Husain–Kuchař model as the Carrollian limit of the Holst term

Dark torsion oscillations and bounces induced by Barbero-Immirzi and quantum correction on Einstein-Cartan gravity with very light inflatons

In this paper, we extend Shaposhnikov et al.'s parity violating the Einstein–Cartan–Holst action by adding to Holst term H, a Proca photon–torsion coupling χpt = 10−24 as computed by De Sabbata, Garcia de Andrade, and Sivaram. The strength of Holst term is obtained, in the case of early universe torsion as, T ∼ 1 MeV. The gravity part is the Planck mass product with the Holst term. The photon mass in this case yields m2 γ H ∼ 10−69 GeV4. Therefore, in this case, the photon interacts very weakly with spin-torsion matter in Einstein–Cartan (EC) gravity and the strength of the Maxwell–Proca–Holst interaction is much weaker than in the pure gravity sector. For dark photons, this situation changes drastically since a dark photon mass reaches 1.5 GeV, and from this mass and T = 10−3 GeV, one obtains a Maxwell–Proca–Holst strength of 10−6 GeV4, which is now comparable with the gravity sector. Dynamo mechanism competes with the chirality and dissipation by the handness of the magnetic field with respect to the torsion trace vector to regenerate the magnetic field decay. Bombacigno and Mantovani recently found a sign of the Immirzi parameter in the Holst–Nieh–Yan extension of EC gravity. Here, we also find torsion waves for the Immirzi inverse parameter in the sense that this divergence of torsion trace is porportional to the Immirzi field.

We investigate the consequences of the ambiguity of the minimal coupling procedure for Einstein-Cartan gravity with the Holst term and fermions. A new insight is provided into the nature and physical relevance of coupling procedures considered hitherto in the context of Ashtekar-Barbero-Immirzi formalism with fermions. The issue of physical effects of the Immirzi parameter in semiclassical theory is reinvestigated. We argue that the conclusive answer to the question of its measurability will not be possible until the more fundamental problem of nonuniqueness of gravity-induced fermion interaction in Einstein-Cartan theory is solved.

The Holst term represents an interesting addition to the Einstein–Cartan theory of gravity with torsion. When this term is present the contact interactions between vector and axial vector fermion currents gain an extra parity-violating component. We re-derive this interaction using a simple representation for the Holst term. The same representation serves as a useful basis for the calculation of one-loop divergences in the theory with external fermionic currents and cosmological constant. Furthermore, we explore the possibilities of the on-shell version of the renormalization group and construct equations for the running of dimensionless parameters related to currents and for the effective Barbero–Immirzi parameter.

In this paper, we revisit the null boundary gravitational charge in the Newman-Penrose formalism with special emphasis on the charges from local Lorentz transformations. We find that there is one more charge derived from the local Lorentz transformation and the new charge is purely from the Holst term. This reveals a remarkable fact that trivial terms which do not change classical equations of motion can not only affect the boundary degrees of freedom through their contributions to the boundary charges but also have their own rights to create new boundary degrees of freedom.

We provide a Hamiltonian derivation of recently discovered dual BMS charges. In order to do so, we work in the first order formalism and add to the usual Palatini action, the Holst term, which does not contribute to the equations of motion. We give a method for finding the leading order integrable dual charges à la Wald-Zoupas and construct the corresponding charge algebra. We argue that in the presence of fermions, the relevant term that leads to dual charges is the topological Nieh-Yan term.

In this work, we investigate the effects of the torsion–fermionic interaction on the energy levels of fermions within a Riemann–Cartan geometry using a model-independent approach. We consider the case of fermions minimally coupled to the background torsion as well as non-minimal extensions via additional couplings with the vector and axial fermionic currents which include parity-breaking interactions. In the limit of zero-curvature, and for the cases of constant and spherically symmetric torsion, we find a Zeeman-like effect on the energy levels of fermions and anti-fermions depending on whether they are aligned/anti-aligned with respect to the axial vector part of the torsion (or to specific combination of torsion quantities), and determine the corresponding fine-structure energy transitions. We also discuss non-minimal couplings between fermionic fields and torsion within the Einstein–Cartan theory and its extension to include the (parity-breaking) Holst term. Finally we elaborate on the detection of torsion effects related to the splitting of energy levels in astrophysics, cosmology and solid state physics using current capabilities.

One of the main features of unified models, based on affine geometries, is that all possible interactions and fields naturally arise under the same standard. Here, we consider, from the effective Lagrangian of the theory, the torsion induced 4-fermion interaction. In particular, how this interaction affects the cosmological term, supposing that a condensation occurs for quark fields during the quark-gluon/hadron phase transition in the early universe. We explicitly show that there is no parity-violating pseudo-scalar density, dual to the curvature tensor (Holst term) and the spinor-bilinear scalar density has no mixed couplings of A-V form. On the other hand, the space-time dimensionality cannot be constrained from multidimensional phenomenological models admitting torsion.

We explore the relation of the Holst term with the Nieh–Yan term in terms of metric variables. We show that the Holst term indeed affects the classical equations of motion in the presence of matter with spin. Therefore, the correct term to add to the Einstein–Hilbert action such that the equations of motion are not affected is the Nieh–Yan term. We then calculate the torsion charge due to this term in the context of a perfect fluid sphere with torsion and show that it vanishes once a horizon is formed but not otherwise. We also show that on adding torsion to general relativity Einstein's equations are no longer holographic in torsion although they continue to be so for the metric.

We deform the anti-de Sitter algebra by adding additional generators [Formula: see text], forming in this way the negative cosmological constant counterpart of the Maxwell algebra. We gauge this algebra and construct a dynamical model with the help of a constrained BF theory. It turns out that the resulting theory is described by the Einstein–Cartan action with Holst term, and the gauge fields associated with the Maxwell generators [Formula: see text] appear only in topological terms that do not influence dynamical field equations. We briefly comment on the extension of this construction, which would lead to a nontrivial Maxwell fields dynamics.

We embed the loop quantum gravity Barbero-Immirzi parameter and field within an action describing 4D, $\mathcal{N}=1$ supergravity and thus within a low-energy effective action of superstring/M theory. We use the fully gauge-covariant description of supergravity in (curved) superspace. The gravitational constant is replaced with the vacuum expectation value of a scalar field, which in local supersymmetry is promoted to a complex, covariantly chiral scalar superfield. The imaginary part of this superfield couples to a supersymmetric Holst term. The Holst term also serves as a starting point in the loop quantum gravity action. This suggest the possibility of a relation between loop quantum gravity and supersymmetric string theory, where the Barbero-Immirzi parameter and field of the former play the role of the supersymmetric axion in the latter. Adding matter fermions in loop quantum gravity may require the extension of the Holst action through the Nieh-Yan topological invariant, while in pure, matter-free supergravity their supersymmetric extensions are the same. We show that, when the Barbero-Immirzi parameter is promoted to a field in the context of 4D supergravity, it is equivalent to adding a dynamical complex chiral (dilaton-axion) superfield with a nontrivial kinetic term (or K\ahler potential), coupled to supergravity.

We analyze a modified f(R) theory of gravity in the Palatini formulation, when a Holst term endowed with a dynamical Immirzi field is included. We study the basic features of the model, especially in view of eliminating the torsion field via the Immirzi field and the scalar-tensor degrees of freedom of the f(R) model. The main task of this study is the investigation of the morphology of the gravitational wave polarization when their coupling to a circle of test particles is considered. We first observe that the dynamics of the scalar mode of the f(R) Lagrangian is frozen out, since its first order term identically vanishes. This allows a detailed characterization of the linearized theory, which outlines the emergence of a modified Newtonian potential in the static limit, and when time independence is relaxed a standard gravitational wave plus the scalar wave associated to the Immirzi field. Investigating the effect of the coupling of this scalar-tensor wave on a circle of test particles, we arrive to define two effective gravitational polarizations, corresponding to an equivalent phenomenological wave, whose morphology is anomalous with respect the standard case of general relativity. In fact, the particle circle suffers modifications as it was subjected to modified plus and cross modes, whose specific features depend on the model free parameters and are, in principle, detectable via a data analysis procedure.

The action of loop quantum gravity includes the Holst term and/or the Nieh--Yan term in addition to the Ricci scalar. These terms are expected to couple nonminimally to the Higgs. Thus the Holst and Nieh--Yan terms contribute to the classical equations of motion, and they can have a significant impact on inflation. We derive inflationary predictions in the parameter space of the nonminimal couplings, including nonminimally coupled terms up to dimension 4. Successful inflation is possible even with zero or negative coupling of the Ricci scalar. Notably, inflation supported by the nonminimally coupled Holst term alone gives almost the same observables as the original metric formulation plateau Higgs inflation. A nonminimally coupled Nieh--Yan term alone cannot give successful inflation. When all three terms are considered, the predictions for the spectral index and tensor-to-scalar ratio span almost the whole range probed by upcoming experiments. This is not true for the running of the spectral index, and many cases are highly tuned.

In recent years, gravitational models motivated by quantum corrections to gravity which introduce higher order terms like \(R^{2}\) or terms in which the Riemann tensor is not symmetric have been studied by several authors in the form of a general Brans-Dicke type model containing the Ricci scalar, the Holst term and the Nieh-Yan invariant. In this paper we focus on the less explored Jordan frame of such theories and in the comparison between both this frame and the Einstein one. Furthermore, we discuss the role of the transformation of the torsion under conformal transformations and show that the transformation proposed in this paper (extended conformal transformation) contains a special case of the projective transformation of the connection used in some of the papers that motivated this work. We discuss the role and advantages of the extended conformal transformation and show that this new approach can have interesting consequences by working with different variables such as the metric and torsion. Moreover, we study the stability of the system via a dynamical analysis in the Jordan frame, this in order to analyze whether or not we have the fixed points that can be later identified as the inflationary attractor and the unstable fixed point where inflation could take place. Finally we study the scale invariant case of the general model in the Jordan frame. We find out that both the scalar spectral index and the tensor-to-scalar ratio are in agreement with the latest Planck results.

In this work, we study the symmetry breaking conditions, given by a (anti)de Sitter-valued vector field, of a full (anti)de Sitter-invariant MacDowell–Mansouri inspired action. We show that under these conditions, the action breaks down to General Relativity with a cosmological constant, the four-dimensional topological invariants, as well as the Holst term. We obtain the equations of motion of this action, and analyze the symmetry breaking conditions.