A Critical Review of Classical Bouncing Cosmologies (1406.2790v4)

Abstract: Given the proliferation of bouncing models in recent years, we gather and critically assess these proposals in a comprehensive review. The Planck data shows an unmistakably red, quasi scale-invariant, purely adiabatic primordial power spectrum and no primary non-Gaussianities. While these observations are consistent with inflationary predictions, bouncing cosmologies aspire to provide an alternative framework to explain them. Such models face many problems, both of the purely theoretical kind, such as the necessity of violating the NEC and instabilities, and at the cosmological application level, as exemplified by the possible presence of shear. We provide a pedagogical introduction to these problems and also assess the fitness of different proposals with respect to the data. For example, many models predict a slightly blue spectrum and must be fine-tuned to generate a red spectral index; as a side effect, large non-Gaussianities often result. We highlight several promising attempts to violate the NEC without introducing dangerous instabilities at the classical and/or quantum level. If primordial gravitational waves are observed, certain bouncing cosmologies, such as the cyclic scenario, are in trouble, while others remain valid. We conclude that, while most bouncing cosmologies are far from providing an alternative to the inflationary paradigm, a handful of interesting proposals have surfaced, which warrant further research. The constraints and lessons learned as laid out in this review might guide future research.

• The paper critically assesses bouncing models by exploring NEC violation techniques and strategies to suppress anisotropies via ekpyrotic phases.
• It examines the viability of perturbation theory across the bounce, advocating the use of stable gauges like the harmonic formulation.
• The paper recommends future efforts in model refinement, quantum gravity integration, and advanced numerical simulations to align predictions with observations.

A Critical Review of Classical Bouncing Cosmologies

Overview

The paper of bouncing cosmologies aims to provide alternatives to the inflationary paradigm, seeking to address issues such as the horizon problem, curvature, and the presence of a singularity in the Big Bang model. This paper by Battefeld and Peter offers a comprehensive review of the various classical bouncing cosmologies proposed in the literature, critically assessing their viability against both theoretical and observational benchmarks.

Classical Bouncing Models versus Inflation

Classical bouncing cosmologies propose an early contracting phase followed by a bounce that leads to the current phase of expansion, contrasting with the rapid expansion posited by inflationary theories. The authors note that observations from the PLANCK satellite, indicating a red, quasi-scale-invariant, purely adiabatic primordial power spectrum, are generally consistent with inflationary predictions. However, they argue that bouncing cosmologies can also provide a viable framework to explain these observations, albeit with their unique theoretical challenges.

Theoretical Challenges and Observational Constraints

Bouncing models often contend with several theoretical hurdles:

• Null Energy Condition (NEC) Violation: Most bouncing models require a violation of the NEC to realize a bounce. While this can lead to instabilities, the paper highlights promising approaches to achieve NEC violation without introducing dangerous instabilities, such as through ghost condensates and Galileon fields.
• Instabilities and Anisotropies: A key issue in these models is the growth of anisotropies during contraction which can adversely affect the predictions post-bounce if not adequately controlled. Solutions often involve incorporating an ekpyrotic phase with a steep potential which suppresses these anisotropies.
• Gravitational Waves: The potential detection of primordial gravitational waves poses significant constraints. The matter bounce models predict a large tensor-to-scalar ratio, which can conflict with observations if not properly managed.

The Viability of Perturbation Theory

The review emphasizes the importance of maintaining perturbation theory validity through the bounce. Perturbations of cosmological relevance, particularly concerning gauge choices and matching conditions across the bounce, remain a significant point of research. For instance, variables that exhibit pathological behavior near the bounce have been identified, suggesting that the harmonic gauge might offer a more stable framework for studying perturbations across the bounce.

Observational Predictions and Current Models

The paper examines several specific models and their predictions:

• Ekpyrotic and Cyclic Models: These propose a universe cycle of contraction, bounce, and expansion, which might naturally solve issues of anisotropy and curvature. However, their weak gravitational wave signal on cosmological scales could be a disadvantage if the BICEP2 gravitational wave results are confirmed.
• String Gas Cosmology and the S-Brane Bounce: These provide mechanisms for nonsingular bounces based on fundamental string theory symmetries. However, they face challenges associated with high-energy relic production and moduli stabilization in the Hagedorn phase.

Future Directions

The authors suggest several avenues for future research to enhance the potential of bouncing cosmologies:

1. Refinement of Models: Continued refinement of bounce models, focusing on avoiding instabilities and ensuring the cosmological constraints while predicting realistic signatures.
2. Quantum Gravity Considerations: Quantum gravity adaptations may offer more comprehensive solutions, especially concerning singularities and in the context of string theory.
3. Advanced Numerical Simulations: Utilization of advanced numerical techniques to track perturbations through bounces and validate the mathematical frameworks that predict the observational outcomes.
4. Observational Tests: Developing distinct predictions that can be tested with future astronomical observations, serving as critical experiments to differentiate between inflationary and bouncing cosmologies.

Conclusion

The review underscores the scientific value of exploring classical bouncing cosmologies despite the challenges and complexity involved. By meticulously investigating the ingredients required for a bounce and its observational signatures, this work encourages the continued development of alternative cosmological models. It stimulates discourse on the need for innovative approaches to model the universe's earliest epochs, potentially bringing exciting developments to cosmology and theoretical physics.