Energy-momentum Tensor Research Articles

Gravitational waves during Higgs inflation from complex geometrical scalar-tensor theory of gravity

In this paper we investigate tensor fluctuations of the metric at the end of a Higgs inflationary period in the context of a recently introduced complex geometrical scalar-tensor theory of gravity. In our model the Higgs field has a geometrical origin and the affine connection is determined by the Palatini’s principle. Additionally, we consider an extra contribution to the tensor-fluctuations equation coming from the vacuum term in the energy–momentum tensor associated to the Higgs field. The Higgs potential is rescaled by the non-canonicity function of the kinetic term of the field which is modified by the symmetry group of the background geometry. We obtain a nearly scale invariant spectrum and a scalar to tensor ratio in agreement with PLANCK 2018 cosmological results.

Cosmic energy density: particles, fields and the vacuum

We revisit the cosmic evolution of the energy density of a quantized free scalar field and assess under what conditions the particle production and classical field approximations reproduce its correct value. Because the unrenormalized energy-momentum tensor diverges in the ultraviolet, it is necessary to frame our discussion within an appropriate regularization and renormalization scheme. Pauli-Villars avoids some of the drawbacks of adiabatic subtraction and dimensional regularization and is particularly convenient in this context. In some cases, we can predict the evolution of the energy density irrespectively of the quantum state of the field modes. To further illustrate our results we focus however on the in vacuum, the preferred quantum state singled out by inflation, and explore to what extent the latter determines the subsequent evolution of the energy density regardless of the unknown details of reheating. We contrast this discussion with examples of transitions to radiation domination that avoid some of the problems of the one commonly studied in the literature, and point out some instances in which the particle production or the classical field approximations lead to the incorrect energy density. Along the way, we also elaborate on the connection of our analysis to dynamical dark energy models and axion-like dark matter candidates.

A topologically charged four-dimensional wormhole and the energy conditions

In this research work, our primary focus revolves around the examination of a specific category of traversable wormholes known as topologically charged generalized Schwarzschild-Simpson-Visser-type wormhole, ds 2 = -(1-(2M/√(x 2+b 2))) dt 2+(1-(2M/√(x 2+b 2)))-1 ·(dx 2/α2)+(x 2+a 2) (dθ 2+sin2 θ dϕ 2). This wormhole is uniquely defined by a pair of key parameters including global monopole charge. A noteworthy outcome of our investigation is the observation that the energy-momentum tensor associated with this wormhole complies with both the weak energy condition (WEC) and the null energy condition (NEC). Furthermore, incorporation of global monopole charge introduces a substantial influence on the curvature properties of wormhole space-time and various associated physical quantities derived from this geometry.

Hilbert’s energy–momentum tensor extended

In classical field models, Hilbert’s energy–momentum tensor for a matter field is defined by a variational derivative of a Lagrangian with respect to the metric tensor. Constitutive relationships between fundamental field variables are a subject that is dealt with by a wide range of models in solid-state physics. In this case, a higher-order constitutive tensor replaces the second-order metric tensor. A similar premetric description with a linear constitutive relation has recently been provided for classical field models of gravity and electrodynamics. In this paper, we analyze the extension of the Hilbert definition of the energy–momentum tensor to models with general linear constitutive law. In order to treat integrals on a differential manifold covariantly, we need the differential forms description. It follows that the Lagrangian, electromagnetic current, and energy–momentum current must all be represented as twisted 4-forms, 3-forms, and vector-valued 3-forms, respectively. The constitutive relation then appears as a linear map on forms. We derive a commutative variation identity for an arbitrary linear map, enabling direct variation processes without having to deal with the individual components. We present evidence for the close relationship between the explicit form of the energy–momentum current of Hilbert’s type and the commutative-variation identity. A variety of field models with a general linear constitutive law are subject to this construction.

Renormalons in the energy-energy correlator

The energy-energy correlator (EEC) is an observable of wide interest for collider physics and Standard Model measurements, due to both its simple theoretical description in terms of the energy-momentum tensor and its novel features for experimental studies. Significant progress has been made in both applications and higher-order perturbative predictions for the EEC. Here, we analyze the nature of the asymptotic perturbative series for the EEC by determining its analytic form in Borel space under the bubble-sum approximation. This result provides information on the leading and subleading nonperturbative power corrections through renormalon poles. We improve the perturbative convergence of the overline{textrm{MS}} series for the EEC by removing its leading renormalon using an MSR scheme, which is independent of the bubble-sum approximation. Using the leading MSR scheme power correction determined by fits to thrust, we find good agreement with EEC OPAL data already at mathcal{O} ( {alpha}_s^2 ).

Energy condition of wormhole and thin shell by assuming conformal symmetry in teleparallel-Rastall gravity

The static spherically symmetric wormhole solution for a non-isotropic perfect fluid energy-momentum tensor within the context of teleparallel-Rastall gravity is investigated. First, by imposing static and non-static conformal symmetry on the static spherically symmetric space-time metric, we investigated the null energy condition at the throat of traversable wormholes and showed that the null energy condition in the throat and its neighborhood is violated. Secondly, with the aim of minimize the usage of exotic matter, we found regions where the energy conditions are valid at the junction surface. We found that in the static case of conformal symmetry solution, the null energy condition (NEC), weak energy condition (WEC), and Strong energy condition (SEC) are valid for different λ 0 parameters. Moreover, we obtained that for the non-static symmetric solution of conformal symmetry, the NEC and WEC are satisfied for different sets of parameters. Finally, we have explored the stable regions by the parameter η 2 (square speed of sound) for different sets of parameters.

Formula omitted]- inflation: Sourced by energy–momentum squared gravity

In this paper, we examine chaotic inflation within the context of the energy–momentum squared gravity (EMSG) focusing on the energy–momentum powered gravity (EMPG) that incorporates the functional f(T2)∝(T2)β in the Einstein–Hilbert action, in which β is a constant and T2≡TμνTμν where Tμν is the energy–momentum tensor, which we consider to represent a single scalar field with a power-law potential. We also demonstrate that the presence of EMSG terms allows the single-field monomial chaotic inflationary models to fall within current observational constraints, which are otherwise disfavored by Planck and BICEP/Keck findings. We show that the use of a non-canonical Lagrangian with chaotic potential in EMSG can lead to significantly larger values of the non-Gaussianity parameter, fNlequi whereas EMSG framework with canonical Lagrangian gives rise to results similar to those of the standard single-field model.

General Fractional Noether Theorem and Non-Holonomic Action Principle

Using general fractional calculus (GFC) of the Luchko form and non-holonomic variational equations of Sedov type, generalizations of the standard action principle and first Noether theorem are proposed and proved for non-local (general fractional) non-Lagrangian field theory. The use of the GFC allows us to take into account a wide class of nonlocalities in space and time compared to the usual fractional calculus. The use of non-holonomic variation equations allows us to consider field equations and equations of motion for a wide class of irreversible processes, dissipative and open systems, non-Lagrangian and non-Hamiltonian field theories and systems. In addition, the proposed GF action principle and the GF Noether theorem are generalized to equations containing general fractional integrals (GFI) in addition to general fractional derivatives (GFD). Examples of field equations with GFDs and GFIs are suggested. The energy–momentum tensor, orbital angular-momentum tensor and spin angular-momentum tensor are given for general fractional non-Lagrangian field theories. Examples of application of generalized first Noether’s theorem are suggested for scalar end vector fields of non-Lagrangian field theory.

Weyl conformal geometry vs Weyl anomaly

Weyl conformal geometry is a gauge theory of scale invariance that naturally brings together the Standard Model (SM) and Einstein gravity. The SM embedding in this geometry is possible without new degrees of freedom beyond SM and Weyl geometry, while Einstein gravity is generated by the broken phase of this symmetry. This follows a Stueckelberg breaking mechanism in which the Weyl gauge boson becomes massive and decouples, as discussed in the past [1–3]. However, Weyl anomaly could break explicitly this gauge symmetry, hence we study it in Weyl geometry. We first note that in Weyl geometry metricity can be restored with respect to a new differential operator ( hat{nabla} ) that also enforces simultaneously a Weyl-covariant formulation. This leads to a metric-like Weyl gauge invariant formalism that enables one to do quantum calculations directly in Weyl geometry, rather than use a Riemannian (metric) geometry picture. The result is the Weyl-covariance in d dimensions of all geometric operators ( hat{R} , etc) and of their derivatives ( hat{nabla} μ hat{R} , etc), including the Euler-Gauss-Bonnet term. A natural (geometric) Weyl-invariant dimensional regularisation of quantum corrections exists and Weyl gauge symmetry is then maintained and manifest at the quantum level. This is related to a non-trivial current of this symmetry, the divergence of which cancels the trace of the energy-momentum tensor. The “usual” Weyl anomaly and Riemannian geometry are recovered in the (spontaneously) broken phase. The relation to holographic Weyl anomaly is discussed.

The Cornell black hole

The Cornell potential can be derived from a recently proposed non-local extension of Abelian electrodynamics. Non-locality can be alternatively described by an extended charge distributions in Maxwell electrodynamics. We state that in these models the energy momentum tensor necessarily requires the presence of the interaction term between the field and the charge itself. We show that this extended form of energy momentum tensor leads to an exact solution of the Einstein equations describing a charged AdS black hole. We refer to it as the “Cornell black hole”(CBH). Identifying the effective cosmological constant with the pressure of Van der Waals fluid, we study the gas-liquid phase transition and determine the critical parameters.

When tadpoles matter: one-loop corrections for spectator Higgs in inflation

We consider the classical attractor regime of the spectator Abelian Higgs model in power-law inflation, and compute the one-loop corrections to its evolution. For computations we utilize dimensional regularization and the propagators in the unitary gauge. The corrections to both the scalar condensate and the energy-momentum tensor exhibit secular ultraviolet contributions, that tend to slow down the rolling of the scalar down its potential, and drive it away from the classical attractor. These corrections need not be suppressed if the U(1) charge is much larger than the scalar self-coupling, which is seen already in flat space. In addition, at late times the secular corrections necessarily invalidate the perturbative loop expansion. We find the late time secular corrections to be captured by the renormalization group, which opens up the possibility to resum them past the breakdown of perturbativity.

Generalization of Noether Theorem and action principle for non-Lagrangian theories

A non-Lagrangian field theory is a theory whose field equations cannot be derived from the action principle. The action principle is described by holonomic variational equations. These equations can be used only for standard field theories, equations of which can be represented as Euler–Lagrange equations for some Lagrangian density. In the general case, one should use non-holonomic variational equations to obtain a wider class of field equations. In this paper, it is proposed to use the Sedov non-holonomic variational equation as a generalization of action principle. Examples of application of non-holonomic variational equations to derive various field equations are suggested. The standard Noether theorem is formulated for the standard (Lagrangian) field theory with an action functional and expresses the invariance of the Lagrangian with respect to some continuous group of transformations. In this paper, a generalization of Noether’s theorem for non-Lagrangian field theories is proposed and proved by using the non-holonomic variational equation. The expression of Noether current is described in the general case of non-Lagrangian field theory. The energy–momentum tensor, orbital angular-momentum tensor and spin angular-momentum tensor are given for non-Lagrangian field theories. Examples of application of generalized first Noether’s theorem are suggested for scalar end vector fields of non-Lagrangian field theory. An important result of this paper is the proof of possibility of existence of some analogues of dissipative structures in non-Lagrangian field theories and some properties of such structures are suggested.

Slow-roll inflation in modified gravity* *PKS acknowledges the Science and Engineering Research Board, Department of Science and Technology, Government of India for financial support to carry out research project No.: CRG/2022/001847 and IUCAA

In this study, we explore the concept of cosmological inflation within the framework of the theory of gravity, where f is a general function of the torsion scalar T and the trace of the energy-momentum tensor. It is assumed that the conditions of slow-roll inflation are applicable in gravity. To determine different observables related to inflation, such as the tensor-to-scalar ratio r, scalar spectral index , spectral index , and tensor spectral index , the Hubble slow-roll parameters are utilized for a particular model of . Lastly, an assessment is carried out to determine the feasibility of the models by conducting a numerical analysis of the parameters. The findings indicate that it is feasible to achieve compatibility with the observational measurements of slow-roll parameters by utilizing different values of the free parameters.

Reconstructing inflation and reheating in [formula omitted] gravity

In this work we study the reconstruction of an inflationary universe in the context of a theory of gravity f(ϕ)T, in which T corresponds to the trace of energy momentum tensor. To realize this reconstruction during the inflationary epoch, we consider as attractor the scalar spectral index ns in terms of the number of e-folds N, in the framework of the slow-roll approximation. By assuming a specific function f(ϕ) together with the simplest attractor ns(N), we find different expressions for the reconstructed effective potential V(ϕ). Additionally, we analyze the era of reheating occurs after of the reconstruction obtained during the inflationary epoch. In this scenario we determine the duration and temperature during the reheating epoch, in terms of the equation of state parameter and of the observational parameters. In this context, the different parameters associated to the reconstructed model are restricted during the scenarios of inflation and reheating by considering the recent astronomical observations.

Reconstruction of [formula omitted] Lagrangian for various cosmological scenarios

In this paper we explore a reconstruction scheme in the background of the f(T,T) gravity theory for different cosmological scenarios, where T is the scalar torsion and T is the trace of the energy-momentum tensor. Using the reconstruction technique f(T,T) Lagrangian is constructed for different cosmological eras such as dust, ΛCDM, perfect fluid, etc. Both minimal and non-minimal matter coupled models are considered for this purpose. Different cosmological scenarios such as power law expansion, de-Sitter expansion, etc. have been considered, and using them Lagrangian functionals are constructed. Mathematical viabilities of all the constructed functionals have been investigated. The physical implications of the obtained solutions are discussed in detail. To check the cosmological compatibility of the constructed f(T,T) functionals we have generated plots of important parameters like the equation of state parameter and deceleration parameter. It is seen that the reconstructed models are perfectly compatible with the late time accelerated expansion of the universe.

B-type anomaly coefficients for the D3-D5 domain wall

We compute type-B Weyl anomaly coefficients for the domain wall version of N=4 SYM that is holographically dual to the D3-D5 probe-brane system with flux. Our starting point is the explicit expression for the improved energy momentum tensor of N=4 SYM. We determine the two-point function of this operator in the presence of the domain wall and extract the anomaly coefficients from the result. In the same process we determine the two-point function of the displacement operator.

Traversable wormholes with static spherical symmetry and their stability in higher-curvature gravity

The solutions of traversable wormholes and their geometries are investigated in higher-curvature gravity with boundary terms for each case under the presence of anisotropic, isotropic and barotropic fluids in detail. For each case, the effective energy-momentum tensor violates the null energy condition throughout the wormhole throat. The null and weak energy conditions are also analyzed for ordinary matters. The regions that physically viable wormhole solutions can exist are explicitly shown. Furthermore, it is found that the range of the viable regions exhibits an alternating pattern of expansion and contraction. The present analyses can reveal the regions in which traversable wormholes can be constructed for anisotropic, isotropic and barotropic fluids cases with incorporating realistic matter contents, leading to fundamental physics insights into the feasible construction of wormholes in higher-curvature gravity with boundary term. The main achievements of this work, in contrast to previous studies, are its thorough investigation of traversable wormholes within the framework of higher-curvature gravity with boundary terms, its extensive consideration of various fluid types, and the explicit identification of regions where stable wormhole solutions can exist.

Effects of wave propagation in canonical Poisson gauge theory under an external magnetic field

The non-commutative electrodynamics based on the canonical Poisson gauge theory is studied in this paper. For a pure spatial non-commutativity, we investigate the plane wave solutions in the presence of a constant and uniform magnetic background field for the classical electrodynamics in canonical Poisson gauge theory. We obtain the properties of the medium ruled by the permittivity and the permeability tensors in terms of the non-commutative parameter, with the electrodynamics equations in the momentum space. Using the plane wave solutions mentioned, the dispersion relations are modified by the magnetic background, and the correspondent group velocity is affected by the spatial non-commutative parameter. We construct the energy-momentum tensor and discuss the conserved components of this tensor in the spatial non-commutative case. The birefringence phenomenon is showed through the modified dispersion relations, that depends directly on the non-commutative corrections and also on the magnetic background field. Using the bound of the polarized vacuum with laser (PVLAS) experiment for the vacuum magnetic birefringence, we estimate a theoretical value for the spatial non-commutative parameter.

Quark confinement in Schwarzchild-like space–time with a metric generated by a nongravitational Yukawa-like strong field

In this work, we use the approach recently introduced by Barros to study hadron spectra and some quark confinement properties in a Schwarzchild-like space–time generated by a nongravitational field. As a starting point, for the nongravitational field, we make the choice of a strong Yukawa-like field whose associated potential is a generalized Yukawa-like potential, typical of strong interactions. Then, from the latter field, the energy momentum tensor is constructed, the Einstein field equations are solved and the curvature function of the Schwarzchild metric is obtained. The correspondence principle applied to the Schwarzchild metric has enable us to construct the Dirac equation in the latter space. The resolution of the coupled differential equations of Dirac made it possible to obtain the energy spectrum of the strong interaction. The latter is obtained in a more general form than in the previous investigations. Then, the energy spectrum, masses and confinement radius of few hadrons are estimated and compared with experimental data and other theoretical studies. In most considered cases, our predictions are found to be in good agreement with experimental data. The good agreement observed between our outcomes and the experiment can be attributed to the choice of our potential, which has more free parameters than in past studies with the same approach.

Physically viable strange quark star models in modified teleparallel gravity

The aim of this paper is to develop the isotropic and anisotropic quark stars configurations in the context of [Formula: see text] gravity in the static spherically symmetric background. To explore the combined effects of torsion scalar [Formula: see text] and the trace of energy–momentum tensor (EMT) [Formula: see text] on relativistic astrophysics, we use diagonal as well as non-diagonal tetrad fields. By considering the conformal Killing vectors along with the MIT bag model, the interior solutions of the field equations corresponding to the linear [Formula: see text] model (in which [Formula: see text] are the constants and [Formula: see text] indicates the cosmological constant) are calculated. The feasibility of the obtained solutions is confirmed by implementing several physical tests. The model parameters are constrained subject to the existence and stability of the quark star models. We formulate the energy constraints, stability equations, mass function, compactness and redshift factor, and present the graphical analysis of all physical quantities. It is found that the derived solutions for both diagonal and non-diagonal tetrad exhibit well-behaved profiles in the framework of modified teleparallel gravity.