We consider spatially homogeneous and isotropic cosmologies with non-zero torsion. Given the high symmetry of these universes, we adopt a specific form for the torsion tensor that preserves the homogeneity and isotropy of the spatial surfaces. Employing both covariant and metric-based techniques, we derive the torsional versions of the continuity, the Friedmann and the Raychaudhuri equations. These formulae demonstrate how, by playing the role of the spatial curvature, or that of the cosmological constant, torsion can drastically change the evolution of the classic homogeneous and isotropic Friedmann universes. In particular, torsion alone can lead to exponential expansion. For instance, in the presence of torsion, the Milne and the Einstein-de Sitter universes evolve like the de Sitter model. We also show that, by changing the expansion rate of the early universe, torsion can affect the primordial nucleosynthesis of helium-4. We use this sensitivity to impose strong cosmological bounds on the relative strength of the associated torsion field, requiring that its ratio to the Hubble expansion rate lies in the narrow interval (−0.005813, +0.019370) around zero. Interestingly, the introduction of torsion can reduce the production of primordial helium-4, unlike other changes to the standard thermal history of an isotropic universe. Finally, turning to static spacetimes, we find that there exist torsional analogues of the classic Einstein static universe, with all three types of spatial geometry. These models can be stable when the torsion field and the universe's spatial curvature have the appropriate profiles.Since then, the EC theory (also known as ECKS theory) has been formally established and has received considerable recognition, as it provides the simplest classical extension of Einstein's general relativity (see [3] for a recent review and references therein).The EC theory postulates an asymmetric affine connection for the spacetime, in contrast to the symmetric Christoffel symbols of Riemannian spaces. In technical terms, torsion is described by the antisymmetric part of the non-Riemannian affine connection [1]. Therefore, in addition to the metric tensor, there is an independent torsional field, which also contributes to the total gravitational "pull". Geometrically speaking, curvature reflects the fact that the parallel transport of a vector along a closed loop in a Riemannian space depends on the path. The presence of torsion adds extra complications, since the aforementioned loop does not necessarily close. In a sense, curvature forces the spacetime to bend and torsion twists it. Dynamically, spacetime torsion is triggered by the intrinsic angular momentum (spin) of the matter, whereas spacetime curvature is caused by the mere presence of matter. This distinction is reflected in two sets of formulae, known as the Einstein-Cartan and the Cartan field equations.The literature contains a number of suggestions for experimentally testing gravitational theories with non-zero torsion (see [4] for a representativ...

We propose that several of the anomalies that have been observed at large angular scales in the CMB have a common origin in a cosmic bounce that took place before the inflationary era. The bounce introduces a new physical scale in the problem, which breaks the almost scale invariance of inflation. As a result, the state of scalar perturbations at the onset of inflation is no longer the Bunch–Davies vacuum, but it rather contains excitations and non-Gaussianity, which are larger for infrared modes. We argue that the combined effect of these excitations and the correlations between CMB modes and longer wavelength perturbations, can account for the observed power suppression, for the dipolar asymmetry, and it can also produce a preference for odd-parity correlations. The model can also alleviate the tension in the lensing amplitude A L. We adopt a phenomenological viewpoint by considering a family of bounces characterized by a couple of parameters. We identify the minimum set of ingredients needed for our ideas to hold, and point out examples of theories in the literature where these conditions are met.

No abstract

Anomalies in the cosmic microwave background (CMB) refer to features that have been observed, mostly at large angular scales, and which show some tension with the statistical predictions of the standard ΛCDM model. In this work, we focus our attention on power suppression, dipolar modulation, a preference for odd parity, and the tension in the lensing parameter AL. Though the statistical significance of each individual anomaly is inconclusive, collectively they are significant, and could indicate new physics beyond the ΛCDM model. In this article, we present a brief, but pedagogical introduction to CMB anomalies and propose a common origin in the context of loop quantum cosmology.