On energy conditions and stability in effective loop quantum cosmology

We demonstrate that a Bjorken expanding strongly coupled $\mathcal{N}=4$ Supersymmetric Yang-Mills plasma can display dynamically-driven violations of the dominant and also the weak energy condition during hydrodynamization. In addition, we find that a period of vanishing entropy production in far-from-equilibrium stages induces later violations of the dominant energy condition in the strongly coupled plasma. Such violations cannot occur in a classical description of hydrodynamization and suggest that the inclusion of quantum effects in transport can lead to new phenomena in these regimes, even for systems without anomalies or spin.

Ellis–Bronnikov (EB) wormholes require violation of null energy conditions at the ‘throat’. This problem was cured by a simple modification of the ‘shape function’, which introduces a new parameter mge 2 (m=2 corresponds to the EB model). This leads to a generalised (GEB) version. In this work, we consider a model where the GEB wormhole geometry is embedded in a five dimensional warped background. We studied the status of all the energy conditions in detail for both EB and GEB embedding. We present our results analytically (wherever possible) and graphically. Remarkably, the presence of decaying warp factor leads to satisfaction of weak energy conditions even for the EB geometry, while the status of all the other energy conditions are improved compared to the four dimensional scenario. Besides inventing a new way to avoid the presence of exotic matter, in order to form a wormhole passage, our work reveals yet another advantage of having a warped extra dimension.

In this work, we have studied how incorporating viscous fluids leads to exact bounce cosmological solutions in general relativity (GR) framework. Specifically, we propose a novel parameterization of bulk viscosity coefficient of the form [Formula: see text], where [Formula: see text], with [Formula: see text] being some positive constants and [Formula: see text] being the bounce epoch. We investigate how this form of bulk viscosity may assist in explaining the early universe’s behavior, with a particular focus on non-singular bounce scenario by studying the various energy conditions and other related cosmological observables and how the model parameters affect the evolution of the Universe. We demonstrate that the null energy conditions (NEC) and strong energy conditions (SEC) violation occurs at the bounce point while dominant energy conditions (DEC) is satisfied. Finally, we carried out a stability check based on linear order perturbation to the Hubble parameter. We found that the perturbation vanishes asymptotically at later times, which indicates a stable behavior of the bounce scenario.

The study of energy conditions has many significant applications in general relativistic and cosmological contexts. This paper explores the energy conditions in the framework of the most general scalar-tensor theory with field equations involving second-order derivatives. For this purpose, we use flat FRW universe model with perfect fluid matter contents. By taking power law ansatz for scalar field, we discuss the strong, weak, null, and dominant energy conditions in terms of deceleration, jerk, and snap parameters. Some particular cases of this theory likek-essence model, modified gravity theories and so forth. are analyzed with the help of the derived energy conditions, and the possible constraints on the free parameters of the presented models are determined.

Of the various energy conditions which can be assumed when studying mathematical general relativity, intuitively the simplest is the weak energy condition μ⩾0 which simply states that the observed mass-energy density must be non-negative. This energy condition has not received as much attention as the so-called dominant energy condition. When the natural question of the Penrose inequality in the context of the weak energy condition arose, we could not find any results in the literature, and it was not immediately clear whether the inequality would hold, even in spherical symmetry. This led us to constructing a spherically symmetric asymptotically flat initial data set satisfying the weak energy condition which violates the ‘usual’ formulations of the Penrose conjecture. This does not contradict (Malec and Murchadha 1994 Phys. Rev. D 49 6931–4), as there the data is assumed to be maximal. Our result is unexpected and interesting because the heuristic argument behind the Penrose inequality relies on the black hole area law which holds when the weak energy condition is satisfied. Our methods also lead to a counter example to the positive mass theorem assuming the weak energy condition.

Nonperturbative quantum geometric effects in loop quantum cosmology (LQC) predict a ${\ensuremath{\rho}}^{2}$ modification to the Friedmann equation at high energies. The quadratic term is negative definite and can lead to generic bounces when the matter energy density becomes equal to a critical value of the order of the Planck density. The nonsingular bounce is achieved for arbitrary matter without violation of positive energy conditions. By performing a qualitative analysis we explore the nature of the bounce for inflationary and cyclic model potentials. For the former we show that inflationary trajectories are attractors of the dynamics after the bounce implying that inflation can be harmoniously embedded in LQC. For the latter difficulties associated with singularities in cyclic models can be overcome. We show that nonsingular cyclic models can be constructed with a small variation in the original cyclic model potential by making it slightly positive in the regime where scalar field is negative.

Wormhole and time machine are very interesting objects in general relativity. However, they need exotic matters which are impossible in classical level to support them. But if we introduce the quantum effects of gravity into the stress-energy tensor, these peculiar objects can be constructed self-consistently. Fortunately, loop quantum cosmology (LQC) has the potential to serve as a bridge connecting the classical theory and quantum gravity. Therefore it provides a simple way for the study of quantum effect in the semiclassical case. As is well known, loop quantum cosmology is very successful to deal with the behavior of early universe. In the early stage, if taken the quantum effect into consideration, inflation is natural because of the violation of every kind of local energy conditions. Similar to the inflationary universe, the violation of the averaged null energy condition is the necessary condition for the traversable wormholes. In this paper, we investigate the averaged null energy condition in LQC in the framework of effective Hamiltonian, and find out that LQC do violate the averaged null energy condition in the massless scalar field coupled model.

In contrast to previous work in the field, we construct the loop quantum cosmology (LQC) of the flat isotropic model with a massless scalar field in the absence of higher order curvature corrections to the gravitational part of the Hamiltonian constraint. The matter part of the constraint contains the inverse triad operator which can be quantized with or without the use of a Thiemann-like procedure. With the latter choice, we show that the LQC quantization is identical to that of the standard Wheeler–DeWitt theory (WDW) wherein there is no singularity resolution. We argue that the former choice leads to singularity resolution in the sense of a well-defined, regular (backward) evolution through and beyond the epoch where the size of the universe vanishes. Our work along with that of the seminal work of Ashtekar, Pawlowski and Singh (APS) clarifies the role, in singularity resolution, of the three ‘exotic’ structures in this LQC model, namely: curvature corrections, inverse triad definitions and the ‘polymer’ nature of the kinematic representation. We also critically examine certain technical assumptions made by APS in their analysis of WDW semiclassical states and point out some problems stemming from the infrared behaviour of their wavefunctions.

In general relativity, the energy conditions are invoked to restrict general energy-momentum tensors ${T}_{\ensuremath{\mu}\ensuremath{\nu}}$ in different frameworks, and to derive general results that hold in a variety of general contexts on physical grounds. We show that in the standard Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) approach, where the equation of state of the cosmological fluid is unknown, the energy conditions provide model-independent bounds on the behavior of the distance modulus of cosmic sources as a function of the redshift for any spatial curvature. We use the most recent type Ia supernovae (SNe Ia) observations, which include the new Hubble Space Telescope SNe Ia events, to carry out a model-independent analysis of the energy conditions violation in the context of the standard cosmology. We show that both the null (NEC), weak (WEC), and dominant (DEC) conditions, which are associated with the existence of the so-called phantom fields, seem to have been violated only recently ($z\ensuremath{\lesssim}0.2$), whereas the condition for attractive gravity, i.e., the strong energy condition (SEC) was first violated billions of years ago, at $z\ensuremath{\gtrsim}1$.

We show that the Einstein field equations with a negative cosmological constant can admit black hole solutions whose thermodynamics coincides with that of logotropic fluids, recently investigated to heal some cosmological and astrophysical issues. For this purpose, we adopt the Anton–Schmidt equation of state, which represents a generalized version of logotropic fluids. We thus propose a general treatment to obtain an asymptotic anti-de Sitter metric, reproducing the thermodynamic properties of both Anton–Schmidt and logotropic fluids. Hence, we explore how to construct suitable spacetime functions, invoking an event horizon and fulfilling the null, weak, strong and dominant energy conditions. We further relax the strong energy condition to search for possible additional solutions. Finally, we discuss the optical properties related to a specific class of metrics and show how to construct an effective refractive index depending on the spacetime functions and the thermodynamic quantities of the fluid under study. We also explore possible departures with respect to the case without the fluid.

In the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) approach to model the Universe the violation of the so-called energy conditions is related to some important properties of the Universe as, for example, the current and the inflationary accelerating expansion phases. The energy conditions are also necessary in the formulation and proofs of Hawking-Penrose singularity theorems. In two recent articles we have derived bounds from energy conditions and made confrontations of these bounds with supernovae data. Here, we extend these results in following way: first, by using our most recent statistical procedure for calculating new q(z) estimates from the \emph{gold} and \emph{combined} type Ia supernovae samples; second, we use these estimates to obtain a new picture of the energy conditions fulfillment and violation for the recent past ($z\leq 1 $) in the context of the standard cosmology.

We study new solutions of black bounce spacetimes formulated in $f(T)$ gravity in four dimensions. First, we present the case of a diagonal tetrad, where a constraint arises in the equations of motion, which is divided into the cases of null torsion, constant torsion, and Teleparallel. The Null Energy Condition (NEC) is still always violated, which implies that the other energy conditions are violated. The solutions are regular in all spacetime and the solution with null torsion exhibits discontinuity between the energy conditions outside and inside the event horizon. Second, we present the case of non-diagonal tetrads. This case is divided into a Simpson-Visser type model and a quadratic model. The NEC continues to be violated, implying a violation of the other energy conditions. The solutions are regular in all spacetimes. An interesting result is that due to the possibility that the area associated with the metric is different from $4\pi r^2$, the no-go theorem established in the usual $f(T)$ is violated, appearing the new possibility $g_{00}=-g^{11}$, for the components of the metric.

This paper investigates the wormhole solutions in Rastall theory of gravity using the Karmarkar conditions. For this purpose, we choose a shape function (SF) that connects two asymptotically flat regions. We also discuss the wormhole configuration by plotting three-dimensional (3D) analysis of the embedding diagram in Euclidean space. Furthermore, we also observe the detailed graphical representation of energy conditions using the considered SF. The violation of energy conditions, especially null energy conditions (NEC), indicates the existence of exotic matter and wormholes. Hence, it can be concluded that our calculated results in the background of Rastall theory of gravity are viable and stable. The exciting feature of this work is the 3D analysis to discuss the viability of wormhole geometry

Minimally deformed regular Bardeen black hole solutions in Rastall theory

Uses the Einstein-Maxwell field equations to derive the fundamental equation of motion for charged null fluid. This equation of motion includes a Lorentz force term. Using this equation, it is shown that charged null fluid always satisfies the weak energy condition. This result is in contrast to previous interpretations of the charged Vaidya solution (a special case of a charged null fluid), which produced violations of the weak energy condition. The errors in the previous interpretations are explained. The new interpretation is then applied explicitly to the charged Vaidya solution.