# Bouncing Cosmologies with Dark Matter and Dark Energy

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## Abstract

**:**

## 1. Introduction

## 2. The ΛCDM Bounce Scenario

#### 2.1. Background Space-Time

#### 2.2. Perturbations

^{−2}[3]. Therefore, this calculation (first completed in [8]) shows that the simplest ΛCDM bounce scenario presented in [7] is ruled out observationally.

## 3. Interacting Dark Matter and Dark Energy

#### 3.1. Background Space-Time

#### 3.2. Perturbations

^{−2}[3]. Importantly, this positive running provides a distinguishable feature of the matter bounce scenario, since typical inflationary and ekpyrotic cosmologies predict ${\alpha}_{s}$ to be negative [16]. This is slightly favored by the latest data analysis which suggests a small positive running of the scalar spectral index [49].

## 4. Observational Signatures

#### 4.1. Positive Running Index ${\alpha}_{s}$

#### 4.2. Tilt of the Tensor Spectrum

#### 4.3. Primordial Non-Gaussianity

#### 4.4. Other Cosmological Constraints

## 5. Bounce Mechanisms

#### 5.1. Loop Quantum Cosmology

#### 5.2. String Cosmology

#### 5.3. f(R) Gravity

#### 5.4. Bounce within an Effective Field Theory

#### 5.5. Fermi Bounce

## 6. Discussion and Conclusion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**The evolution of the effective equation of state w

_{eff}in ΛCDM and interacting dark energy models. Note that time goes from left to right in this plot for a contracting universe. Here we set Γ = 0.0026 and w

_{d}= −1 for demonstration.

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**MDPI and ACS Style**

Cai, Y.-F.; Marcianò, A.; Wang, D.-G.; Wilson-Ewing, E.
Bouncing Cosmologies with Dark Matter and Dark Energy. *Universe* **2017**, *3*, 1.
https://doi.org/10.3390/universe3010001

**AMA Style**

Cai Y-F, Marcianò A, Wang D-G, Wilson-Ewing E.
Bouncing Cosmologies with Dark Matter and Dark Energy. *Universe*. 2017; 3(1):1.
https://doi.org/10.3390/universe3010001

**Chicago/Turabian Style**

Cai, Yi-Fu, Antonino Marcianò, Dong-Gang Wang, and Edward Wilson-Ewing.
2017. "Bouncing Cosmologies with Dark Matter and Dark Energy" *Universe* 3, no. 1: 1.
https://doi.org/10.3390/universe3010001