# Dark Energy and Inflation from Gravitational Waves

## Abstract

**:**

## 1. Cosmological Acceleration from Classical Gravitational Waves

^{123}gravitons to create the observed Hubble constant. This number has nothing to do with vacuum energy, which is a possible solution to the “old cosmology constant problem”.

#### 1.1. Introduction

#### 1.2. De Sitter Acceleration from Classical Gravitational Waves

#### 1.3. De Sitter State of Empty Space as the Exact Solution to BBGKY Chain

#### 1.4. Classical Gravitational Waves vs. Quantum Gravitons

#### 1.5. Conclusion

## 2. Gravitons in the Universe4

#### 2.1. Introduction

#### 2.2. The Scheme of the Yang-Mills Quantum Theory

#### 2.3. Scheme of Quantum Theory of Gravitation

#### The Einstein Equations in Normal Coordinates Can Be Obtained in the Following Way

The existing quantum theory of gravity is reduced by means of identical transformations to the operator equations in the Heisenberg representation in the Hamiltonian gauge with the canonical rules for quantizing gravitons and ghosts.

#### 2.4. Extrapolation

#### 2.5. The Problem of the Physical Nature of Ghosts

#### 2.6. One-Loop Approximation

#### 2.7. Conclusion

## 3. Cosmological Acceleration from Virtual Gravitons

#### 3.1. Introduction

#### 3.2. De Sitter State from Gravitons

## 4. Consistency with Observational Data

#### 4.1. Dark Energy

#### 4.1.1. Coincidence Problem

#### 4.1.2. The Threshold Problem

#### 4.1.3. ${\mathsf{\Lambda}}_{vacuum}/{\mathsf{\Lambda}}_{observable}\approx {10}^{123}$ Controversy

#### 4.1.4. The Need to Compare Theory with Other Observational Data

#### 4.2. Inflation

#### 4.2.1. CMB Anisotropy from Fluctuations of Number of Gravitons

#### 4.2.2. Spectrum of Metric Fluctuations

## 5. Origin of Acceleration

#### 5.1. Wick Rotation

#### 5.2. Where Does the Energy Come from?

#### 5.3. Gravitational Waves vs. Scalar Field

#### 5.4. Virtual Gravitons vs. Classical Gravitational Waves

#### 5.5. Conclusion

## 6. Cosmological Scenario

## Acknowledgments

## Conflicts of Interest

## Appendix A. Stochastic Nonlinear Gravitational Waves in an Isotropic Universe15

#### Appendix A.1. Definitions of the Background and Fluctuations

- (1)
- In Einstein’s Equation (A10), the sorting of free indices is carried out according to the rule $i\le k$
- (2)
- The objects of the theory are mixed tensors ${X}_{i}{}^{k}$ and ${\psi}_{i}{}^{k}$, in which the sorting of free indices is carried out according to the same rule $i\le k$. These rules provide the same number of independent equations and independent functions as in the standard formulation of Einstein’s equations.
- (3)
- The derivative of the matrix function with respect to the vector parameter is determined before the expansion of the matrix function with respect to the tensor argument, i.e.,$${X}_{i;l}{}^{k}={X}_{i}{}^{m}{\psi}_{m;l}{}^{k}$$