We extend the treatment of quantum cosmology to a manifold with torsion. We adopt a model of Einstein-Cartan-Sciama-Kibble compatible with the cosmological principle. The universe wavefunction will be subject to a $\mathcal{PT}$-symmetric Hamiltonian. With a vanishing energy-momentum tensor, the universe evolution in the semiclassical and classical regimes is shown to reflect a two-stage inflationary process induced by torsion.
Cosmology with non-perturbative quantum corrections resulting from torsion is considered. It is shown that the evolution of closed, open and flat Universes is changed because of the presence of a non-zero dispersion of quantum torsion. The evolution of a Universe with quantum torsion and with one type of average curvature can be similar to the evolution of a Universe without quantum torsion and with another type of average curvature. For the description of the non-perturbative quantum torsion, a vector field approximation is applied.
We study the cosmology of a quadratic metric-compatible torsionful gravity theory in the presence of a perfect hyperfluid. The gravitational action is an extension of the Einstein-Cartan theory given by the usual Einstein-Hilbert contribution plus all the admitted quadratic parity even torsion scalars and the matter action also exhibits a dependence on the connection. The equations of motion are obtained by regarding the metric and the metric-compatible torsionful connection as independent variables. We then consider a Friedmann-Lemaître-Robertson-Walker background, analyze the conservation la…
We study cosmological consequences of the dark spinor model when torsion is included. Only some components of the torsion are allowed to be non-vanishing in homogeneous and isotropic cosmology, but there exist freedoms in the choice of these components which is consistent with the evolution equations. We exploit this and discuss several cases which can result in interesting cosmological consequences. Especially, we show that there exist exact cosmological solutions in which the Universe began its acceleration only recently and this solution is an attractor. This corresponds to a specific form …
In the context of scalar-torsion theory we investigate the evolution of the cosmological anisotropies for a Kantowski-Sachs background geometry. We study the phase-space of the gravitational field equations by determining the admitted stationary points and study their stability properties. For the potential function of the non-minimally coupled scalar field we assume the exponential and the power-law functions. Finally, we make use of Poincare variables in order to investigate the existence of stationary points at the infinity regime of the dynamics.
Variation of the 4-D string cosmology action with dynamical torsion and massless dilatons lead to an expression of torsion in terms of massless dilatons in the case of de Sitter inflation.The solution is approximated according to the COBE data.
Gravitational stability of torsion and inflaton field in a four-dimensional spacetime de Sitter solution in scalar-tensor cosmology where Cartan torsion propagates is investigated in detail. Inflaton and torsion evolution equations are derived by making use of a Lagrangean method. Stable and unstable modes for torsion and inflatons are found to be dependent of the background torsion and inflaton fields. Present astrophysical observations favour a stable mode for torsion since this would explain why no relic torsion imprint has been found on the Cosmic Background Radiation in the universe.
We apply the statefinder diagnostic to the torsion cosmology, in which an accounting for the accelerated universe is considered in term of a Riemann-Cartan geometry: dynamic scalar torsion. We find that there are some typical characteristic of the evolution of statefinder parameters for the torsion cosmology that can be distinguished from the other cosmological models. Furthermore, we also show that statefinder diagnostic has a direct bearing on the critical points. The statefinder diagnostic divides the torsion parameter $a_1$ into differential ranges, which is in keeping with the requirement…
We have studied the torsion cosmology model in Kaluza-Klein theory. We considered two simple models in which the torsion vectors are $A_μ=(α,0,0,0)$ and $A_μ=a(t)^2(0,β,β,β)$, respectively. For the first model, the accelerating expansion of the Universe can be not explained without dark energy which is similar to that in the standard cosmology. But for the second model, we find that without dark energy the effect of torsion can give rise to the accelerating expansion of the universe and the alleviation of the well-known age problem of the three old objects for appropriated value of the model p…
Fluctuations on de Sitter solution of Einstein-Cartan field equations are obtained in terms of the matter density primordial density fluctuations and spin-torsion density and matter density fluctuations obtained from COBE data. Einstein-de Sitter solution is shown to be unstable even in the absence of torsion.The spin-torsion density fluctuation to generate a deflationary phase is computed from the COBE data.
The field equation of orthodox general relativity are written in the context of a geometry with non-vanishing torsion, the Absolute Parallelism (AP) geometry. An AP-structure, with homogeneity and isotropy, is used for cosmological applications. The resulting dynamical equations are those of FRW-Standard cosmology, which have many problems e.g. singularity, particle horizons, ...etc. We suggest a new scheme for investigating the effect of torsion on the dynamics of FRW-Cosmology, without changing the basic structure of general relativity. It is shown that some of these problems will disappear …
Homogeneous isotropic spatial flat cosmological models with two torsion functions in vacuum are built and investigated in the framework of de Sitter gauge theory of gravity. It is shown that by certain choices of parameters of gravitational Lagrangian the cosmological equations have some exact constant solutions that turn out to be stable de Sitter critical points of dynamical systems and can explain observable acceleration of cosmological expansion. The role of the space-time torsion provoking the acceleration of cosmological expansion is shown.
f(R)-gravity with geometric torsion (not related to any spin fluid) is considered in a cosmological context. We derive the field equations in vacuum and in presence of perfect-fluid matter and discuss the related cosmological models. Torsion vanishes in vacuum for almost all arbitrary functions f(R) leading to standard General Relativity. Only for f(R)=R^{2}, torsion gives contribution in the vacuum leading to an accelerated behavior . When material sources are considered, we find that the torsion tensor is different from zero even with spinless material sources. This tensor is related to the …
We study Weyssenhoff spin fluids in Bianchi type-I cosmological models, within the framework of torsional f(R)-gravity; the resulting field equations are derived and discussed in both Jordan and Einstein frames, clarifying the role played by the spin and the non-linearity of the gravitational Lagrangian f(R) in generating the torsional dynamical contributions. The general conservation laws holding for f(R)-gravity with torsion are employed to provide the conditions needed to ensure the preservation of the Hamiltonian constraint and the consequent correct formulation of the associated initial v…
This paper deals with the symmetry analysis of the Einstein Cartan theory which is an extension of the General Relativity and it accounts for the space-time torsion. We begin by applying Noether Theorem to the Lagrangian of the FRW type cosmology with torsion and choose a point transformation: $(a,ϕ,N)\rightarrow(u,v,W)$, such that one of the transformed variable is cyclic for the Lagrangian. Then using the conserved charge, which is obtained by applying Noether theorem, and the constant of motion, we get the solutions and conclude that due to the presence of torsion the FRW type cosmology is …
In this work, we study some thermodynamical aspects associated with torsion in a flat FLRW spacetime cosmic evolution. By implementing two Ansatze for the torsion term, we find that the model admits a phantom regime or a quintessence behavior. This scheme differs from the $Λ$CDM model at the thermodynamical level. The resulting cosmic expansion is not adiabatic, the fulfillment of the second law of thermodynamics requires a positive torsion term, and the temperature of the cosmic fluid is always positive. The entropy of the torsion phantom scenario is negative, but introducing chemical potenti…
We solve one of the open problems in Einstein-Cartan theory, namely we find a natural matter source whose spin angular momentum tensor is compatible with the cosmological principle. We analyze the resulting evolution equations and find that an epoch of accelerated expansion is an attractor. The torsion field quickly decays in that period. Our results are interpreted in the context of the standard model of cosmology.
The thermodynamics is extented to spacetimes with spin-torsion density.Impplications to Einstein-Cartan-de Sitter inflationary phases are discussed.A relation between the spin-torsion density,entropy and temperature is presented.A lower limit for the radius of the Universe may be obtained from the spin-torsion density and the Planck lenght.
In this work we investigate the effects of torsion in the framework of Einstein-Cartan theory in early cosmology. We study solutions for a homogeneous and isotropic relativistic Weyssenhoff spin fluid with dynamical timelike axial current, also homogeneous and isotropic. The general solutions can mostly be described by means of three particular solutions. The properties of these solutions (such as singularity avoidance and primordial or late accelerated expansion) are analysed and depend on the relations between the source parameters.
We propose a simple scenario which explains why our Universe appears spatially flat, homogeneous and isotropic. We use the Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity which naturally extends general relativity to include the spin of matter. The torsion of spacetime generates gravitational repulsion in the early Universe filled with quarks and leptons, preventing the cosmological singularity: the Universe expands from a state of minimum but finite radius. We show that the dynamics of the closed Universe immediately after this state naturally solves the flatness and horizon problems i…
Poincaré gauge theory of gravity offers opportunities to solve some principal problems of general relativity theory and modern cosmology. In the frame of this theory the gravitational interaction can have the repulsion character in the case of usual gravitating matter with positive values of energy density and pressure satisfying energy dominance condition. Cosmological consequences of gravitational repulsion are considered in the case of homogeneous isotropic models in connection with the problem of cosmological singularity and dark energy problem of general relativity theory. Regular Big Ban…
In this work we present a generalized Brans-Dicke lagrangian including a non-minimally coupled Gauss-Bonnet term without imposing the vanishing torsion condition. In the resulting field equations, the torsion is closely related to the dynamics of the scalar field, i.e., if non-minimally coupled terms are present in the theory, then the torsion must be present. For the studied lagrangian we analyze the cosmological consequences of an effective torsional fluid and we show that this fluid can be responsible for the current acceleration of the universe. Finally, we perform a detailed dynamical sys…
We show that the Einstein-Cartan-Sciama-Kibble theory of gravity with torsion not only extends general relativity to account for the intrinsic spin of matter, but it may also eliminate major problems in gravitational physics and answer major questions in cosmology. These problems and questions include: the origin of the Universe, the existence of singularities in black holes, the nature of inflation and dark energy, the origin of the matter-antimatter asymmetry in the Universe, and the nature of dark matter.
Cosmological solutions for homogeneous isotropic models in the framework of the Poincaré gauge theory of gravity based on gravitational Lagrangian adopted in the paper by Kun-Feng Shie, James M. Nester and Hwei-Jang Yo (Phys. Rev. D \textbf{78}, 023522 (2008)) are discussed. Cosmological solutions for accelerating Universe obtained in referred paper are compared with corresponding solutions of standard $ΛCDM$-model and also with cosmological solution obtained by authors of this Comment.
We study Dirac spinors in Bianchi type-I cosmological models, within the framework of torsional $f(R)$-gravity. We find four types of results: the resulting dynamic behavior of the universe depends on the particular choice of function $f(R)$; some $f(R)$ models do not isotropize and have no Einstein limit, so that they have no physical significance, whereas for other $f(R)$ models isotropization and Einsteinization occur, and so they are physically acceptable, suggesting that phenomenological arguments may select $f(R)$ models that are physically meaningful; the singularity problem can be avoi…
In the Einstein-Cartan space $U_4$, an axial vector torsion together with a scalar field connected to a local scale factor have been considered. By combining two particular terms from the SO(4,1) Pontryagin density and then modifying it in a SO(3,1) invariant way, we get a Lagrangian density with Lagrange multipliers. Then under FRW-cosmological background, where the scalar field is connected to the source of gravitation, the Euler-Lagrange equations ultimately give the constancy of the gravitational constant together with only three kinds of energy densities representing mass, radiation and c…
In this letter, we study the late-time evolution of a torsion cosmology only with the spin-$0^+$ mode. We find three kinds of analytical solutions with a constant affine scalar curvature. In the first case, it is not physical because the matter density will be negative. In the second case, it shows that the dark energy can be mimicked in the torsion cosmological model. In the third case, the characteristic of late-time evolution is similar to that of the universe of matter dominant. And we also find a kind of expression with the non-constant curvature that the periodic character of numerical c…
Investigations of the dynamic modes of the Poincare gauge theory of gravity found only two good propagating torsion modes; they are effectively a scalar and a pseudoscalar. Cosmology affords a natural situation where one might see observational effects of these modes. Here we consider only the ``scalar torsion'' mode. This mode has certain distinctive and interesting qualities. In particular this type of torsion does not interact directly with any known matter and it allows a critical non-zero value for the affine scalar curvature. Via numerical evolution of the coupled nonlinear equations we …
In a recent letter by H. Davoudiasl, R. Kitano, T. Li and H. Murayama ``The new Minimal Standard Model'' (NMSM) was constructed that incorporates new physics beyond the Minimal Standard Model (MSM) of particle physics. The authors follow the principle of minimal particle content and therefore adopt the viewpoint of particle physicists. It is shown that a generalisation of the geometric structure of spacetime can also be used to explain physics beyond the MSM. It is explicitly shown that for example inflation, i.e. an exponentially expanding universe, can easily be explained within the framewor…
Metric perturbations the stability of solution of Einstein-Cartan cosmology (ECC) are given. The first addresses the stability of solutions of Einstein-Cartan (EC) cosmological model against Einstein static universe background. In this solution we show that the metric is stable against first-order perturbations and correspond to acoustic oscillations. The second example deals with the stability of de Sitter metric also against first-order perturbations. Torsion and shear are also computed in these cases. The resultant perturbed anisotropic spacetime with torsion is only de Sitter along one dir…
The Einstein-Cartan-Sciama-Kibble theory of gravity removes the constraint of general relativity that the affine connection be symmetric by regarding its antisymmetric part, the torsion tensor, as a dynamical variable. The minimal coupling between the torsion tensor and Dirac spinors generates a spin-spin interaction which is significant in fermionic matter at extremely high densities. We show that such an interaction averts the unphysical big-bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. This scenario also e…
We consider cosmological solution for Einstein gravity with massive fermions with a four-fermion coupling, which emerges from the Holst action and is related to the Barbero-Immirzi (BI) parameter. This gravitational action is an important object of investigation in a non-perturbative formalism of quantum gravity. We study the equation of motion for for the Dirac field within the standard Friedman-Robertson-Walker (FRW) metric. Finally, we show the theory with BI parameter and minimally coupling Dirac field, in the zero mass limit, is equivalent to an additional term which looks like a perfect …
It is found that the deviation of an effective potential from the quartic form is related to the metric and vector torsion dependencies of the effective potential in the vector torsion coupled conformally induced gravity.
Recently Salim et al [JCAP (2007)], have shown that galactic dynamo seeds can be possibly attainable in bouncing cosmological models with QED Lagrangeans. In this paper we generalise their result by include torsion of spacetime in bouncing cosmology. It is shown that by considering a semi-minimal photon-torsion coupling and a Lagrangean of the type $RF^{2}$ it is possible to find a fast decoupling between magnetic and torsion fields in the contracting phases of the universe. Besides torsion field decays as $K\sim{a^{2/3}}$ while the magnetic field grows as $B\sim{a^{-5.5}}$ thus explaining the…
A cosmological model in an Einstein-Cartan framework endowed with torsion is studied. For a torsion function assumed to be proportional to Hubble expansion function, namely $ϕ=-αH$, the contribution of torsion function as a dark matter component is studied in two different approaches. In the first one, the total matter energy density is altered by torsion coupling $α$, giving rise to an effective dark matter and cosmological constant terms that reproduce quite well the flat cosmic concordance model. In the second approach, starting with just standard baryonic matter plus a cosmological constan…
In this paper, the dynamical attractor and heteroclinic orbit have been employed to make the late-time behaviors of the model insensitive to the initial condition and thus alleviate the fine-tuning problem in the torsion cosmology. The late-time de Sitter attractor indicates that torsion cosmology is an elegant scheme and the scalar torsion mode is an interesting geometric quantity for physics. The numerical solutions obtained by Nester et al. are not periodic solutions, but are quasi-periodic solutions near the focus for the coupled nonlinear equations.
A Friedmann like cosmological model in Einstein-Cartan framework is studied when the torsion function is assumed to be proportional to a single $ϕ(t)$ function coming just from the spin vector contribution of ordinary matter. By analysing four different types of torsion function written in terms of one, two and three free parameters, we found that a model with $ϕ(t)=- αH(t) \big({ρ_{m}(t)}/{ρ_{0c}}\big)^n$ is totally compatible with recent cosmological data, where $α$ and $n$ are free parameters to be constrained from observations, $ρ_m$ is the matter energy density and $ρ_{0c}$ the critical d…
Earlier Bamba et al [JCAP (2012)] have obtained cosmological magnetic fields in teleparallel torsion theories of gravity that are not compatible with galactic dynamos. This result agrees with previous ones obtained by the author which shows [Phys Lett B (2012)] that anti-dynamo generalised theorem to torsion theories forbides such kind of dynamos to explain galactic magnetic fields of the order of $μ$G. More recently the author has suggested [IJAA (2012)] that a sort of Biermann battery could be obtained in torsioned cosmology. Nevertheless in this paper we show that this can be a particular r…
A cosmology of Poincare gauge theory is developed, where several properties of universe corresponding to the cosmological equations with the pseudoscalar torsion function are investigated. The cosmological constant is found to be the intrinsic torsion and curvature of the vacuum universe and is derived from the theory naturally rather than added artificially, i.e. the dark energy originates from geometry and includes the cosmological constant but differs from it. The cosmological constant puzzle, the coincidence and fine tuning problem are relieved naturally at the same time. By solving the co…
This Thesis is devoted to the study of Metric-Affine Theories of Gravity and Applications to Cosmology. The thesis is organized as follows. In the first Chapter we define the various geometrical quantities that characterize a non-Riemannian geometry. In the second Chapter we explore the MAG model building. In Chapter 3 we use a well known procedure to excite torsional degrees of freedom by coupling surface terms to scalars. Then, in Chapter 4 which seems to be the most important Chapter of the thesis, at least with regards to its use in applications, we present a step by step way to solve for …
The idea of gauge theories of gravity predicts that there should exist not only the massless graviton but also massive particles carrying the gravitational force. We study the cosmology in a quadratic gravity with dynamical torsion where gravity may be interpreted as a gauge force associated with the Poincaré group. In addition to the massless spin-2 graviton, the model contains four non-ghost massive particle species: a couple of spin-0, a spin-1 and a spin-2. Supposing the restoration of the local Weyl invariance in the UV limit and the parity invariance, we find the most general minisupersp…
Within the context of the Fermi-bounce curvaton mechanism, we analyze the one-loop radiative corrections to the four fermion interaction, generated by the non-dynamical torsion field in the Einstein-Cartan-Holst-Sciama-Kibble theory. We show that contributions that arise from the one-loop radiative corrections modify the energy-momentum tensor, {\it mimicking} an effective Ekpyrotic fluid contribution. For these reasons, we call this effect {\it quantum Ekpyrotic} mechanism. This leads to the dynamical washing out of anisotropic contributions to the energy-momentum tensor, without introducing …
In this paper we consider the most general least-order derivative theory of gravity in which not only curvature but also torsion is explicitly present in the Lagrangian, and where all independent fields have their own coupling constant: we will apply this theory to the case of ELKO fields, which is the acronym of the German \textit{Eigenspinoren des LadungsKonjugationsOperators} designating eigenspinors of the charge conjugation operator, and thus they are a Majorana-like special type of spinors; and to the Dirac fields, the most general type of spinors. We shall see that because torsion has a…
In the context of the metric-affine Chern-Simons gravity endowed with projective invariance, we derive analytical solutions for torsion and nonmetricity in the homogeneous and isotropic cosmological case, described by a flat Friedmann-Robertson-Walker metric. We discuss in some details the general properties of the cosmological solutions in the presence of a perfect fluid, such as the dynamical stability and the emergence of big bounce points, and we examine the structure of some specific solutions reproducing de Sitter and power law behaviours for the scale factor. Then, we focus on first-ord…
I review a string-inspired cosmological model, with gravitational anomalies present at very early epochs, which includes a totally antisymmetric torsion, that in (3+1)-dimensions is equivalent to a pseudoscalar (Kalb-Ramond, string-model independent) axion field. Upon condensation of primordial gravitational waves (GW), that are created at a pre-inflationary era, the model leads to inflation of the so-called running-vacuum-model (RVM) type, which is realised without the need for external inflaton fields, being due to the non-linearities that characterise the gravitational theory. The model pro…
We discuss an extended Teleparallel gravity models comprising functions of scalar invariants constructed by torsion, torsion Gauss-Bonnet and boundary terms. We adopt the Noether Symmetry Approach to select the functional forms, the first integrals and, eventually, the exact solutions of the dynamics in the context of flat Friedman-Robertson-Walker cosmology. Standard perfect fluid matter, minimally coupled to geometry, is considered. Several physically consistent models are derived with related exact solutions.
We study the properties of gravity and bulk fields living in a torsion warped braneworld. The torsion is driven by a background vector whose norm provides a source for the bulk cosmological constant. For a vector as the derivative of a scalar field, we find new isotropic and anisotropic thick brane geometries. We analyse the features of bosonic and fermionic fields in this isotropic and in standing wave scenarios. The background vector provides nonminimal coupling between the field and the geometry leading to modifications in the Kaluza-Klein states. The spinor connection is modified by the to…
Criteria for the existence of de Sitter inflation with dilaton fields in four-dimensional space-times with torsion is discussed.The relation between matter density perturbation and the spin-density perturbation is stablished based on this criteria.From COBE data it is shown that there is a linear relationship between the spin-torsion density and temperature of the Universe for the case where matter density dominates the kinetic part of dilaton fields.
The possibility to distinguish Dirac from Majorana fermion by gravitational interaction and torsion coupling is discussed. The scattering of both Dirac and Majorana particles are the same in the spherically symmetric gravitational field up to the first order perturbation of the fermion-gravity interaction. The scattering behaviors of Dirac and Majorana fermion are also the same by axial vector torsion but different by vector torsion. We get the conclusion that the scattering by vector torsion field can distinguish the Dirac from Majorana neutrino.
Many black hole spacetimes with a 3-form field exhibit a hidden symmetry encoded in a torsion generalization of the principal Killing--Yano tensor. This tensor determines basic properties of such black holes while also underlying the separability of the Hamilton--Jacobi, Klein--Gordon, and (torsion-modified) Dirac field equations in their background. As a specific example, we consider the Chong--Cvetič--Lü--Pope black hole of $D=5$ minimal gauged supergravity and show that the torsion-modified vector field equations can also be separated, with the principal tensor playing a key role in the sep…
Poincarè gauge theory (PGT) is an alternative gravity theory, which attempts to bring the gravity into the gauge-theoretic frame, where the Lagrangian is quadratic in torsion and curvature. Recently, the cosmological models with torsion based on this theory have drawn many attentions, which try to explain the cosmic acceleration in a new way. Among these PGT cosmological models, the one with only even parity dynamical modes -- SNY model, for its realistic meaning, is very attractive. In this paper, we first analyze the past-time cosmic evolution of SNY model analytically. And based on these re…
We investigate the cosmological aspects of the most general parity preserving Metric-Affine Gravity theory quadratic in torsion and non-metricity in the presence of a cosmological hyperfluid. The equations of motion are obtained by varying the action with respect to the metric and the independent affine connection. Subsequently, considering a Friedmann-Lemaître-Robertson-Walker background, we derive the most general form of the modified Friedmann equations for the full quadratic theory. We then focus on a characteristic sub-case involving only two quadratic contributions given in terms of tors…
