Matter Bounce Cosmology with the f(T) Gravity (1104.4349v2)

Abstract: We show that the f(T) gravitational paradigm, in which gravity is described by an arbitrary function of the torsion scalar, can provide a mechanism for realizing bouncing cosmologies, thereby avoiding the Big Bang singularity. After constructing the simplest version of an f(T) matter bounce, we investigate the scalar and tensor modes of cosmological perturbations. Our results show that metric perturbations in the scalar sector lead to a background-dependent sound speed, which is a distinguishable feature from Einstein gravity. Additionally, we obtain a scale-invariant primordial power spectrum, which is consistent with cosmological observations, but suffers from the problem of a large tensor-to-scalar ratio. However, this can be avoided by introducing extra fields, such as a matter bounce curvaton.

• The paper introduces a matter bounce model using f(T) gravity to eliminate the Big Bang singularity.
• The methodology employs a semi-analytic approach with a specific scale factor leading to a scale-invariant primordial spectrum.
• Perturbation analysis shows a high tensor-to-scalar ratio that is mitigated by a proposed matter bounce curvaton scenario.

Essay on "Matter Bounce Cosmology with the $f(T)$ Gravity"

The paper "Matter Bounce Cosmology with the $f(T)$ Gravity" by Yi-Fu Cai et al. presents a cosmological model that explores the avoidance of the Big Bang singularity through the framework of $f(T)$ gravity, a modified gravitational theory based upon the formalism of teleparallel gravity. This paper is a substantial addition to the array of cosmological models aiming to provide an alternative narrative to the standard Lambda Cold Dark Matter ($\Lambda$CDM) model's singularity toward the genesis of the universe.

The authors investigate a matter bounce scenario enabled by $f(T)$ gravity, wherein the early universe contracts, reaches a minimum size at the bounce, and subsequently expands, thus circumventing the initial singularity characteristic of conventional cosmological models. They consider a specific functional form of the scale factor to facilitate semi-analytic calculations and delineate the corresponding functional form of $f(T)$ that permits such a bouncing cosmology. Their model hinges on a crucial upshot of $f(T)$ gravity: the effective violation of the null energy condition, which has been linked to the possibility of bounces and cyclic occurrences in the evolutions of such spacetimes.

The cosmological perturbation analysis makes up a critical portion of this investigation. The authors apply the conventional perturbation theory to evolve the gravitational potential $\Phi_k$ and examine the implications for the primordial power spectrum. Their findings suggest that the scenario yields a scale-invariant power spectrum, which aligns with current cosmological observational data. This attribute of the model is particularly noteworthy as it parallels a core feature of inflationary cosmology—although derived here without invoking inflaton fields typical of inflationary setups.

A pivotal issue noted in the paper is the prototypical difficulty of matter bounce models: handling the high tensor-to-scalar ratio generated. The authors remark that the matter bounce curvaton scenario they propose—where extra light scalar fields are introduced—can effectively mitigate this challenge via kinetic amplification during the nonsingular bounce phase.

Overall, the implications of this paper are multifaceted. Practically, it opens up the possibility of forming bouncing cosmologies within the field of modified gravity theories, particularly without resorting to quantum gravity effects. Theoretically, it helps unravel the correlation between torsion-based gravitational alternatives like $f(T)$ gravity and self-consistent cosmological scenarios such as bouncing models—broadening the paradigm of cosmological evolution beyond singularities.

Future research emanating from this work could elucidate several outstanding questions in cosmology. In particular, the implications of $f(T)$ gravity might be applied to other realms within cosmology and theoretical physics, potentially offering new insights into the cosmological constant problem, dark energy models, and the unification of fundamental forces.

In conclusion, this paper illustrates the richness of alternative cosmological models offered by modified theories such as $f(T)$ gravity and advances a crucial dialogue about the reconciliation of observed cosmological phenomena with theoretical constructs. As the authors suggest, further advancements in observational cosmology could serve to test the predictions of these models, providing necessary data to either constrain or support such frameworks.