Narrow Results

The inflationary scenario in spatially homogeneous and anisotropic Bianchi Type I spacetime with exponential potential $V=e^{-\lambda \varphi }$, $\lambda >0$ and average scale factor (R) is considered as $R^3=ABC=e^{\lambda \varphi (t)}$ is discussed. The model isotropizes in special case and asymptotically. The spatial volume increases with time representing inflationary scenario and the expansion continues for long enough, thus solving the horizon problem. The model represents decelerating and accelerating phases of universe in special case. Also, the model is singularity free at t = 0. In special case, i.e. when constants b = 0, k = 0, then the model leads to FLRW model for which we have the average scale factor $R\propto t^{2/3}$, $𝜃\propto 1/t$ and deceleration parameter $(q)=\frac{1}{2}$. This paper gives the answer why anisotropic and homogeneous Bianchi Type I spacetime is considered than FRW model to discuss inflationary scenario.

In this paper we show how to study under the self-similarity hypothesis a perfect fluid Bianchi I model with variables G and Λ, but under the condition div T≠0. We arrive to the conclusion that: G and Λ are decreasing time functions (the sign of Λ depends on the equation of state), while the exponents of the scale factor must satisfy the conditions and , ∀ω ∈ (-1, 1), relaxing in this way the Kasner conditions. We also show the connection between the behavior of G and the Weyl tensor.

Bianchi type-I string cosmological models with time dependent gauge function (β) within the framework of Lyra geometry is presented. To get the deterministic model of the universe, we assume that the eigenvalue of shear tensor is proportional to the expansion (θ). This leads to A = (BC)ⁿ where A, B, C are metric potential and n is a constant. The physical and geometrical aspects of the model are discussed in detail. In a special case, the behavior of the model in terms of cosmic time t for is also discussed.

Bianchi Type I dust filled universe in the frameworks of Lyra geometry in the presence of magnetic field is investigated. To get the deterministic model of the universe, we have also assumed that the eigenvalue of shear tensor is proportional to the expansion (θ) in the model. This leads to A = (BC)ⁿ where A, B and C are metric potentials and n is a constant. The physical and geometrical aspects of the model related with astronomical observations are also discussed.

In this work, we investigate the anisotropic Bianchi type I cosmological model in the chiral set-up in a twofold manner. Firstly, we consider a quintessence plus a $k$-essence-like model, where two scalar fields but only one potential term is considered. Secondly, we look at a model where in addition to the two scalar fields the two potential terms are taken into account as well as the standard kinetic energy and the mixed term. Regarding this second model, it is shown that two possible cases can be studied: a quintom-like case and a quintessence-like case. In each of the models, we were able to find both classical and quantum analytical solutions.

In this work, we study the dynamical evolution of a homogeneous and anisotropic, noncommutative (NC) Bianchi I (BI) model coupled to a radiation perfect fluid. Our first motivation is determining if the present model tends to a homogeneous and isotropic NC Friedmann–Robertson–Walker (FRW) model, during its evolution. In order to simplify our task, we use the Misner parametrization of the BI metric. In terms of that parametrization the BI metric has three metric functions: the scale factor $a(t)$ and the two parameters ${\beta }_{\pm }(t)$, which measure the spatial anisotropy of the model. Our second motivation is trying to describe the present accelerated expansion of the universe using noncommutativity (NCTY). The NCTY is introduced by two nontrivial Poisson brackets between some geometrical as well as matter variables of the model. We recover the description in terms of commutative variables by introducing some variables transformations that depend on the NC parameter. Using those variables’ transformations, we rewrite the total NC Hamiltonian of the model in terms of commutative variables. From the resulting Hamiltonian, we obtain the dynamical equations for a generic perfect fluid. In order to solve these equations, we restrict our attention to a model in which the perfect fluid is radiation. We solve, numerically, these equations and compare the NC solutions to the corresponding commutative ones. The comparison shows that the NC model may be considered as a possible candidate for describing the accelerated expansion of the universe. Finally, we obtain estimates for the NC parameter and compare the main results of the NC BI model coupled to radiation with the same NC BI model coupled to other perfect fluids. As our main result, we show that the solutions, after some time, produce an isotropic universe. Based on that result, we can speculate that the solutions may represent an initial anisotropic stage of our Universe, that later, due to the expansion, became isotropic.

We present perfect fluid Bianchi type-I cosmological models with time-dependent cosmological term $\mathrm{\Lambda }$. Exact solutions of the Einstein’s field equations are presented via a suitable functional form for Hubble parameter $H$, which yields a model of the universe that represents initially decelerating and late-time accelerating expansion. We discuss, in the context of some vacuum decay laws, cosmological implications of the corresponding solutions. The physical and geometrical features of the models are also discussed.

We show that the Nieh-Yan topological invariant breaks projective symmetry and loses its topological character in presence of non vanishing nonmetricity. The notion of the Nieh-Yan topological invariant is then extended to the generic metric-affine case, defining a generalized Nieh-Yan term, which allows to recover topologicity and projective invariance, independently. As a concrete example a class of modified theories of gravity is considered and its dynamical properties are investigated in a cosmological setting. In particular, bouncing cosmological solutions in Bianchi I models are derived. Finite time singularities affecting these solutions are analysed, showing that the geodesic completeness and the regular behavior of scalar perturbations in these space-times are not spoiled.