Canonical Scalar Field Research Articles

Dynamical system analysis for scalar field potential in teleparallel gravity

AbstractIn this paper, we have presented a power law cosmological model and its dynamical system analysis in $$f(T,\phi )$$ f ( T , ϕ ) gravity, where T is the torsion scalar and $$\phi $$ ϕ is the canonical scalar field. The two well-motivated forms of the non-minimal coupling function $$F(\phi )$$ F ( ϕ ) , the exponential form and the power law form, with exponential scalar field potential, are investigated. The dynamical system analysis is performed by establishing the dimensionless dynamical variables, and the critical points were obtained. The evolution of standard density parameters is analysed for each case. The behaviour of the equation of state (EoS) and deceleration parameter agree with the result of recent cosmological observations. The model parameters are constrained using the existence and the stability conditions of the critical points describing different epochs of the evolution of the Universe.

Barrow holographic dark energy: reconstruction within Saez-Ballester theory in Kantowski-Sachs universe

Within the framework of the Saez-Ballester theory, the Barrow Holographic Dark Energy (BHDE) has been reconstructed. This reconstruction was carried out in a homogeneous and anisotropic KS universe that was filled with BHDE. The study examined both non-interacting and interacting scenarios, with the future event horizon serving as the IR cut-off. The analysis focused on the evolution of the equation of State parameter for both cases, as well as the trajectories of wDE−w′DE . Additionally, the study investigated the inflation of the Universe filled with BHDE by plotting the slow-roll parameters. Furthermore, a connection between the canonical scalar field and BHDE was explored, as the presence of a scalar field is often associated with inflation. Finally, the tensor-to-scalar ratio r is plotted which seems to lie within the acceptable range.

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.

Roles of boundary and equation-of-motion terms in cosmological correlation functions

We revisit the properties of total time-derivative terms as well as terms proportional to the free equation of motion (EOM) in a Schwinger-Keldysh formalism. They are relevant to the correct calculation of correlation functions of curvature perturbations in the context of inflationary Universe. We show that these two contributions to the action play different roles in the operator or the path-integral formalism, but they give the same correlation functions as each other. As a concrete example, we confirm that the Maldacena's consistency relations for the three-point correlation function in the slow-roll inflationary scenario driven by a minimally coupled canonical scalar field hold in both the operator and path-integral formalisms. We also give some comments on loop calculations.

Non-uniform knot (NUK) SIAC post-processing of flow fields produced through unstructured grid adaptation and optimization

As the finite element method (FEM) and the finite volume method (FVM), both their traditional and high-order variants, continue their proliferation into various applied engineering disciplines, adaptive mesh refinement and optimization strategies have increased in their importance when solving real-world computational fluid mechanics applications. The post-processing and visualization of the resulting flow fields present two significant analysis and visualization challenges. The first challenge is the handling of elemental continuity, which is often only C0 continuous (in continuous Galerkin methods) or piecewise discontinuous (in discontinuous Galerkin methods). The second challenge is that, depending on the flow regime and the geometric configurations for which adaptive meshing strategies are used, the meshes generated are often highly anisotropic. The (uniform knot) line-SIAC (L-SIAC) filter has been proposed as a way of handling elemental continuity issues in an accuracy-conserving manner with the added benefit of casting the data in a smooth context even if the representation is element discontinuous. In this paper, we demonstrate that the state-of-the-art adaptive L-SIAC filter, designed for mildly anisotropic meshes, suffers degradation in the quality of the post-processed solution when applied to the types of highly anisotropic meshes produced through adaptive mesh refinement and optimization. Hence, a new Non-Uniform Knot (NUK) L-SIAC filter is proposed that automatically conforms to the underlying mesh anisotropy. We demonstrate that the new filter behaves similarly to the adaptive L-SIAC filter when applied to uniform and mildly anisotropic meshes, and furthermore we show the superiority of the NUK L-SIAC filter when applied to highly anisotropic meshes. The newly formulated filter is applied to 2D canonical scalar fields and used to visualize 2D and 3D fluid flow simulation results.

Gravitating kinks with asymptotically flat metrics

In this work, we consider a two-dimensional (2D) dilaton gravity model where the dilaton kinetic term is modified by an additional derivative coupling term . In the case with a canonical scalar matter field, the field equations of this model have a simple first-order formalism, from which exact static kink solutions can be constructed. The novelty of these solutions is that the corresponding metric can be asymptotically flat rather than asymptotically anti-de Sitter. The linear stability and the localization of scalar matter fields are also studied. It was found that the solutions are stable against small linear perturbations, and the localization of scalar matter fields can be realized by introducing scalar-kink interactions.

Generalized Lagrangian for canonical and non-canonical scalar field

In this paper, we proposed a generalized Lagrangian for three different classes of scalar fields namely quintessence ([Formula: see text]), phantom ([Formula: see text]) and tachyonic ([Formula: see text]) parameterized by [Formula: see text]. These three scalar fields can be described by a common single Lagrangian called generalized scalar field Lagrangian (GSL). We obtain mathematically consistent forms of generalized equations of motion parameterized by [Formula: see text]. It can recover the individual equation of motion of quintessence, phantom and tachyon scalar fields from generalized equation of motion of the unified scalar field.

Scalar gravitational waves can be generated even without direct coupling between Dark Energy and ordinary matter

We point out, the scalar sector of gravitational perturbations may be excited by an isolated astrophysical system immersed in a universe whose accelerated expansion is not due to the cosmological constant, but due to extra field degrees of freedom. This is true even if the source of gravitational radiation did not couple directly to these additional fields. We illustrate this by considering a universe driven by a single canonical scalar field. By working within the gauge-invariant formalism, we solve for the electric components of the linearised Weyl tensor to demonstrate that both the gravitational massless spin-2 (transverse-traceless) tensor and the (Bardeen) scalar modes are generated by a generic astrophysical source. For concreteness, the Dark Energy scalar field is either released from rest, or allowed to asymptote toward the minimum in a certain class of potentials; and we compute the traceless tidal forces induced by gravitational radiation from a hypothetical compact binary system residing in such a universe. Though their magnitudes are very small compared to the tensors', spin zero gravitational waves in such a canonical scalar driven universe are directly sensitive to both the Dark Energy equation of state and the eccentricity of the binary's orbit.

Kink solutions in generalized 2D dilaton gravity

We study static kink solutions in a generalized two-dimensional dilaton gravity model, where the kinetic term of the dilaton is generalized to be an arbitrary function of the canonical one X=−12(∇φ)2, say F(X), and the kink is generated by a canonical scalar matter field ϕ. It is found that for arbitrary F(X), the background field equations have a simple first-order formalism, and the linear perturbation equation can always be written as a Schrödinger-like equation with factorizable Hamiltonian operator. After choosing appropriate F(X) and superpotential, we obtain a sine-Gordon type kink solution with pure AdS2 metric. The linear perturbation issue of this solution becomes an exactly solvable conformal quantum mechanics problem, if one of the model parameter takes a critical value.

Scalar-induced gravitational wave interpretation of PTA data: the role of scalar fluctuation propagation speed

Pulsar timing arrays gathered evidence of the presence of a gravitational wave background around nHz frequencies. If the gravitational wave background was induced by large and Gaussian primordial fluctuations, they would then produce too many sub-solar mass primordial black holes. We show that if at the time of gravitational wave generation the universe was dominated by a canonical scalar field, with the same equation of state as standard radiation but a higher propagation speed of fluctuations, one can explain the gravitational wave background with a primordial black hole counterpart consistent with observations. Lastly, we discuss possible ways to test this model with future gravitational wave detectors.

Background Constraints on Dark Energy Models

Due to the gravitational attraction of all the matter in the universe, the expansion rate of the cosmos has changed over time, decreasing (decelerating) in past, and more recently speeding up (accelerating). The hypothesis that the Universe is expanding quickly and is spatially nearing its limit now has a lot of cosmological evidence to back it up (assuming the density is at least somewhat time-independent). The majority of cosmologists believe that “dark energy” is to blame for the accelerated cosmological expansion that has been witnessed. The cosmological constant, an additional constant to the Einstein field equation, can be used to explain why the universe is expanding faster than before. The ΛCDM model is the simplest and most common model in use. Besides this, there are also dark energy models like the Barotropic fluid model, canonical scalar field model, and non-canonical scalar field model. We analyse the background constraints on dark energy models using current cosmological data available. We also present the comparison between dark energy models using Bayesian statistics.

Quintessence scalar field of Kaniadakis holographic dark energy model with statefinder analysis

This paper explores the quintessence reconstruction and statefinder perspective of Kaniadakis holographic dark energy model in a flat universe with future event horizon as an IR-cutoff. The cosmological parameters of this model were re-examined from the quintessence behavior aspect. Also we reconstruct, [Formula: see text], the potential of quintessence scalar field, which shows the best fit with joint analysis data of JLA+CC+BAO for the priors [Formula: see text], [Formula: see text]. In the [Formula: see text]–[Formula: see text] phase space, the freezing-tracker model represents our canonical scalar field. This model exhibits quintessence behavior in the statefinder ([Formula: see text]–[Formula: see text]) plane for model parameters [Formula: see text] and [Formula: see text] that are close to [Formula: see text] and [Formula: see text]. The present values of deceleration [Formula: see text], statefinder [Formula: see text], jerk [Formula: see text] and model parameters [Formula: see text] are consistent with the limits of the observational data. Using the distance modulus [Formula: see text], we also fit 580 SN Type I Union2.1 data sets to our model.

A parametric view of Hubble parameter for scalar field dark energy model

Abstract: In our present work, we have considered a simple parametric form of the Hubble parameter (H) for a canonical scalar field model described within a spatially flat FRW spacetime framework. Here we have considered a well-behaved parametrization scheme of the normalized Hubble parameter to explain the expansión history of the universe. Under this scenario, we have obtained the analytic solutions for various relevant cosmological parameters. We have also reconstructed the potential function V( φ) for the scalar field φ. It has been found that the deceleration parameter (q) shows exactly the nature which is well expected, i.e., an accelerated expansión for low z limit and deceleration for high z limit, which is essential for the structure formation of the Universe. Detailed data analysis has been carried out to check the viability of the proposed theoretical model by using combined dataset SNIa+H(z)+BAO/CMB and put constraints on the cosmological parameters, viz. the present value of the Hubble parameter H0.

Investigation of the Cosmic evolution in the presence of non-relativistic neutrinos

The neutrinos of the early universe evolved from a relativistic phase at very early times to a massive particle behavior at later times. First, the kinetic energy of neutrinos is relativistic, and as a result, neutrinos can be described as massless particles. As the Universe expands, the temperature drops and the kinetic energy decreases, and the neutrinos turn into a non-relativistic phase with a non-negligible mass. In this paper, we first put constraints on the total mass of neutrinos. Then we investigate the effect of neutrinos on the CMB power spectrum, P(k), in the case of massless and massive neutrinos using the publicly available Boltzmann code CAMB and we prove that when neutrino coupled to scalar field the CMB power spectrum has a little shift, which means that the power spectrum of CMB is greatly affected by the background energy density and the accelerated expansion of the Universe. Furthermore, we investigate the effect of perturbed quintessence on this spectrum and find that the highest peaks of this spectrum are shifted to smaller scales. Also, we estimate the Deceleration–Acceleration(DA) redshift transition (z da) using the coupling canonical scalar field with neutrinos. For Pantheon data we obtain z da = 0.7 ± 0.05 and for CC data z da = 0.68 ± 0.03. In the presence of neutrinos the DA redshift transition is z da = 0.42 ± 0.03 for Pantheon data and z da = 0.49 ± 0.05 for CC data. These results indicate that neutrinos can affect this phase transition. The results obtained in this article show that when the mass of neutrinos increases, the value of the background energy density increases, resulting in a higher power spectrum peak. Also, by examining the effect of coupling neutrinos to dark energy, we find that the transition occurs at lower redshift.

Exact Bianchi type-I inflationary model with non-minimally coupled scalar field

In the present work, we try to build up an inflationary model within the framework of Bianchi type-I spacetime using a non-minimally coupled, homogeneous, self-interacting canonical scalar field. Specifically, using the Lie symmetry method, we are able to find some novel exact solutions to the Einstein field equations by assuming a power-law relationship between the scalar field and average scale factor. These symmetry-based solutions have been used to derive the values of some important parameters of the anisotropic universe. In this anisotropic model, we find that the volume of space expands with time in an inflationary scenario, depicting the Universe’s accelerating phases. An important characteristic of this model is that it initially represents anisotropic spacetime and then isotropizes the spacetime as time goes on, which favors recent cosmological observations.

Swampland criteria and constraints on inflation in a f(R,T) gravity theory

In this paper, we worked in the framework of an inflationary [Formula: see text] theory in the presence of a canonical scalar field. More specifically, the [Formula: see text] gravity. The values of the dimensionless parameters [Formula: see text] and [Formula: see text] are taken to be [Formula: see text] and [Formula: see text]. The motivation for this study was the striking similarities between the slow-roll parameters of the inflationary model used in this work and the ones obtained by the rescaled Einstein–Hilbert gravity inflation [Formula: see text]. We examined a variety of potentials to determine if they agree with the current Planck Constraints. In addition, we checked whether these models satisfy the Swampland Criteria and we specified the exact region of the parameter space that produces viable results for each model. As we mention in Sec. 4, the inflationary [Formula: see text] theory used in this work cannot produce a positive [Formula: see text] which implies that the stochastic gravitational wave background will not be detectable.

Inflationary dynamics and swampland criteria for modified Gauss-Bonnet gravity compatible with GW170817

In this article we present an alternative formalism for the inflationary phenomenology of rescaled Einstein-Gauss-Bonnet models which are in agreement with the GW170817 event. By constraining the propagation velocity of primordial tensor perturbations, an approximate form for the time derivative of the scalar field coupled to the Gauss-Bonnet density is extracted. In turn, the overall degrees of freedom decrease and similar to the case of the canonical scalar field, only one scalar function needs to be designated, while the other is extracted from the continuity equation of the scalar field. We showcase explicitly that the slow-roll indices can be written in a closed form as functions of three dimensionless parameters, namely $x=\frac{1}{2\alpha}\bigg(\frac{\kappa\xi'}{\xi''}\bigg)^2$, $\beta=8H^2\xi''$ and $\gamma=\frac{\xi'\xi'''}{\xi''^2}$ and in turn, we prove that the Einstein-Gauss-Bonnet model can in fact produce a blue-tilted tensor spectral index if the condition $\beta\geq1$ is satisfied, which is possible only for Einstein-Gauss-Bonnet models with $\xi''(\phi_k)>0$. Afterwards, a brief comment on the running of the spectral indices is made where it is shown that $a_{\mathcal{S}}(k_*)$ and $a_{\mathcal{T}}(k_*)$ in the constrained case are approximately of the order $\mathcal{O}(10^{-3})$, if not smaller. Last but not least, we examine the conditions under which the Swampland criteria are satisfied. We connect the tracking condition related to scalar field theories with the present models, and we highlight the important feature of the models we propose that the tracking condition can be satisfied only if the Swampland criteria are simultaneously satisfied, however the cases with $\xi\sim1/V$ and $\xi\sim V$ are excluded, as they cannot describe the inflationary era properly.

Observational Imprints of Enhanced Scalar Power on Small Scales in Ultra Slow Roll Inflation and Associated Non-Gaussianities

The discovery of gravitational waves from merging binary black holes has generated considerable interest in examining whether these black holes could have a primordial origin. If a significant number of black holes have to be produced in the early universe, the primordial scalar power spectrum should have an enhanced amplitude on small scales, when compared to the COBE normalized values on the large scales that is strongly constrained by the anisotropies in the cosmic microwave background. In the inflationary scenario driven by a single, canonical scalar field, such power spectra can be achieved in models that permit a brief period of ultra slow roll inflation during which the first slow roll parameter decreases exponentially. In this review, we shall consider a handful of such inflationary models as well as a reconstructed scenario and examine the extent of formation of primordial black holes and the generation of secondary gravitational waves in these cases. We shall also discuss the strength and shape of the scalar bispectrum and the associated non-Gaussianity parameter that arise in such situations. We shall conclude with an outlook wherein we discuss the wider implications of the increased strengths of the non-Gaussianities on smaller scales.

Cosmological stability in [formula omitted] gravity

In gravitational theories where a canonical scalar field ϕ with a potential V(ϕ) is coupled to a Gauss-Bonnet (GB) term G with the Lagrangian f(ϕ,G), we study the cosmological stability of tensor and scalar perturbations in the presence of a perfect fluid. We show that, in decelerating cosmological epochs with a positive tensor propagation speed squared, the existence of nonlinear functions of G in f always induces Laplacian instability of a dynamical scalar perturbation associated with the GB term. This is also the case for f(G) gravity, where the presence of nonlinear GB functions f(G) is not allowed during the radiation- and matter-dominated epochs. A linearly coupled GB term with ϕ of the form ξ(ϕ)G can be consistent with all the stability conditions, provided that the scalar-GB coupling is subdominant to the background cosmological dynamics.

Modified Starobinsky inflation by the R ln (□) R term

In the context of effective theories of gravity, a minimalist bottom-up approach which takes into account 1-loop quantum corrections leads to modifications in the Einstein-Hilbert action through the inclusion of four extra terms: R 2, CκραβCκραβ , R ln (□) R and Cκραβ ln(□) Cκραβ . The first two terms are necessary to guarantee the renormalizability of the gravitational theory, and the last two terms (nonlocal terms) arise from the integration of massless/light matter fields. This work aims to analyze how one of the nonlocal terms, namely R ln(□) R, affects the Starobinsky inflation. We consider the nonlocal term as a small correction to the R 2 term, and we demonstrate that the model behaves like a local model in this context. In addition, we show that the approximate model in the Einstein frame is described by a canonical scalar field minimally coupled to general relativity. Finally, we study the inflationary regime of this model and constrain its free parameters through observations of CMB anisotropies.