Towards a Nonsingular Bouncing Cosmology (1206.2382v2)

Abstract: We present a nonsingular bouncing cosmology using single scalar field matter with non-trivial potential and non-standard kinetic term. The potential sources a dynamical attractor solution with Ekpyrotic contraction which washes out small amplitude anisotropies. At high energy densities the field evolves into a ghost condensate, leading to a nonsingular bounce. Following the bounce there is a smooth transition to standard expanding radiation and matter dominated phases. Using linear cosmological perturbation theory we track each Fourier mode of the curvature fluctuation throughout the entire cosmic evolution. Using standard matching conditions for nonsingular bouncing cosmologies we verify that the spectral index does not change during the bounce. We show there is a controlled period of exponential growth of the fluctuation amplitude for the perturbations (but not for gravitational waves) around the bounce point which does not invalidate the perturbative treatment. This growth induces a natural suppression mechanism for the tensor to scalar ratio of fluctuations. Moreover, we study the generation of the primordial power spectrum of curvature fluctuations for various types of initial conditions. For the pure vacuum initial condition, on scales which exit the Hubble radius in the phase of Ekpyrotic contraction, the spectrum is deeply blue. For thermal particle initial condition, one possibility for generating a scale-invariant spectrum makes use of a special value of the background equation of state during the contracting Ekpyrotic phase. If the Ekpyrotic phase is preceded by a period of matter-dominated contraction, the primordial power spectrum is nearly scale-invariant on large scales (scales which exit the Hubble radius in the matter-dominated phase) but acquires a large blue tilt on small scales.

• The paper introduces a single scalar field mechanism that drives a nonsingular bounce using ghost condensate dynamics and non-standard kinetic terms.
• The analytic and numerical study demonstrates controlled amplification of metric perturbations, ensuring scale-invariance and stability across cosmic phases.
• The model mitigates the anisotropy problem during Ekpyrotic contraction and offers clear predictions for CMB observational tests.

An Analysis of "Towards a Nonsingular Bouncing Cosmology"

The paper "Towards a Nonsingular Bouncing Cosmology" by Yi-Fu Cai, Damien A. Easson, and Robert Brandenberger explores a cosmological model proposing a nonsingular bounce using a scalar field approach. The authors aim to address critical challenges faced by the "matter bounce" and Ekpyrotic models in cosmology by integrating properties of both.

The paper begins with a review of the limitations of the matter bounce model, primarily concerning scale-invariance and stability towards anisotropies during the contracting phase. This model traditionally demands the Null Energy Condition (NEC) violation, commonly achieved through matter components like quintom or ghost fields. The work introduces a single scalar field with a dynamic potential and non-standard kinetic terms, leading to a nonsingular bounce while controlling instabilities.

Model Description and Background Evolution

The model is founded on a scalar field, denoted as $\phi$, that incorporates features from ghost condensate and Galileon-inspired formulations. The Lagrangian comprises a kinetic function $K(\phi, X)$ and a Galileon-type operator, allowing for a phase where $\phi$ acquires a ghost condensate state, triggering NEC violation and a bounce.

The potential is structured to induce a phase of Ekpyrotic contraction, which helps suppress anisotropies and creates a favorable setup for a bounce. The results suggest a transition through a ghost condensate phase yields a smooth continuum from contraction through the bounce into expansion, providing a solution free from the anisotropy problem.

Cosmological Perturbations and Dynamics

The paper meticulously tracks metric perturbations across four cosmic evolution phases: initial setting, Ekpyrotic contraction, the bounce, and post-bounce. Of particular interest is the behavior of perturbations during the ghost condensate-driven bounce, where the model ensures that the spectrum of density perturbations does not encounter a significant spectral tilt change, crucial for matching present-day cosmological observables.

The analytical and numerical investigations reveal that while there is exponential growth of fluctuations during the bounce, this does not hamper the model’s validity as long as controls are in place regarding the bounce scale relative to Planckian physics. Thus, fluctuations exhibit a controlled amplification, which importantly translates into a reduced tensor-to-scalar ratio.

Implications and Future Prospects

This research opens pathways to explore bouncing cosmologies without invoking singular transitions between contraction and expansion. The approach promises more predictive power and stability against perturbative instabilities often implicated in such models.

One compelling aspect is the model's implication for the observed universe's primordial perturbations, particularly the realization of scale-invariance on large scales and suppression of gravitational wave power through the bounce dynamics. Additionally, the analytic tractability of perturbations facilitates avenues for implementing observational tests, as these metrics closely align with CMB observations without requiring inflationary mechanisms.

Future work could concentrate on refining the model parameters and investigating interactions between multiple matter components during the bounce. Moreover, crafting a coherent narrative on initial condition settings and evolution paths when integrating more exotic physics, like high-energy corrections from quantum gravity, remains a forward-looking priority.

In summary, "Towards a Nonsingular Bouncing Cosmology" contributes a robust framework to the pursuit of alternative cosmological models, equipped with mechanisms to avoid past inconsistencies, thus inviting deeper exploration and experimental scrutiny in the cosmology community.