Posts Tagged scalar field

Recent Postings from scalar field

Late time solution for interacting scalar in accelerating spaces [Cross-Listing]

We consider stochastic inflation in an interacting scalar field in spatially homogeneous accelerating space-times with a constant principal slow roll parameter $\epsilon$. We show that, if the scalar potential is scale invariant (which is the case when scalar contains quartic self-interaction and couples non-minimally to gravity), the late-time solution on accelerating FLRW spaces can be described by a probability distribution function (PDF) $\rho$ which is a function of $\varphi/H$ only, where $\varphi=\varphi(\vec x)$ is the scalar field and $H=H(t)$ denotes the Hubble parameter. We give explicit late-time solutions for $\rho\rightarrow \rho_\infty(\varphi/H)$, and thereby find the order $\epsilon$ corrections to the Starobinsky-Yokoyama result. This PDF can then be used to calculate e.g. various $n-$point functions of the (self-interacting) scalar field, which are valid at late times in arbitrary accelerating space-times with $\epsilon=$ constant.

Late time solution for interacting scalar in accelerating spaces [Cross-Listing]

We consider stochastic inflation in an interacting scalar field in spatially homogeneous accelerating space-times with a constant principal slow roll parameter $\epsilon$. We show that, if the scalar potential is scale invariant (which is the case when scalar contains quartic self-interaction and couples non-minimally to gravity), the late-time solution on accelerating FLRW spaces can be described by a probability distribution function (PDF) $\rho$ which is a function of $\varphi/H$ only, where $\varphi=\varphi(\vec x)$ is the scalar field and $H=H(t)$ denotes the Hubble parameter. We give explicit late-time solutions for $\rho\rightarrow \rho_\infty(\varphi/H)$, and thereby find the order $\epsilon$ corrections to the Starobinsky-Yokoyama result. This PDF can then be used to calculate e.g. various $n-$point functions of the (self-interacting) scalar field, which are valid at late times in arbitrary accelerating space-times with $\epsilon=$ constant.

Electrodynamics on Cosmological Scales [Cross-Listing]

Maxwell’s equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero net charge Maxwell’s equations always fail regardless of the spacetime symmetry and the charge distribution. The two paradoxes indicate that Maxwell’s equations need to be modified to be applicable to the universe as a whole. We consider two types of modified Maxwell equations, both of which can address the paradoxes. One is the Proca-type equation, which contains a photon mass term, i.e., a term proportional to the vector potential of the electromagnetic field. We show that this term can naturally arise if the electromagnetic field is coupled to a complex scalar field. If the complex scalar field is interpreted as describing charged pion particles, the mean mass density of charged pions in the universe gives rise to an effective photon mass with a Compton wavelength comparable to the Hubble radius of the universe. The other type of modified Maxwell equations contains a term with the electromagnetic field potential vector coupled to the spacetime curvature tensor. We show that this term can naturally arise if the Maxwell equation in a flat spacetime is written in terms of a symmetric tensor instead of the anti-symmetric tensor and then extended to a curved spacetime through the "minimal substitution rule". Some consequences of the modified Maxwell equations are investigated. The results show that for reasonable parameters the modification does not affect existing experiments and observations. However, we argue that, the modified equations may be testable in appropriate astrophysical and cosmological environments.

Scalar mass stability bound in a simple Yukawa-theory from renormalisation group equations

Functional Renormalisation Group equations are constructed for a simple fermion-scalar Yukawa-model with discrete chiral symmetry, including also the effect of a nonzero composite fermion background beyond the conventional scalar condensate. Two approximate versions consistent with the scale dependent equations of motion are solved, taking into account also field renormalisation. The lower bound for the mass of the scalar field is determined requiring the stability of effective potential in the full momentum range, from the cutoff down to vanishing momentum. Close agreement is demonstrated with the results of previous studies done exclusively in presence of scalar condensate. A semiquantitative explanation is provided both for the negligible effect of the wave-function renormalisation and the narrow dispersion in the scalar mass bounds found from different approximation schemes.

Scalar mass stability bound in a simple Yukawa-theory from renormalisation group equations [Cross-Listing]

Functional Renormalisation Group equations are constructed for a simple fermion-scalar Yukawa-model with discrete chiral symmetry, including also the effect of a nonzero composite fermion background beyond the conventional scalar condensate. Two approximate versions consistent with the scale dependent equations of motion are solved, taking into account also field renormalisation. The lower bound for the mass of the scalar field is determined requiring the stability of effective potential in the full momentum range, from the cutoff down to vanishing momentum. Close agreement is demonstrated with the results of previous studies done exclusively in presence of scalar condensate. A semiquantitative explanation is provided both for the negligible effect of the wave-function renormalisation and the narrow dispersion in the scalar mass bounds found from different approximation schemes.

Teleparallel quintessence with a non-minimal coupling to a boundary term [Cross-Listing]

We propose a new model in the teleparallel framework where we consider a scalar field non-minimally coupled to both the torsion $T$ and a boundary term given by the divergence of the torsion vector $B=\frac{2}{e}\partial_\mu (eT^\mu)$. This is inspired by the relation $R=-T+B$ between the Ricci scalar of general relativity and the torsion of teleparallel gravity. This theory in suitable limits incorporates both the non-minimal coupling of a scalar field to torsion, and the non-minimal coupling of a scalar field to the Ricci scalar. We analyse the cosmology of such models, and we perform a dynamical systems analysis on the case when we have only a pure coupling to the boundary term. It is found that the system generically evolves to a late time accelerating attractor solution without requiring any fine tuning of the parameters. A dynamical crossing of the phantom barrier is also shown to be possible.

Curvature Perturbation and Domain Wall Formation with Pseudo Scaling Scalar Dynamics [Cross-Listing]

Cosmological dynamics of scalar field with a monomial potential $\phi^{n}$ with a general background equation of state is revisited. It is known that if $n$ is smaller than a critical value, the scalar field exhibits a coherent oscillation and if $n$ is larger it obeys a scaling solution without oscillation. We study in detail the case where $n$ is equal to the critical value, and find a peculiar scalar dynamics which is neither oscillating nor scaling solution, and we call it a pseudo scaling solution. We also discuss cosmological implications of a pseudo scaling scalar dynamics, such as the curvature perturbation and the domain wall problem.

Curvature Perturbation and Domain Wall Formation with Pseudo Scaling Scalar Dynamics [Cross-Listing]

Cosmological dynamics of scalar field with a monomial potential $\phi^{n}$ with a general background equation of state is revisited. It is known that if $n$ is smaller than a critical value, the scalar field exhibits a coherent oscillation and if $n$ is larger it obeys a scaling solution without oscillation. We study in detail the case where $n$ is equal to the critical value, and find a peculiar scalar dynamics which is neither oscillating nor scaling solution, and we call it a pseudo scaling solution. We also discuss cosmological implications of a pseudo scaling scalar dynamics, such as the curvature perturbation and the domain wall problem.

Scalar field cosmology modified by the Generalized Uncertainty Principle [Cross-Listing]

We consider quintessence scalar field cosmology in which the Lagrangian of the scalar field is modified by the Generalized Uncertainty Principle. We show that the perturbation terms which arise from the deformed algebra are equivalent with the existence of a second scalar field, where the two fields interact in the kinetic part. Moreover, we consider a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker spacetime (FLRW), and we derive the gravitational field equations. We show that the modified equation of state parameter $w_{GUP}$ can cross the phantom divide line; that is $w_{GUP}<-1$. Furthermore, we derive the field equations in the dimensionless parameters, the dynamical system which arises is a singular perturbation system in which we study the existence of the fixed points in the slow manifold. Finally, we perform numerical simulations for some well known models and we show that for these models with the specific initial conditions, the parameter $w_{GUP}$ crosses the phantom barrier.

Scalar field cosmology modified by the Generalized Uncertainty Principle [Cross-Listing]

We consider quintessence scalar field cosmology in which the Lagrangian of the scalar field is modified by the Generalized Uncertainty Principle. We show that the perturbation terms which arise from the deformed algebra are equivalent with the existence of a second scalar field, where the two fields interact in the kinetic part. Moreover, we consider a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker spacetime (FLRW), and we derive the gravitational field equations. We show that the modified equation of state parameter $w_{GUP}$ can cross the phantom divide line; that is $w_{GUP}<-1$. Furthermore, we derive the field equations in the dimensionless parameters, the dynamical system which arises is a singular perturbation system in which we study the existence of the fixed points in the slow manifold. Finally, we perform numerical simulations for some well known models and we show that for these models with the specific initial conditions, the parameter $w_{GUP}$ crosses the phantom barrier.

Entanglement Dynamics of Detectors in an Einstein Cylinder [Cross-Listing]

We investigate how nontrivial topology affects the entanglement dynamics between a detector and a quantum field and between two detectors mediated by a quantum field. Nontrivial topology refers to both that of the base space and that of the bundle. Using a derivative-coupling Unruh-DeWitt-like detector model interacting with a quantum scalar field in an Einstein cylinder S1 (space) x R1 (time), we see the beating behaviors in the dynamics of the detector-field entanglement and the detector-detector entanglement, which distinguish from the results in the non-compact (1+1) dimensional Minkowski space. The beat patterns of entanglement dynamics in an untwisted and twisted fields with the same parameter values are different simply because of different spectrum of the eigen-modes. In terms of the physically measurable momentum of the detectors, we find that the contribution by the zero mode in a normal field to entanglement dynamics has no qualitative difference from those by the nonzero modes.

Oscillons and oscillating kinks in the Abelian-Higgs model

We study the classical dynamics of the Abelian Higgs model employing an asymptotic multiscale expansion method, which uses the ratio of the Higgs to the gauge field amplitudes as a small parameter. We derive an effective nonlinear Schr\"{o}dinger equation for the gauge field, and a linear equation for the scalar field containing the gauge field as a nonlinear source. This equation is used to predict the existence of oscillons and oscillating kinks for certain regimes of the ratio of the Higgs to the gauge field masses. Results of numerical simulations are found to be in very good agreement with the analytical findings, and show that the oscillons are robust, while kinks are unstable. It is also demonstrated that oscillons emerge spontaneously as a result of the onset of the modulational instability of plane wave solutions of the model. Connections of the obtained solutions with the phenomenology of superconductors is discussed.

Effects of local features of the inflaton potential on the spectrum and bispectrum of primordial perturbations

We study the effects of a class of features of the potential of slow-roll inflationary models corresponding to a step symmetrically dumped by an even power negative exponential factor. We compute the effects on the background evolution and on the scalar and tensor perturbations. This class of features differs from other branch-type features considered previously because the potential is only affected in a limited range of the scalar field value, and is symmetric respect to the location of the feature. As a consequence this type of features only affects the spectrum and bispectrum in a narrow range of scales which leave the horizon during the time interval corresponding to the modification of the potential, contrary to branch-type features which have effects on all the perturbation modes leaving the horizon when the field value is within the interval defining the branch. When the scalar field enters the range affected by the feature the slow-roll conditions are temporarily violated, but once the field leaves the interval affected by the feature the slow roll regime is re-established. The tensor-to-scalar ration, the spectrum and bispectrum of primordial curvature perturbations are affected by oscillations around the scale $k_0$ exiting the horizon at the time $\tau_0$ of the feature. The amplitude of the oscillations depends on the parameters defining the feature, and the effects are larger when the potential has a steeper change, since in this case the slow-roll violation is also stronger. Due to the local nature of their effects these type of features could be used to model local glitches of the power spectrum without affecting other scales.

Ultraviolet asymptotics for quasiperiodic AdS_4 perturbations [Cross-Listing]

Spherically symmetric perturbations in AdS-scalar field systems of small amplitude epsilon approximately periodic on time scales of order 1/epsilon^2 (in the sense that no significant transfer of energy between the AdS normal modes occurs) have played an important role in considerations of AdS stability. They are seen as anchors of stability islands where collapse of small perturbations to black holes does not occur. (This collapse, if it happens, typically develops on time scales of the order 1/epsilon^2.) We construct an analytic treatment of the frequency spectra of such quasiperiodic perturbations, paying special attention to the large frequency asymptotics. For the case of a self-interacting phi^4 scalar field in a non-dynamical AdS background, we arrive at a fairly complete analytic picture involving quasiperiodic spectra with an exponential suppression modulated by a power law at large mode numbers. For the case of dynamical gravity, the structure of the large frequency asymptotics is more complicated. We give analytic explanations for the general qualitative features of quasiperiodic solutions localized around a single mode, in close parallel to our discussion of the probe scalar field, and find numerical evidence for logarithmic modulations in the gravitational quasiperiodic spectra existing on top of the formulas previously reported in the literature.

Large N limit of supersymmetric Chern-Simons-matter model: breakdown of superconformal symmetry

In this work we study some properties of the three dimensional $U(N)$ SUSY Chern-Simons coupled to a scalar field in the fundamental representation in the large $N$ limit. For large $N$ we show that the theory has two phases, one which is conformally invariant, and other where the superconformal symmetry is broken and masses for the matter fields are generated.

Dark matter relic density in scalar-tensor gravity revisited

We revisit the calculation of dark matter relic abundances in scalar-tensor gravity using a generic form $A(\varphi_*) = e^{\beta\varphi_*^2/2}$ for the coupling between the scalar field $\varphi_*$ and the metric, for which detailed Big Bang Nucleosynthesis constraints are available. We find that BBN constraints restrict the modified expansion rate in these models to be almost degenerate with the standard expansion history at the time of dark matter decoupling. In this case the maximum level of enhancement of the dark matter relic density was found to be a factor of $\sim 3$, several orders of magnitude below that found in previous investigations.

Continuity of Scalar Fields With Logarithmic Correlations [Cross-Listing]

We apply select ideas from the modern theory of stochastic processes in order to study the continuity/roughness of scalar quantum fields. A scalar field with logarithmic correlations (such as a massless field in 1+1 spacetime dimensions) has the mildest of singularities, making it a logical starting point. Instead of the usual inner product of the field with a smooth function, we introduce a moving average on an interval which allows us to obtain explicit results and has a simple physical interpretation. Using the mathematical work of Dudley, we prove that the averaged random process is in fact continuous, and give a precise modulus of continuity bounding the short-distance variation.

Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory

Clarifying the locality properties of higher-spin gravity is a pressing task, but notoriously difficult due to the absence of a weakly-coupled flat regime. The simplest non-trivial case where this question can be addressed is the quartic self-interaction of the AdS scalar field present in the higher-spin multiplet. We investigate this issue in the context of the holographic duality between the minimal bosonic higher-spin theory on AdS$_4$ and the free $O\left(N\right)$ vector model in three dimensions. In particular, we determine the exact explicit form of the derivative expansion of the bulk scalar quartic vertex. The quartic vertex is obtained from the field theory four-point function of the operator dual to the bulk scalar, by making use of our previous results for the Witten diagrams of higher-spin exchanges. This is facilitated by establishing the conformal block expansions of both the boundary four-point function and the dual bulk Witten diagram amplitudes. We show that the vertex we find satisfies a generalised notion of locality.

The evolution of cosmological perturbations and the production of non-Gaussianities through a nonsingular bounce: indications for a no-go theorem in single field matter bounce cosmologies [Cross-Listing]

Assuming that curvature perturbations and gravitational waves originally arise from vacuum fluctuations in a matter-dominated phase of contraction, we study the dynamics of the cosmological perturbations evolving through a nonsingular bouncing phase described by a generic single scalar field Lagrangian minimally coupled to Einstein gravity. In order for such a model to be consistent with the current upper limits on the tensor-to-scalar ratio, there must be an enhancement of the curvature fluctuations during the bounce phase. We show that, while it remains possible to enlarge the amplitude of curvature perturbations due to the non-trivial background evolution, this growth is very limited because of the conservation of curvature perturbations on super-Hubble scales. We further perform a general analysis of the evolution of primordial non-Gaussianities through the bounce phase. By studying the general form of the bispectrum we show that the non-Gaussianity parameter $f_{\mathrm{NL}}$ (which is of order unity before the bounce phase) is enhanced during the bounce phase if the curvature fluctuations grow. Hence, in such nonsingular bounce models with matter given by a single scalar field, there appears to be a tension between obtaining a small enough tensor-to-scalar ratio and not obtaining a value of $f_{\mathrm{NL}}$ in excess of the current upper bounds. This conclusion may be considered as a "no-go" theorem for single field matter bounce cosmologies starting with vacuum initial conditions for the fluctuations.

The evolution of cosmological perturbations and the production of non-Gaussianities through a nonsingular bounce: indications for a no-go theorem in single field matter bounce cosmologies [Cross-Listing]

Assuming that curvature perturbations and gravitational waves originally arise from vacuum fluctuations in a matter-dominated phase of contraction, we study the dynamics of the cosmological perturbations evolving through a nonsingular bouncing phase described by a generic single scalar field Lagrangian minimally coupled to Einstein gravity. In order for such a model to be consistent with the current upper limits on the tensor-to-scalar ratio, there must be an enhancement of the curvature fluctuations during the bounce phase. We show that, while it remains possible to enlarge the amplitude of curvature perturbations due to the non-trivial background evolution, this growth is very limited because of the conservation of curvature perturbations on super-Hubble scales. We further perform a general analysis of the evolution of primordial non-Gaussianities through the bounce phase. By studying the general form of the bispectrum we show that the non-Gaussianity parameter $f_{\mathrm{NL}}$ (which is of order unity before the bounce phase) is enhanced during the bounce phase if the curvature fluctuations grow. Hence, in such nonsingular bounce models with matter given by a single scalar field, there appears to be a tension between obtaining a small enough tensor-to-scalar ratio and not obtaining a value of $f_{\mathrm{NL}}$ in excess of the current upper bounds. This conclusion may be considered as a "no-go" theorem for single field matter bounce cosmologies starting with vacuum initial conditions for the fluctuations.

The evolution of cosmological perturbations and the production of non-Gaussianities through a nonsingular bounce: indications for a no-go theorem in single field matter bounce cosmologies

Assuming that curvature perturbations and gravitational waves originally arise from vacuum fluctuations in a matter-dominated phase of contraction, we study the dynamics of the cosmological perturbations evolving through a nonsingular bouncing phase described by a generic single scalar field Lagrangian minimally coupled to Einstein gravity. In order for such a model to be consistent with the current upper limits on the tensor-to-scalar ratio, there must be an enhancement of the curvature fluctuations during the bounce phase. We show that, while it remains possible to enlarge the amplitude of curvature perturbations due to the non-trivial background evolution, this growth is very limited because of the conservation of curvature perturbations on super-Hubble scales. We further perform a general analysis of the evolution of primordial non-Gaussianities through the bounce phase. By studying the general form of the bispectrum we show that the non-Gaussianity parameter $f_{\mathrm{NL}}$ (which is of order unity before the bounce phase) is enhanced during the bounce phase if the curvature fluctuations grow. Hence, in such nonsingular bounce models with matter given by a single scalar field, there appears to be a tension between obtaining a small enough tensor-to-scalar ratio and not obtaining a value of $f_{\mathrm{NL}}$ in excess of the current upper bounds. This conclusion may be considered as a "no-go" theorem for single field matter bounce cosmologies starting with vacuum initial conditions for the fluctuations.

Stability of a tachyon braneworld [Cross-Listing]

Within the braneworld paradigm the tachyonic scalar field has been used to generate models that attempt to solve some of the open problems that physics faces nowadays, both in cosmology and high energy physics as well. When these field configurations are produced by the interplay of higher dimensional gravity with some matter content, braneworld models must prove to be stable under small fluctuations of the background matter fields, among other consistency tests. Here we present a complete proof of the stability under scalar perturbations of tachyonic thick braneworlds with an embedded maximally symmetric 4D space-time, revealing its physical consistency. This family contains a recently reported tachyonic de Sitter thick braneworld which possesses a series of appealing properties. These features encompasses complete regularity, asymptotic flatness (instead of being asymptotically dS/AdS even when it contains a negative bulk cosmological constant and the relevant 3-brane has dS symmetry), and a graviton spectrum with a single bound state that accounts for the 4D graviton, separated from the continuum of Kaluza-Klein massive graviton excitations by a mass gap.

Stability of a tachyon braneworld

Within the braneworld paradigm the tachyonic scalar field has been used to generate models that attempt to solve some of the open problems that physics faces nowadays, both in cosmology and high energy physics as well. When these field configurations are produced by the interplay of higher dimensional gravity with some matter content, braneworld models must prove to be stable under small fluctuations of the background matter fields, among other consistency tests. Here we present a complete proof of the stability under scalar perturbations of tachyonic thick braneworlds with an embedded maximally symmetric 4D space-time, revealing its physical consistency. This family contains a recently reported tachyonic de Sitter thick braneworld which possesses a series of appealing properties. These features encompasses complete regularity, asymptotic flatness (instead of being asymptotically dS/AdS even when it contains a negative bulk cosmological constant and the relevant 3-brane has dS symmetry), and a graviton spectrum with a single bound state that accounts for the 4D graviton, separated from the continuum of Kaluza-Klein massive graviton excitations by a mass gap.

Chemical potential driven phase transition of black holes in AdS space

Einstein-Maxwell theory conformally coupled to a scalar field in D dimensions may exhibit a phase transition at low temperature whose endpoint is an asymptotically Anti-de Sitter black hole with a scalar field profile that is regular everywhere outside and on the horizon. This provides a tractable model to study the phase transition of hairy black holes in Anti-de Sitter space in which the backreaction on the geometry can be solved analytically.

The Statistical Model with Interpartial Scalar Conformally Invariant Interaction

A closed mathematical model of the statistical self-gravitating system of scalar charged particles for conformal invariant scalar interactions is constructed on the basis of relativistic kinetics and gravitation theory. Asymptotic properties of the model are investigated in the ultrarelativistic limit. It is shown, that scalar charge density automatically generates scalar field effective mass and the value of this mass is found. In the paper it is proved the asymptotic conformal invariance of constitutive equations in case of homogenous isotropic Universe. Also it is proved the asymptotic conformal invariance of field equations at the early stages of cosmological evolution.

Mass inflation near the central singularity in spherical collapse

We study spherical scalar collapse toward a black hole formation, and examine the asymptotic dynamics near the central singularity of the formed Schwarzschild black hole. It is found that, due to strong backreaction of a scalar field on the geometry, the mass parameter inflates in the vicinity of the singularity. In collapse, the Misner-Sharp mass is a locally conserved quantity, not providing information on the black hole mass that is measured at asymptotically flat regions.

About the cosmological constant in geometric scalar theory of gravity [Cross-Listing]

In this paper we study how to include the cosmological constant in geometric scalar theory of gravity (GSG). Firstly we show that the cosmological constant could not be modeled by a matter field, unlike in General Relativity. We also show that a spherically symmetric matter distribution, over the de Sitter vacuum, does not produce the Kottler solution and no black hole. To circumvent this problem we introduce an coupling term between the scalar field and the vacuum curvature in way to provide the Kottler solution. We also apply the original (GSGI) and the modified (GSGII) geometric scalar theory of gravity to the Friedmann-Robertson-Walker cosmology. A numerical analysis indicates that GSGII is most sensible to the cosmological constant them GSGI.

About the cosmological constant in geometric scalar theory of gravity

In this paper we study how to include the cosmological constant in geometric scalar theory of gravity (GSG). Firstly we show that the cosmological constant could not be modeled by a matter field, unlike in General Relativity. We also show that a spherically symmetric matter distribution, over the de Sitter vacuum, does not produce the Kottler solution and no black hole. To circumvent this problem we introduce an coupling term between the scalar field and the vacuum curvature in way to provide the Kottler solution. We also apply the original (GSGI) and the modified (GSGII) geometric scalar theory of gravity to the Friedmann-Robertson-Walker cosmology. A numerical analysis indicates that GSGII is most sensible to the cosmological constant them GSGI.

Dark sector impact on gravitational collapse of an electrically charged scalar field

Dark matter and dark energy are dominating components of the Universe. Their presence affects the course and results of processes, which are driven by the gravitational interaction. The objective of the paper was to examine the influence of the dark sector on the gravitational collapse of an electrically charged scalar field. A phantom scalar field was used as a model of dark energy in the system. Dark matter was modeled by a complex scalar field with a quartic potential, charged under an U(1)-gauge field. The dark components were coupled to the electrically charged scalar field via the exponential coupling and the gauge field-Maxwell field kinetic mixing, respectively. Complete non-linear simulations of the investigated process were performed. They were conducted from regular initial data to the end state, which was the matter dispersal or a singularity formation in a spacetime. During the collapse in the presence of dark energy dynamical wormholes and naked singularities were formed in emerging spacetimes. The wormhole throats were stabilized by the violation of the null energy condition, which occurred due to a significant increase of a value of the phantom scalar field function in its vicinity. The square of mass parameter of the dark matter scalar field potential controlled the formation of a Cauchy horizon or wormhole throats in the spacetime. The joint impact of dark energy and dark matter on the examined process indicated that the former decides what type of an object forms, while the latter controls the amount of time needed for the object to form. Additionally, the dark sector suppresses the natural tendency of an electrically charged scalar field to form a dynamical Reissner-Nordstr\"{o}m spacetime during the gravitational collapse.

Dark sector impact on gravitational collapse of an electrically charged scalar field [Cross-Listing]

Dark matter and dark energy are dominating components of the Universe. Their presence affects the course and results of processes, which are driven by the gravitational interaction. The objective of the paper was to examine the influence of the dark sector on the gravitational collapse of an electrically charged scalar field. A phantom scalar field was used as a model of dark energy in the system. Dark matter was modeled by a complex scalar field with a quartic potential, charged under an U(1)-gauge field. The dark components were coupled to the electrically charged scalar field via the exponential coupling and the gauge field-Maxwell field kinetic mixing, respectively. Complete non-linear simulations of the investigated process were performed. They were conducted from regular initial data to the end state, which was the matter dispersal or a singularity formation in a spacetime. During the collapse in the presence of dark energy dynamical wormholes and naked singularities were formed in emerging spacetimes. The wormhole throats were stabilized by the violation of the null energy condition, which occurred due to a significant increase of a value of the phantom scalar field function in its vicinity. The square of mass parameter of the dark matter scalar field potential controlled the formation of a Cauchy horizon or wormhole throats in the spacetime. The joint impact of dark energy and dark matter on the examined process indicated that the former decides what type of an object forms, while the latter controls the amount of time needed for the object to form. Additionally, the dark sector suppresses the natural tendency of an electrically charged scalar field to form a dynamical Reissner-Nordstr\"{o}m spacetime during the gravitational collapse.

Supporting wormholes by spacetime parity and topology in the Lovelock-Brans-Dicke gravity

Following the recent theory of Lovelock-Brans-Dicke gravity, we continue to investigate the conditions to support traversable wormholes by the gravitational effects of spacetime parity and topology, which arise from the nonminimal couplings of a background scalar field with the Chern-Pontryagin density and the Gauss-Bonnet invariant. The flaring-out condition indicates that a Morris-Thorne-type wormhole can be maintained by violating the generalized null energy conditions, and thus also breaking down the generalized weak, strong, and dominant energy conditions. Meanwhile, the standard energy conditions in general relativity may still be respected by the classical matter fields. To meet these requirements, the two topological effects have to dominate over the other sources of gravity, and the scalar field is preferred to be noncanonical.

Supporting wormholes by spacetime parity and topology in the Lovelock-Brans-Dicke gravity [Cross-Listing]

Following the recent theory of Lovelock-Brans-Dicke gravity, we continue to investigate the conditions to support traversable wormholes by the gravitational effects of spacetime parity and topology, which arise from the nonminimal couplings of a background scalar field with the Chern-Pontryagin density and the Gauss-Bonnet invariant. The flaring-out condition indicates that a Morris-Thorne-type wormhole can be maintained by violating the generalized null energy conditions, and thus also breaking down the generalized weak, strong, and dominant energy conditions. Meanwhile, the standard energy conditions in general relativity may still be respected by the classical matter fields. To meet these requirements, the two topological effects have to dominate over the other sources of gravity, and the scalar field is preferred to be noncanonical.

Supporting wormholes by spacetime parity and topology in Lovelock-Brans-Dicke gravity [Replacement]

Following the recent theory of Lovelock-Brans-Dicke gravity, we continue to investigate the conditions to support traversable wormholes by the gravitational effects of spacetime parity and topology, which arise from the nonminimal couplings of a background scalar field to the Chern-Pontryagin density and the Gauss-Bonnet invariant. The flaring-out condition indicates that a Morris-Thorne-type wormhole can be maintained by violating the generalized null energy condition, and thus also breaking down the generalized weak, strong, and dominant energy conditions; meanwhile, analyses of the zero-tidal-force solution show that the standard energy conditions in general relativity can still be respected by the physical matter threading the wormhole. In this situation, the two topological effects have to dominate over the ordinary-matter source of gravity, and the scalar field is preferred to be noncanonical. Also, we find that it is easier in Lovelock-Brans-Dicke than Brans-Dicke gravity to support wormholes while have the standard energy conditions protected.

Supporting wormholes by spacetime parity and topology in Lovelock-Brans-Dicke gravity [Replacement]

Following the recent theory of Lovelock-Brans-Dicke gravity, we continue to investigate the conditions to support traversable wormholes by the gravitational effects of spacetime parity and topology, which arise from the nonminimal couplings of a background scalar field to the Chern-Pontryagin density and the Gauss-Bonnet invariant. The flaring-out condition indicates that a Morris-Thorne-type wormhole can be maintained by violating the generalized null energy condition, and thus also breaking down the generalized weak, strong, and dominant energy conditions; meanwhile, analyses of the zero-tidal-force solution show that the standard energy conditions in general relativity can still be respected by the physical matter threading the wormhole. In this situation, the two topological effects have to dominate over the ordinary-matter source of gravity, and the scalar field is preferred to be noncanonical. Also, we find that it is easier in Lovelock-Brans-Dicke than Brans-Dicke gravity to support wormholes while have the standard energy conditions protected.

Dark Energy and Dark Matter From Hidden Symmetry of Gravity Model with a Non-Riemannian Volume Form [Replacement]

We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume-forms (covariant integration measure densities) on the spacetime manifold – one standard Riemannian given by the square-root of the determinant of the pertinent Riemannian metric and another non-Riemannian volume-form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless "dust" fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding appropriate perturbation, which breaks the above hidden symmetry and along with this it couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe’s epoch without evolution pathologies.

Dark Energy and Dark Matter From Hidden Symmetry of Gravity Model with a Non-Riemannian Volume Form

We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume-forms (covariant integration measure densities) on the spacetime manifold – one standard Riemannian given by the square-root of the determinant of the pertinent Riemannian metric and another non-Riemannian volume-form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless "dust" fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding appropriate perturbation, which breaks the above hidden symmetry and along with this it couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe’s epoch without evolution pathologies.

Dark Energy and Dark Matter From Hidden Symmetry of Gravity Model with a Non-Riemannian Volume Form [Cross-Listing]

We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume-forms (covariant integration measure densities) on the spacetime manifold – one standard Riemannian given by the square-root of the determinant of the pertinent Riemannian metric and another non-Riemannian volume-form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless "dust" fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding appropriate perturbation, which breaks the above hidden symmetry and along with this it couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe’s epoch without evolution pathologies.

Dark Energy and Dark Matter From Hidden Symmetry of Gravity Model with a Non-Riemannian Volume Form [Replacement]

We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume-forms (covariant integration measure densities) on the spacetime manifold – one standard Riemannian given by the square-root of the determinant of the pertinent Riemannian metric and another non-Riemannian volume-form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless "dust" fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding appropriate perturbation, which breaks the above hidden symmetry and along with this it couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe’s epoch without evolution pathologies.

Dark Energy and Dark Matter From Hidden Symmetry of Gravity Model with a Non-Riemannian Volume Form [Replacement]

We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume-forms (covariant integration measure densities) on the spacetime manifold – one standard Riemannian given by the square-root of the determinant of the pertinent Riemannian metric and another non-Riemannian volume-form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless "dust" fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding appropriate perturbation, which breaks the above hidden symmetry and along with this it couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe’s epoch without evolution pathologies.

Dark Energy and Dark Matter From Hidden Symmetry of Gravity Model with a Non-Riemannian Volume Form [Replacement]

We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume-forms (covariant integration measure densities) on the spacetime manifold – one standard Riemannian given by the square-root of the determinant of the pertinent Riemannian metric and another non-Riemannian volume-form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless "dust" fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding appropriate perturbation, which breaks the above hidden symmetry and along with this it couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe’s epoch without evolution pathologies.

Dark Energy and Dark Matter From Hidden Symmetry of Gravity Model with a Non-Riemannian Volume Form [Replacement]

We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume-forms (covariant integration measure densities) on the spacetime manifold – one standard Riemannian given by the square-root of the determinant of the pertinent Riemannian metric and another non-Riemannian volume-form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless "dust" fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding appropriate perturbation, which breaks the above hidden symmetry and along with this it couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe’s epoch without evolution pathologies.

Dark Energy and Dark Matter From Hidden Symmetry of Gravity Model with a Non-Riemannian Volume Form [Replacement]

We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume-forms (covariant integration measure densities) on the spacetime manifold – one standard Riemannian given by the square-root of the determinant of the pertinent Riemannian metric and another non-Riemannian volume-form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless "dust" fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding appropriate perturbation, which breaks the above hidden symmetry and along with this it couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe’s epoch without evolution pathologies.

Dark Energy and Dark Matter From Hidden Symmetry of Gravity Model with a Non-Riemannian Volume Form [Cross-Listing]

We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume-forms (covariant integration measure densities) on the spacetime manifold – one standard Riemannian given by the square-root of the determinant of the pertinent Riemannian metric and another non-Riemannian volume-form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless "dust" fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding appropriate perturbation, which breaks the above hidden symmetry and along with this it couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe’s epoch without evolution pathologies.

Inflationary Potentials from the Exact Renormalisation Group [Cross-Listing]

We show that an inflationary slow-roll potential can be derived as an IR limit of the non-perturbative exact renormalisation group equation for a scalar field within the mean-field approximation. The result follows without having to specify a Lagrangian for the UV theory at the Planck scale. All we assume is that the theory contains a scalar mode with suppressed coupling to other UV fields. The resulting effective potential gives rise to slow-roll inflation, which is fully consistent with the recent observations.

Inflationary Potentials from the Exact Renormalisation Group [Cross-Listing]

We show that an inflationary slow-roll potential can be derived as an IR limit of the non-perturbative exact renormalisation group equation for a scalar field within the mean-field approximation. The result follows without having to specify a Lagrangian for the UV theory at the Planck scale. All we assume is that the theory contains a scalar mode with suppressed coupling to other UV fields. The resulting effective potential gives rise to slow-roll inflation, which is fully consistent with the recent observations.

Inflationary Potentials from the Exact Renormalisation Group

We show that an inflationary slow-roll potential can be derived as an IR limit of the non-perturbative exact renormalisation group equation for a scalar field within the mean-field approximation. The result follows without having to specify a Lagrangian for the UV theory at the Planck scale. All we assume is that the theory contains a scalar mode with suppressed coupling to other UV fields. The resulting effective potential gives rise to slow-roll inflation, which is fully consistent with the recent observations.

Holographic Trace Anomaly and Local Renormalization Group [Replacement]

The Hamilton-Jacobi method in holography has produced important results both at a renormalization group (RG) fixed point and away from it. In this paper we use the Hamilton-Jacobi method to compute the holographic trace anomaly for four- and six-dimensional boundary conformal field theories (CFTs), assuming higher-derivative gravity and interactions of scalar fields in the bulk. The scalar field contributions to the anomaly appear in CFTs with exactly marginal operators. Moving away from the fixed point, we show that the Hamilton-Jacobi formalism provides a deep connection between the holographic and the local RG. We derive the local RG equation holographically, and verify explicitly that it satisfies Weyl consistency conditions stemming from the commutativity of Weyl scalings. We also consider massive scalar fields in the bulk corresponding to boundary relevant operators, and comment on their effects to the local RG equation.

Holographic Trace Anomaly and Local Renormalization Group

The Hamilton-Jacobi method in holography has produced important results both at a renormalization group (RG) fixed point and away from it. In this paper we use the Hamilton-Jacobi method to compute the holographic trace anomaly for four- and six-dimensional boundary conformal field theories (CFTs), assuming higher-derivative gravity and interactions of scalar fields in the bulk. The scalar field contributions to the anomaly appear in CFTs with exactly marginal operators. Moving away from the fixed point, we show that the Hamilton-Jacobi formalism provides a deep connection between the holographic and the local RG. We derive the local RG equation holographically, and verify explicitly that it satisfies Weyl consistency conditions stemming from the commutativity of Weyl scalings. We also consider massive scalar fields in the bulk corresponding to boundary relevant operators, and comment on their effects to the local RG equation.

Constraints on scalar coupling to electromagnetism

I review experimental and observational constraints on a possible non-minimal coupling of a scalar field to electromagnetism (dilatonic coupling). Such a coupling is motivated from recent quasar spectrum observations that indicate a possible spatial and/or temporal variation of the fine-structure constant. I consider a dilatonic coupling of the form $B_F(\phi)=1+g\phi$. The strongest bounds on $g$ come from weak equivalence principle tests which impose the constraint $g<1.6 \times 10^{-17} GeV^{-1}$. This constraint is strong enough to rule out this class of models as a cause for an observable cosmological variation of the fine structure constant unless chameleon type mechanism is present.

The fate of a Universe driven by a linear potential [Cross-Listing]

We study the fate of our Universe assuming that the present accelerated stage is due to a scalar field in a linear potential. Such a Universe would bounce and collapse in the future. We solve numerically and analytically the equations of motion for the scalar field and the scale factor. In particular, we relate the duration of the accelerated stage, the bounce and the collapse with the mass of the field and, thus, with the current value of equation of state $w$. We obtain an expression which predicts the age of the Universe for a given $w+1$. The present constraints on $w$ imply that the Universe will not collapse in the next $56$ billion years. Moreover, a cosmological solution to the coincidence problem favors a significant deviation of $w$ from $-1$ such that the Universe collapses in the not too distant future.

 

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