The hidden flat like universe

We study a single-fluid component in a flat like universe (FLU) governed by f (T ) gravity theories, where T is the teleparallel torsion scalar. The FLU model, regardless of the value of the spatial curvature k, identifies a special class of f (T ) gravity theories. Remarkably, FLU f (T ) gravity does not reduce to teleparallel gravity theory. In large Hubble spacetime the theory is consistent with the inflationary universe scenario and respects the conservation principle. The equation of state evolves similarly in all models k = 0, ±1. We study the case when the torsion tensor consists of a scalar field, which enables to derive a quintessence potential from the obtained f (T ) gravity theory. The potential produces Starobinsky-like model naturally without using a conformal transformation, with higher orders continuously interpolate between Starobinsky and quadratic inflation models. The slow-roll analysis shows double solutions, so that for a single value of the scalar tilt (spectral index) n s the theory can predict double tensor-to-scalar ratios r of E-mode and B-mode polarizations.

Astrophysics and Space Science, 2016

In a recent work, a particular class of f (T ) gravity, where T is the teleparallel torsion scalar, has been derived. This class has been identified by flat-like universe (FLU) assumptions . The model is consistent with the early cosmic inflation epoch. A quintessence potential has been constructed from the FLU f (T )-gravity. We show that the first order potential of the induced quintessence is a quasi inverse power law inflation with an additional constant providing an end of the inflation with no need to an extra mechanism. At e-folds N * = 55 before the end of the inflation, this type of potential can perform both E and B modes of the cosmic microwave background (CMB) polarization pattern.

In a recent work, a particular class of f (T ) gravity, where T is the teleparallel torsion scalar, has been derived. This class has been identified by flat-like universe (FLU) assumptions [1]. The model is consistent with the early cosmic inflation epoch. A quintessence potential has been constructed from the FLU f (T )-gravity. We show that the first order potential of the induced quintessence is a quasi inverse power law inflation with an additional constant providing an end of the inflation with no need to an extra mechanism. At e-folds N * = 55 before the end of the inflation, this type of potential can perform both E and B modes of the cosmic microwave background (CMB) polarization pattern.

In the present work we derive an exact solution of an isotropic and homogeneous Universe governed by f (T ) gravity. We show how the torsion contribution to the FRW cosmology can provide a unique origin for both early and late acceleration phases of the Universe. The three models (k = 0, ±1) show a built-in inflationary behavior at some early Universe time; they restore suitable conditions for the hot Big bang nucleosynthesis to begin. Unlike the standard cosmology, we show that even if the Universe initially started with positive or negative sectional curvatures, the curvature density parameter enforces evolution to a flat Universe. The solution constrains the torsion scalar T to be a constant function at all time t, for the three models. This eliminates the need for dark energy (DE). Moreover, when the continuity equation is assumed for the torsion fluid, we show that the flat and closed Universe models violate the conservation principle, while the open one does not. The evolution of the effective equation of state (EoS) of the torsion fluid implies a peculiar trace from a quintessence-like DE to a phantom-like one crossing a matter and radiation EoS in between; then it asymptotically approaches a de Sitter fate.

We derive an exact f (T ) gravity in the absence of ordinary matter in Friedmann-Robertson-Walker (FRW) universe, where T is the teleparallel torsion scalar. We show that vanishing of the energy-momentum tensor T µν of matter does not imply vanishing of the teleparallel torsion scalar, in contrast to general relativity, where the Ricci scalar vanishes. The theory provides an exponential (inflationary) scale factor independent of the choice of the sectional curvature. In addition, the obtained f (T ) acts just like cosmological constant in the flat space model. Nevertheless, it is dynamical in non-flat models. In particular, the open universe provides a decaying pattern of the f (T ) contributing directly to solve the fine-tuning problem of the cosmological constant. The equation of state (EoS) of the torsion vacuum fluid has been studied in positive and negative Hubble regimes. We study the case when the torsion is made of a scalar field (tlaplon) which acts as torsion potential. This treatment enables to induce a tlaplon field sensitive to the symmetry of the spacetime in addition to the reconstruction of its effective potential from the f (T ) theory. The theory provides six different versions of inflationary models. The real solutions are mainly quadratic, the complex solutions, remarkably, provide Higgs-like potential. 98.80.Qc, 04.20.Cv, 98.80.Cq.

The European Physical Journal C, 2014

In the present work we derive an exact solution of an isotropic and homogeneous Universe governed by f (T ) gravity. We show how the torsion contribution to the FRW cosmology can provide a unique origin for both early and late acceleration phases of the Universe. The three models (k = 0, ±1) show a built-in inflationary behavior at some early Universe time; they restore suitable conditions for the hot Big bang nucleosynthesis to begin. Unlike the standard cosmology, we show that even if the Universe initially started with positive or negative sectional curvatures, the curvature density parameter enforces evolution to a flat Universe. The solution constrains the torsion scalar T to be a constant function at all time t, for the three models. This eliminates the need for dark energy (DE). Moreover, when the continuity equation is assumed for the torsion fluid, we show that the flat and closed Universe models violate the conservation principle, while the open one does not. The evolution of the effective equation of state (EoS) of the torsion fluid implies a peculiar trace from a quintessence-like DE to a phantom-like one crossing a matter and radiation EoS in between; then it asymptotically approaches a de Sitter fate.

Journal of the Physical Society of Japan, 2012

In this paper, we study the behavior of perfect fluid and massless scalar field for homogeneous and anisotropic Bianchi type I universe model in f (R, T ) gravity, where R is the Ricci scalar and T is the trace of the energy-momentum tensor. We assume the variation law of mean Hubble parameter to obtain exact solutions of the modified field equations. The physical and kinematical quantities are discussed for both models in future evolution of the universe. We check the validity of null energy condition and conclude that our perfect fluid solution can behave like phantom model. Finally, we find that perfect fluid solutions correspond to massless scalar field models.

Over the past decades, the role of torsion in gravity has been extensively investigated along the main direction of bringing gravity closer to its gauge formulation and incorporating spin in a geometric description. Here we review various torsional constructions, from teleparallel, to Einstein-Cartan, and metric-affine gauge theories, resulting in extending torsional gravity in the paradigm of f(T) gravity, where f(T) is an arbitrary function of the torsion scalar. Based on this theory, we further review the corresponding cosmological and astrophysical applications. In particular, we study cosmological solutions arising from f(T) gravity, both at the background and perturbation levels, in different eras along the cosmic expansion. The f(T) gravity construction can provide a theoretical interpretation of the late-time universe acceleration, and it can easily accommodate with the regular thermal expanding history including the radiation and cold dark matter dominated phases. Furthermore, if one traces back to very early times, a sufficiently long period of inflation can be achieved and hence can be investigated by cosmic microwave background observations, or alternatively, the Big Bang singularity can be avoided due to the appearance of non-singular bounces. Various observational constraints, especially the bounds coming from the large-scale structure data in the case of f(T) cosmology, as well as the behavior of gravitational waves, are described in detail. Moreover, the spherically symmetric and black hole solutions of the theory are reviewed. Additionally, we discuss various extensions of the f(T) paradigm. Finally, we consider the relation with other modified gravitational theories, such as those based on curvature, like f(R) gravity, trying to enlighten the subject of which formulation might be more suitable for quantization ventures and cosmological applications.

Annals of Physics, 1995

We analyze solutions to Friedmann-Robertson-Walker cosmologies in Brans-Dicke theory, where a scalar field is coupled to gravity. Matter is modelled by a γ-law perfect fluid, including false-vacuum energy as a special case. Through a change of variables, we reduce the field equations from fourth order to second order, and they become equivalent to a two-dimensional dynamical system. We then analyze the entire solution space of this dynamical system, and find that many qualitative features of these cosmologies can be gleaned, including standard non-inflationary or extended inflationary expansion, but also including bifurcations of stable or unstable expansion or contraction, noninflationary vacuum-energy dominated models, and several varieties of "coasting," "bouncing," "hesitating," and "vacillating" universes. It is shown that inflationary dogma, which states that a universe with curvature and dominated by inflationary matter will always approach a corresponding flatspace solution at late times, does not hold in general for the scalar-tensor theory, but rather that the occurence of inflation depends upon the initial energy of the scalar field relative to the expansion rate. In the case of flat space (k = 0), the dynamical system formalism generates some previously * E-

Symmetry, 2025

In this paper, we find several teleparallel F(T, B) solutions for a Robertson-Walker (TRW) cosmological spacetime. We first set and solve the F(T, B)-type field equations for a linear perfect fluid. Using similar techniques, we then find new F(T, B) solutions for non-linear perfect fluids with a weak quadratic correction term to the linear equation of state (EoS). Finally, we solve for new classes of F(T, B) solutions for a scalar field source by assuming a power-law scalar field and then an exponential scalar field in terms of the time coordinate. For flat cosmological cases (k = 0 cases), we find new exact and approximate F(T, B) solutions. For non-flat cases (k = ±1 cases), we only find new teleparallel F(T, B) solutions for some specific and well-defined cosmological expansion subcases. We conclude by briefly discussing the impact of these new teleparallel solutions on cosmological processes such as dark energy (DE) quintessence and phantom energy models.