Cosmic Triad Research Articles

Constant‐Roll Inflation in the Generalized SU(2) Proca Theory

AbstractThe generalized SU(2) Proca theory (GSU2P) is a variant of the well known generalized Proca theory where the vector field belongs to the Lie algebra of the SU(2) group of global transformations under which the action is made invariant. New interesting possibilities arise in this framework because of the existence of new interactions of purely non‐Abelian character and new configurations of the vector field resulting in spatial spherical symmetry and the cosmological dynamics being driven by the propagating degrees of freedom. We study the 2D phase space of the system that results when the cosmic triad configuration is employed in the Friedmann–Lemaitre–Robertson–Walker background and find an attractor curve whose attraction basin both covers almost all the allowed region and does not include a Big‐Bang singularity. Such an attractor curve corresponds to a primordial inflationary solution that has the following characteristic properties: 1) it is a de Sitter solution whose Hubble parameter is regulated by a generalized version of the SU(2) group coupling constant, 2) it is constant‐roll including, as a limiting case, the slow‐roll variety, 3) a number of e‐folds is easily reached, 4) it has a graceful exit into a radiation dominated period powered by the canonical kinetic term of the vector field and the Einstein–Hilbert term. The free parameters of the action are chosen such that the tensor sector of the theory is the same as that of general relativity at least up to second‐order perturbations, thereby avoiding the presence of ghost and Laplacian instabilities in the tensor sector as well as making the gravity waves propagate at light speed. This is a proof of concept of the interesting properties that could be found in this scenario when the coupling constants be replaced by general coupling functions and more terms be discovered in the GSU2P.

Gauge-field-induced torsion and cosmic inflation

In this paper, inflation in the framework of Einstein–Cartan theory is revisited. Einstein–Cartan theory is a natural extension of the General Relativity with nonvanishing torsion. The connection on Riemann–Cartan space–time is only compatible with the cosmological principal for a particular form of torsion. We also show this form to be compatible with gauge invariance principle for non-Abelian and Abelian gauge fields under a certain deviced coupling procedure. We adopt an Abelian gauge field in the form of “cosmic triad”. The dynamical field equations are obtained and shown to sustain cosmic inflation with a large number of e-folds. We emphasize that at the end of inflation, torsion vanishes and the theory of Einstein–Cartan reduces to the General Relativity with the usual FRW geometry.

A Kaluza–Klein inspired Brans–Dicke gravity with dark matter and dark energy model

We propose the Kaluza–Klein inspired Brans–Dicke gravity model containing possible existence of dark matter and dark energy. The massive scalar field coupled with gravity in 5 dimensional space–time can be reduced to 4 dimensional gravity along with the dilaton ϕ, gauge fields Aμ, and the tower of scalar fields ηn. Two additional gauge fields are introduced to form “Cosmic Triad” vector field scenario. We then use the dynamical system approach to analyse the critical points and their corresponding physical parameters. We found that in the case where only the zero mode of the Kaluza–Klein scalar is decoupled, the system contains both dark matter and dark energy phase depending on the mass parameter with the presence of the gauge field.

Non-AbelianS-term dark energy and inflation

We study the role that a cosmic triad in the generalized $SU(2)$ Proca theory, specifically in one of the pieces of the Lagrangian that involves the symmetric version $S_{\mu \nu}$ of the gauge field strength tensor $F_{\mu \nu}$, has on dark energy and primordial inflation. Regarding dark energy, the triad behaves asymptotically as a couple of radiation perfect fluids whose energy densities are negative for the $S$ term but positive for the Yang-Mills term. This leads to an interesting dynamical fine-tuning mechanism that gives rise to a combined equation of state parameter $\omega \simeq -1$ and, therefore, to an eternal period of accelerated isotropic expansion for an ample spectrum of initial conditions. Regarding primordial inflation, one of the critical points of the associated dynamical system can describe a prolonged period of isotropic slow-roll inflation sustained by the $S$ term. This period ends up when the Yang-Mills term dominates the energy density leading to the radiation dominated epoch. Unfortunately, in contrast to the dark energy case, the primordial inflation scenario is strongly sensitive to the coupling constants and initial conditions. The whole model, including the other pieces of the Lagrangian that involve $S_{\mu \nu}$, might evade the recent strong constraints coming from the gravitational wave signal GW170817 and its electromagnetic counterpart GRB 170817A.

Dynamical analysis for a vector-like dark energy

In this paper we perform a dynamical analysis for a vector field as a candidate for the dark energy, in the presence of a barothropic fluid. The vector is one component of the so-called cosmic triad, which is a set of three identical copies of an abelian field pointing mutually in orthogonal directions. In order to generalize the analysis, we also assumed the interaction between dark energy and the barotropic fluid, with a phenomenological coupling. Both matter and dark energy eras can be successfully described by the critical points, indicating that the dynamical system theory is a viable tool to analyze asymptotic states of such cosmological models.

The unified first law in “cosmic triad” vector field scenario

In this Letter, we try to apply the unified first law to the “cosmic triad” vector field scenario both in the minimal coupling case and in the non-minimal coupling case. After transferring the non-minimally coupling action in the Jordan frame to the Einstein frame, the correct dynamical equation (Friedmann equation) is gotten in a thermal equilibrium process by using the already existing entropy while the entropy in the non-minimal coupled “cosmic triad” scenario has not been derived. And after transferring the variables back to the Jordan frame, the corresponding Friedmann equation is demonstrated to be correct. For complete arguments, we also calculate the related Misner–Sharp energy in the Jordan and Einstein frames.

The Noether symmetry approach in a ‘cosmic triad’ vector field scenario

To realize the accelerations in the early and late periods of our universe, we need to specify potentials for the dominant fields. In this paper, by using the Noether symmetry approach, we try to find suitable potentials in the ‘cosmic triad’ vector field scenario. Because the equation of state parameter of dark energy has been constrained in the range of −1.21 ⩽ ω ⩽ −0.89 by observations, we derive the Noether conditions for the vector field in quintessence, phantom and quintom models, respectively. In the first two cases, constant potential solutions have been obtained. What is more, a fast decaying point-like solution with power-law potential is also found for the vector field in the quintessence model. For the quintom case, we find an interesting constraint on the field potentials, where C and are constants related to the Noether symmetry.

Cheng–Weyl vector field and its cosmological application

Weyl’s idea on scale invariance was resurrected by Cheng in 1988. The requirement of localscale invariance leads to a completely new vector field, which we call the ‘Cheng–Weylvector field’. The Cheng–Weyl vector field couples only to a scalar field and thegravitational field naturally. It does not interact with other known matter in the standardmodel of particle physics. In the present work, the (generalized) Cheng–Weyl vector fieldcoupled with the scalar field and its cosmological application are investigated. A mixture ofthe scalar field and a so-called ‘cosmic triad’ of three mutually orthogonal Cheng–Weylvector fields is regarded as the dark energy in the universe. The cosmologicalevolution of this ‘mixed’ dark energy model is studied. We find that the effectiveequation-of-state parameter of the dark energy can cross the phantom dividewde = −1 in some cases; the first and second cosmological coincidence problems can be alleviated atthe same time in this model.