Curvature coupled dirac dynamics in curved spacetime

The generalized Palatini variational principle for the gravitational field interacting with a matter field is considered. The contracted Bianchi identities are proved and the reduction of the generalized Einstein-Cartan equations to the set of 6 dynamical equations and 4 constraints is presented.

Effects of expansion-free condition on adiabatic collapse in [formula omitted] gravity

Theories of physics can be considered viable if the initial value problem and the energy conditions are formulated self-consistently. The former allow a uniquely determined dynamical evolution of the system, and the latter guarantee that causality is preserved and that "plausible" physical sources have been considered. In this work, we consider the further degrees of freedom related to curvature invariants and scalar fields in Extended Theories of Gravity (ETG). These new degrees of freedom can be recast as effective perfect fluids that carry different meanings with respect to the standard matter fluids generally adopted as sources of the field equations. It is thus somewhat misleading to apply the standard general relativistic energy conditions to this effective energy-momentum, as the latter contains the matter content and a geometrical quantity, which arises from the ETG considered. Here, we explore this subtlety, extending on previous work, in particular, to cases with the contracted Bianchi identities with diffeomorphism invariance and to cases with generalized explicit curvature-matter couplings, which imply the non-conservation of the energy-momentum tensor. Furthermore, we apply the analysis to specific ETGs, such as scalar-tensor gravity, $f(R)$ gravity and modified Gauss-Bonnet gravity. Interesting results appear such as matter that may exhibit unusual thermodynamical features, for instance, and gravity that retains its attractive character in the presence of negative pressures; or alternatively, we verify that repulsive gravity may occur for standard matter.

Symmetric teleparallel cosmology with boundary corrections

This study extends the scalar curvature term [Formula: see text] within the framework of modified gravity, incorporating both the Ricci scalar [Formula: see text] and the energy–momentum tensor [Formula: see text]. We explore a specific formulation of [Formula: see text] gravity, defined as [Formula: see text], in the context of a spatially homogeneous and anisotropic Bianchi-type-I cosmological model with a perfect fluid. Within this framework, we derive and analyze the modified field equations for both positive and negative values of [Formula: see text]. By utilizing observational datasets, we constrain the model parameters and visualize its cosmological implications. In addition, we examine the validity of the energy conditions (EC) to assess the physical plausibility of the model across cosmic evolution. Our findings show that for [Formula: see text], the model remains stable and aligns with physical expectations. However, for other positive [Formula: see text], anomalous behavior emerges in specific intervals. Furthermore, we validate our model through metric perturbation analysis and cosmological diagnostic tools like [Formula: see text] and [Formula: see text]. The combined analysis of EC and observational diagnostics confirms the physical viability and late-time accelerated expansion behavior of the model within the admissible parameter range.

Warm inflation in a Universe with a Weylian boundary

The generalization of the black hole in three-dimensional spacetime to include an electric charge Q in addition to the mass M and the angular momentum J is given. The field equations are first solved explicitly when Q is small and the general form of the field at large distances is established. The total “hairs ” M, J and Q are exhibited as boundary terms at infinity. It is found that the inner horizon of the rotating uncharged black hole is unstable under the addition of a small electric charge. Next it is shown that when Q = 0 the spinning black hole may be obtained from the one with J = 0 by a Lorentz boost in the ϕ − t plane. This boost is an “illegitimate coordinate transformation ” because it changes the physical parameters of the solution. The extreme black hole appears as the analog of a particle moving with the speed of light. The same boost may be used when Q ̸ = 0 to generate a solution with angular momentum from that with J = 0, 1 although the geometrical meaning of the transformation is much less transparent since in the charged case the black holes are not obtained by identifying points in anti-de Sitter space. The metric is given explicitly in terms of three parameters, ˜ M, ˜ Q and ω which are the “rest mass ” and “rest charge ” and the angular velocity of the boost. These parameters are related to M, J and Q through the solution of an algebraic cubic equation. Altogether, even without angular momentum, the electrically charged 2+1 black hole is somewhat pathological since (i) it exists for arbitrarily negative values of the mass, and (ii) there is no upper bound on the electric charge. 2 1

Recent arguments have indicated that the sum over histories formulation of quantum amplitudes for gravity should include sums over conifolds, a set of histories with more general topology than that of manifolds. This paper addresses the consequences of conifold histories in gravitational functional integrals that also include scalar fields. This study will be carried out explicitly for the generalized Hartle-Hawking initial state, that is the Hartle-Hawking initial state generalized to a sum over conifolds. In the perturbative limit of the semiclassical approximation to the generalized Hartle-Hawking state, one finds that quantum field theory on Einstein conifolds is recovered. In particular, the quantum field theory of a scalar field on de Sitter spacetime with ${\mathrm{RP}}^{3}$ spatial topology is derived from the generalized Hartle-Hawking initial state in this approximation. This derivation is carried out for a scalar field of arbitrary mass and scalar curvature coupling. Additionally, the generalized Hartle-Hawking boundary condition produces a state that is not identical to but corresponds to the Bunch-Davies vacuum on ${\mathrm{RP}}^{3}$ de Sitter spacetime. This result cannot be obtained from the original Hartle-Hawking state formulated as a sum over manifolds as there is no Einstein manifold with round ${\mathrm{RP}}^{3}$ boundary.

In a new model that we proposed, nonperturbative vacuum contributions to the effective action of a free quantized massive scalar field lead to a cosmological solution in which the scalar curvature becomes constant after a time ${t}_{j}$ (when the redshift $z\ensuremath{\sim}1)$ that depends on the mass of the scalar field and its curvature coupling. This spatially flat solution implies an accelerating universe at the present time and gives a good one-parameter fit to high-redshift type Ia supernovae (SNe-Ia) data, and the present age and energy density of the universe. Here we show that the imaginary part of the nonperturbative curvature term that causes the cosmological acceleration implies a particle production rate that agrees with predictions of other methods and extends them to non-zero mass fields. The particle production rate is very small after the transition and is not expected to alter the nature of the cosmological solution. We also show that the equation of state of our model undergoes a transition at ${t}_{j}$ from an equation of state dominated by non-relativistic pressureless matter (without a cosmological constant) to an effective equation of state of mixed radiation and cosmological constant, and we derive the equation of state of the vacuum. Finally, we explain why nonperturbative vacuum effects of this ultralow-mass particle do not significantly change standard early universe cosmology.

The definition of the Einstein 3-form G_a is motivated by means of the contracted 2nd Bianchi identity. This definition involves at first the complete curvature 2-form. The 1-form L_a is defined via G_a = L^b \wedge #(o_b \wedge o_a). Here # denotes the Hodge-star, o_a the coframe, and \wedge the exterior product. The L_a is equivalent to the Einstein 3-form and represents a certain contraction of the curvature 2-form. A variational formula of Salgado on quadratic invariants of the L_a 1-form is discussed, generalized, and put into proper perspective.

The persistent H0 and growth tensions in ΛCDM cosmology motivate a re-examination of the expansion paradigm’s foundational assumptions. The Dead Universe Theory (DUT) proposes an alternative in which observable galaxy separation is not due to metric expansion but results from irreversible, entropy-driven deformation of a viscoelastic spacetime continuum undergoing global gravitational retraction. This work formalizes DUT within a relativistic continuum-mechanics framework. We derive the entropic deformation tensor Ξ_μν from a variational principle and incorporate it into the Einstein field equations as G_μν + Ξ_μν = 8πG T_μν, replacing the cosmological constant with a dynamical, entropy-sourced curvature. A key prediction follows from the asymptotic stability analysis of the resulting system: a unique, non-adjustable growth index γ = (√5 − 1)/2 ≈ 0.6180339887…, the signature of the theory’s Unique Vacuum Attractor. Consequently, a high-precision measurement of the growth index consistent with γ ≈ 0.55 at the <0.01 level would strongly falsify DUT. This formulation provides a falsifiable, thermodynamically grounded geometric description of cosmic dynamics, directly linking late-time acceleration-like phenomena to residual entropy gradients of a “dead” gravitational substrate. Numerical validation of the attractor is available in the mission-grade inference pipeline (repository and preprint DOI provided in the Data/Code Availability statement).

We investigated how a magnetic topological defect affects the vacuum polarization of a charged massive scalar field in a flat (3+1)-dimensional space-time. The defect was modeled as an impenetrable-to-matter-field, finite-thickness tube with magnetic flux inside. We implemented the most general form of the Robin boundary condition on the surface of the magnetic tube, which enables a fully general analysis of the problem. We found that in flat space-time, the total vacuum energy generated by a magnetic topological defect depends on the curvature (ξ), except for special cases corresponding to the Dirichlet and Neumann boundary conditions. By contrast, when Robin’s general boundary conditions are imposed, the induced vacuum energy acquires an explicit dependence on the curvature coupling (ξ), which is significant even in flat space-time. A detailed study of the dependence of the effect on the boundary-condition parameter was carried out. The obtained results highlight the nontrivial role played by boundary conditions in vacuum polarization phenomena.

Radical pair recombination reactions are normally described using a quantum mechanical master equation for the electronic and nuclear spin density operator. The electron spin state selective (singlet and triplet) recombination processes are described with a Haberkorn reaction term in this master equation. Here we consider a general spin state selective electron transfer reaction of a radical pair and use Nakajima-Zwanzig theory to derive the master equation for the spin density operator, thereby elucidating the relationship between non-adiabatic reaction rate theory and the Haberkorn reaction term. A second order perturbation theory treatment of the diabatic coupling naturally results in the Haberkorn master equation with an additional reactive scalar electron spin coupling term. This term has been neglected in previous spin chemistry calculations, but we show that it will often be quite significant. We also show that beyond the second order in perturbation theory, i.e., beyond the Fermi golden rule limit, an additional reactive singlet-triplet dephasing term appears in the master equation. A closed form expression for the reactive scalar electron spin coupling in terms of the Marcus theory parameters that determine the singlet and triplet recombination rates is presented. By performing simulations of radical pair reactions with the exact hierarchical equations of motion method, we demonstrate that our master equations provide a very accurate description of radical pairs undergoing spin-selective non-adiabatic electron transfer reactions. The existence of a reactive electron spin coupling may well have implications for biologically relevant radical pair reactions such as those which have been suggested to play a role in avian magnetoreception.

The metric-affine gauge theory of gravity encompasses a space-time with the following geometrical fields: coframe ϑα, metric g, and an independent linear connection Γαβ. Within this geometrical framework, all four-forms B=dC are constructed which qualify as boundary terms for a gauge Lagrangian, that is, they are GL(4,R)-scalars as well as exact forms derived from Chern–Simons type three-forms C. The result of our search is summarized in Eq. (4.20). The translational piece dCTT is new. The boundary terms effectively serve as Lagrangians for the Bianchi identities of nonmetricity, torsion, and curvature. In the canonical formalism, the normal parts of the Chern–Simons three-forms represent generating functions that are capable of generating new Ashtekar type variables. Eventually, the Bach–Lanczos identity is generalized to the metric-affine space-time.

Sign reversal of resonances via isotropic mixing in NMR spectroscopy