters, we found new exact solutions for the inflaton potential which include power-law, de Sitter, quadratic hilltop and natural inflation, among others. Additionally, a phase-space analysis was performed and it is shown that the exact solutions associated to natural inflation and a “cosh-type” potential, are attractors.

Logarithmic-corrected R2 gravity inflation in the presence of Kalb-Ramond fields

In this paper we shall study the inflationary aspects of a logarithmic corrected R2 Starobinsky inflation model, in the presence of a Kalb-Ramond field in the gravitational action of F(R) gravity. Our main interest is to pin down the effect of this rank two antisymmetric tensor field on the inflationary phenomenology of the F(R) gravity theory at hand. The effects of the Kalb-Ramond field are expected to be strong during the inflationary era, however as the Universe expands, the energy density of the Kalb-Ramond field scales as ∼ a−6 so dark matter and radiation dominate over the Kalb-Ramond field effects. In general, antisymmetric fields constitute the field content of superstring theories, and thus their effect at the low-energy limit of the theory is expected to be significant. As we will show, for a flat Friedmann-Robertson-Walker metric, the Kalb-Ramond field actually reduces to a scalar field, so it is feasible to calculate the observational indices of inflation. We shall calculate the spectral index and the tensor-to-scalar ratio for the model at hand, by assuming two conditions for the resulting Kalb-Ramond scalar field, the slow-roll and the constant-roll condition. As we shall demonstrate, in both the slow-roll and constant-roll cases, compatibility with the latest observational data can be achieved. Also the effect of the Kalb-Ramond field on the inflationary phenomenology is to increase the amount of the predicted primordial gravitational radiation, in comparison to the corresponding f(R) gravities, however the results are still compatible with the observational data.