Homogeneous Scalar Field Research Articles

On the isotropy of temperature fluctuations in passive scalar turbulence

We use direct numerical simulation to investigate the scalar gradient skewness downstream of a square grid element. The passive scalar is generated by applying a constant heat flux on the grid element. We primarily focus on the far-downstream grid-element centerline, where the scalar turbulence is homogeneous, and there are no mean velocity or scalar gradients. In this region, some discrepancy exists in the literature concerning the isotropy of the scalar. To the best of our knowledge, this is the first study that measures scalar gradients in all three directions. We detect nonzero skewness for the lateral scalar gradients, while in the streamwise direction, the skewness is zero. We show, through statistical analysis, that the nonzero values are solely due to steep gradients called cliffs. The cliffs originate from the bars of the grid-element that generate sharp mean scalar gradients along the lateral directions in the near wake. These mean gradients decay as the flow develops downstream, but the convected cliffs remember the generating upstream conditions and, in particular, the direction of the mean scalar gradient. Due to this memory effect, the cliffs align preferentially along a specific direction despite the absence of a local mean scalar gradient, thus making the homogeneous scalar field anisotropic. We also report some hitherto undocumented properties of cliffs and ramps through conditional statistical analysis. Finally, we corroborate our conclusions with two additional simulations, one involving grid-element turbulence in the presence of a transverse mean scalar gradient and the other scalar turbulence due to a heated cylinder.

Motion of rotating black holes in homogeneous scalar fields: A general case

Motion of rotating black holes in homogeneous scalar fields: A general case

Dynamics of Cosmological Scalar Fields Revisited

This paper reviews the dynamics of a single isotropic and homogeneous scalar field φ(t) in the context of cosmological models. A non-standard approach to the solution of the Einstein–Klein–Gordon equations is described which uses the scalar field as the evolution parameter for cosmic dynamics. General conclusions about the qualitative behaviour of the solutions can be drawn, and examples of how to obtain explicit solutions for some cosmological models of interest are given. For arbitrary potentials, analytical results can be obtained from the slow-roll approximation by using a series expansion for the Hubble parameter H[φ], from which a quantitative estimate for the number of e-folds of expansion is obtained. This approach is illustrated with the examples of quadratic potentials and hilltop models, with special consideration of Higgs-type potentials. The GUT-scale is shown to come out of such a model quite naturally. Finally, it is discussed how to find scalar potentials giving rise to a predetermined scalar-field behaviour and the associated evolution of the scale factor.

Cosmology in Lorentzian Regge calculus: causality violations, massless scalar field and discrete dynamics

We develop a model of spatially flat, homogeneous and isotropic cosmology in Lorentzian Regge calculus, employing four-dimensional Lorentzian frusta as building blocks. By examining the causal structure of the discrete spacetimes obtained by gluing such four-frusta in spatial and temporal direction, we find causality violations if the sub-cells connecting spatial slices are spacelike. A Wick rotation to the Euclidean theory can be defined globally by a complexification of the variables and an analytic continuation of the action. Introducing a discrete free massless scalar field, we study its equations of motion and show that it evolves monotonically. Furthermore, in a continuum limit, we obtain the equations of a homogeneous scalar field on a spatially flat Friedmann background. Vacuum solutions to the causally regular Regge equations are static and flat and show a restoration of time reparametrisation invariance. In the presence of a scalar field, the height of a frustum is a dynamical variable that has a solution if causality violations are absent and if an inequality relating geometric and matter boundary data is satisfied. Edge lengths of cubes evolve monotonically, yielding a contracting or an expanding branch of the Universe. In a small deficit angle expansion, the system can be deparametrised via the scalar field and a continuum limit of the discrete theory can be defined which we show to yield the relational Friedmann equation. These properties are obstructed if higher orders of the deficit angle are taken into account. Our results suggest that the inclusion of timelike sub-cells is necessary for a causally regular classical evolution in this symmetry restricted setting. Ultimately, this works serves as a basis for forthcoming investigations on the cosmological path integral within the framework of effective spin foams.

Motion of a rotating black hole in a homogeneous scalar field

Motion of a rotating black hole in a homogeneous scalar field

κ-Exponential Inflation

We investigate a possible inflationary scenario where the expansion of the universe is driven by a slow evolution of a homogeneous single scalar field, whose potential V (φ) is given by an unusual κ-generalized power law. Within the slow-roll approximation we obtain several of the main predictions of the model, as the scalar spectral index, the tensor-to-scalar ratio, the number of e-folds, and the local non-Gaussianity. We also show that this model admits a much wider set of solutions than the usual exponential approach, and that their theoretical predictions are contemplated by the observational data.

Chaotic inflationary universe in Rastall gravity

We study Linde’s chaotic inflation in Rastall gravity with a homogeneous scalar field. In Einstein’s general theory of relativity, Linde obtained chaotic scenario, which emerged from chaotic distribution of scalar field satisfying a limiting value of the initial scalar field ϕo > 3 MP that lies in the quantum gravity. The upper limit on the initial scalar field is obtained for a sufficient inflation to encompass the present universe. In the Rastall gravity, the upper limit is reduced depending on the Rastall parameter γ < 1. The upper limit on ϕo is found to increases for [Formula: see text]. In the later case, sufficient inflation is not permitted and the role of curvaton field is explored for an acceptable early chaotic inflation.

Squeezed Number State Representation of the Inflaton and Particle Production in the FRW Universe

In this study, we use a single-mode squeezed thermal vacuum state formalism and examine the nature of a massive homogeneous scalar field, minimally coupled to the gravity in the framework of semiclassical gravity in the Bianchi type-I universe. We have obtained an estimate leading solution to the semiclassical Einstein equation for the Bianchi type-I universe shows, each scale factor in its respective direction obeys t^(2/3) power-law expansion. The mechanism of the nonclassical thermal cosmological particle production is also analyzed in the Bianchi type-I universe.

Generalized McVittie geometry in Horndeski gravity with matter

We investigate McVittie and generalized McVittie solutions for Horndeski gravity with a spatially homogeneous gravitational scalar field, which is stealth at small scales near the central object but, at large scales, sources the Friedmann--Lema\^{\i}tre--Robertson--Walker universe in which the central inhomogeneity is embedded. Unlike previous studies, we include matter and obtain generalized McVittie solutions in the extended cuscuton model. The possible configurations are classified according to the time dependence of the gravitational coupling, the radial energy flow, the accretion rate onto the central object, and the Hubble rate.

Quantum gravity corrections to the matter dynamics in the presence of a reference fluid

We analyze the effect induced on standard quantum field theory (in a functional approach) by quantum gravity corrections to a pure classical background. In the framework of the Kucha\ifmmode \check{r}\else \v{r}\fi{} and Torre proposal for a gravity-matter theory constrained to a Gaussian reference frame, materialized as a fluid in the system evolution, we consider a Born-Oppenheimer separation of the system, regarding the gravity degrees of freedom as the slow varying component and the matter plus the Gaussian fluid as fast quantum coordinates. The slow gravity component obeys the Wheeler-DeWitt equation, and we consider a Wentzel-Kramer-Brillouin expansion of its quantum dynamics via a Planckian parameter. The main issue of the proposed scenario is that, on one hand, we recover a modified quantum field theory in the presence of a Hermitian Hamiltonian (not affected by nonunitarity as in other approaches) and, on the other hand, we get the Gaussian fluid as a physical clock for such an amended quantum theory (verifying the correct energy conditions). We also show its equivalence with the kinematical action method, used in a previous work, in the homogeneous setting. Then, we implement the proposed paradigm to describe the dynamics of a homogeneous free massless scalar field, living on an isotropic universe, in the presence of a cosmological constant. We completely solve the dynamics up to the first order correction in the Planckian parameter to the standard quantum field theory. We determine the explicit form of the modified scalar field wave function, due to quantum features of the cosmic scale factor evolution. Phenomenological considerations and discussions are provided.

Dynamical analysis of k-essence cosmology in the light of Supernova Ia observations

In this paper, we analyse the JLA data on Supernova observations in the context of $k-$essence dark energy model with Lagrangian $L=VF(X)$, with a constant potential $V$ and the dynamical term $X = (1/2)\nabla_{\mu}\phi\nabla_{\nu}\phi = \dot{\phi}^2/2$ for a homogeneous scalar field $\phi(t)$, in a flat FRW spacetime background. Scaling relations are used to extract temporal behaviour of different cosmological quantities and the form of the function $F(X)$ from the data. We explore how the parameters of the model, viz. value of the constant potential $V$ and a constant $C$ appearing in the emergent scaling relation, control the dynamics of the model in the context of JLA data, by setting up and analysing an equivalent dynamical system described by a set of autonomous equations.

Singularity resolution in gravitational collapse

We investigate the unhindered gravitational collapse of a homogeneous scalar field with nonzero potential, a two-dimensional analog of the Mexican hat-shaped Higgs field potential. The collapsing scalar field is surrounded by an exterior retarded (outgoing) generalized Vaidya spacetime. We prove that the density dependence on the scale factor cannot be expressed as an algebraic function in such a scenario. For a certain transcendental expression of the density of such a field as a function of scale factor, we then show that the collapse evolves to a singularity at an infinite comoving time, which is equivalent to saying that the singularity is avoided altogether. An ultra high density region of the order of Planck length can, however, be reached in a finite comoving time. The absence of the formation of trapped surfaces makes this ultra high density region globally visible.

Bouncing and Coasting Universe with Exact Quantum-Classical Correspondence

When the scale factor of expansion of the universe is written as $ a(t)\equiv Ae^{\alpha(t)}$, with $A$ as some real constant and $\alpha(t)$ a real function, the gravitational action $I_G$ appears in the same form as the matter action $I_M$ for a homogeneous and isotropic scalar field with a specific scale factor-dependent potential. We observe that by making analytic continuation of the Lagrangian function in this $I_G$ to the complex plane of $\alpha$, one can obtain terms corresponding to both parts of a total action that describes a viable cosmological model. The solution gives a bouncing and coasting universe, which first contracts and then expands linearly, with a smooth bounce in between them. Such a bounce, called a Tolman wormhole, is due to a Casimir-like negative energy that appears naturally in the solution. In a novel approach to quantum cosmology, we perform canonical quantization of the above model using the operator method and show that it can circumvent the operator ordering ambiguity in the conventional formalism. It leads to a quantum wave equation for the universe, solving which we get the interesting result that the universe is in a ground state with nonzero energy. This solution is different from the Wheeler-DeWitt wave function and possesses exact quantum-classical correspondence during all epochs.

The Born–Oppenheimer approach to quantum cosmology

The scope of this paper is to compare two different approaches for solving the Wheeler–DeWitt (WDW) equation in the presence of homogeneous matter (inflaton) and perturbations around it. The standard Born–Oppenheimer (BO) decomposition, which consists of factorising out the gravitational wave function and then defining the flow of the time through it, and a more general BO decomposition where the whole minisuperspace wave function (i.e. scale factor and homogeneous scalar field) is factorized out. The two approaches are compared, for simplicity, in the case of a minimally coupled inflaton with a flat potential. Besides being exactly solvable, the model we study is also relevant as a toy model for ultra slow roll and primordial black holes formation. The consistency of the latter decomposition is checked against the former by comparing the resulting perturbation (Mukhanov–Sasaki) equations. Finally a few solutions to the homogeneous WDW not suitable for the traditional BO treatment are presented and the corresponding Mukhanov–Sasaki equations are evaluated.

Noncommutative effective loop quantum cosmology: Inclusion of a potential term

We construct and study a simple noncommutative scheme (theta-deformation) for the effective Loop Quantum Cosmology of the flat Friedmann-Lema\^itre-Robertson-Walker model in the presence of a homogeneous scalar field $\phi$ with a potential $\mathcal{V}(\phi)=\frac{1}{2}m^2\phi^2$. We first conduct a simple analysis from the corresponding Hamilton equations of motion considering a generic term $\mathcal V(\phi)$. It is observed that the characteristic Big Bounce of Loop Quantum Cosmology is preserved under such noncommutative extension. When specializing to the quadratic case, numerical solutions to the corresponding Hamilton equations exhibiting an early inflationary epoch with a sufficiently large number of e-foldings are found. It is concluded that, in this noncommutative setup, solutions exist which are in the overall compatible with the early universe predicted by standard (effective) Loop Quantum Cosmology (i.e. a bouncing and inflationary early universe). The issue of the genericness of a sufficiently long inflationary period on the space of solutions in this noncommutative construct remains to be addressed.

The impact of deformed space—space parameters into canonical scalar field model with exponential potential. The case of spatially flat Friedmann—Lemaître—Robertson—Walker (FLRW) universe

In this work, we propose a model of noncommutative cosmology through the deformation of minisuperspace. We focus on an exponentially potential with a homogeneous scalar field minimally coupled to gravity in the spatially flat universe. To process, we use a particular case of noncommutativity by making a deformation of space coordinates only. Then, we compare results in both the commutative model and the noncommutative one.

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.

Study on early inflationary phase using a new form of non-canonical scalar field model

We study the inflationary phase of the early universe as modeled by a non-canonical scalar field. The homogeneous scalar field equation is derived from a Lagrangian density containing a new form of non-canonical kinetic term and a general potential function. The Lie symmetry is studied and a one parameter Lie point symmetry for the homogeneous scalar field equation is found. We use Lie symmetry generator to construct the exact analytical group invariant closed-form solution of the homogeneous scalar field equation without applying any slow-roll approximation from invariant curve condition. The solution thus obtained is seen to be consistent with the Friedmann equations subject to constraint conditions on the potential parameter $$\lambda $$ . In this scenario, we obtain the values for various inflationary parameters and make useful checks on the observational constraints on the parameters from Planck data by imposing a set of bounds on the parameter $$\lambda $$ of the potential. The results for scalar spectral index ( $$n_S$$ ) and tensor-to-scalar ratio (r) presented in the $$(n_S,\,r)$$ plane in the background of Planck2015 and Planck2018 data are in good agreement with cosmological observations. We find $$r\sim 10^{-3}$$ , the targeted value of r that will be detected by the future CMB observation such as LiteBIRD. Interestingly, most significant primordial non-Gaussianity is also achieved. For theoretical completeness of our non-canonical model, we obtain the allowed parameter space in which the ghosts and Laplacian instabilities are absent. We apply the formulas for slow-roll parameter to explain exit from the inflationary phase using the general potential. We also treat the non-canonical scalar field model equation by the dynamical system theory to provide useful checks on the stability of the critical points and show that the group invariant non-canonical inflationary solution is stable attractor in the phase space.

Cosmology with non-minimal coupled gravity: dynamical study of the inflationary universe in the deformed phase space scenario

In this work, we consider a noncommutative (NC) inflationary model with a homogeneous scalar field non-minimally coupled to gravity. We propose to use a canonical deformation between momenta in a spatially flat Friedmann–Le maitre–Robertson–Walker universe. This particular choice of noncommutativity allows interesting dynamics that other NC models seem not to allow. In this approach, the dimensional parameter $$\theta $$ , which considered as the length of Planck, presents the quantum regime. But also, it is crucial to recover the standard results by taking the appropriate limits of this parameter. To note that the $$1\mathrm{st}$$ Friedmann equation remains unaffected while both the Friedmann acceleration and the Klein-Gordon equations are affected by an additional term linear in the NC parameter.

Interacting tachyonic scalar field

We discuss the coupling between dark energy and matter by considering a homogeneous tachyonic scalar field as a candidate for dark energy. We obtained the functional form of scale factor by assuming that the coupling strength depends linearly on the Hubble parameter and energy density. We also estimated the cosmic age of the Universe for different values of coupling constant.