Dark Energy

The following sections are included:

• Foreword
• Preface
• Contents

The following sections are included:

• The Curved Spacetime
• The Curved Spacetime: An Example
• The Einstein Equation

The following sections are included:

• The Stress Tensor
• Perfect Fluid
• Observers and Energy Conditions
• The Vacuum
• Particles
• Homogeneous Field Configurations

The following sections are included:

• The Cosmological Principle
• Newtonian Cosmology
• FRW Cosmology

The following sections are included:

• The Cosmological Constant Reloaded
• The Theoretical Challenge
• References

As mentioned, before the accelerating expansion of the universe was observed, theorists have already been worrying about the cosmological constant. In this chapter, we will briefly review Weinberg's classification of ideas about the cosmological constant problem [1], before the discovery of dark energy.

We have briefly reviewed Weinberg's classification, now we turn to more recent ideas and models about dark energy. We start from symmetry.

If the anthropic principle is the reason for Λ ∼ 0, one of the necessary conditions is that, Λ is either a continuous variable, or if it is discrete, the interval ΔΛ must be sufficiently small.

Bousso and Polchinski are probably the first to point out that the second possibility is realized in string theory [1] (see also [2] for a review). This is the beginning of studies on the string landscape.

As reviewed in Chapter 5, there is a no-go theorem about tuning mechanism in four spacetime dimensions. As the story of many other no-go theorems, the utility of a no-go theorem is more likely a sign to point out ways out instead of to stop. Also, as some other no-go theorems (such as the story between composed graviton and AdS/CFT), the way out is to go to extra dimensions. In this chapter we discuss some higher dimensional constructions of tuning mechanisms.

Gravity, especially in its quantum aspects, encounters a number of puzzles. Facing those puzzles, it is a long standing question whether to understand or to modify gravity. Modified gravity is now a huge category. Here we shall choose to introduce several classes of models most related to dark energy, namely , MOND, DGP type models and briefly mention other directions.

As reviewed in Chapter 5, the approach of wave function of the universe either results in a probability , or its exponential. The predicted cosmological constant is not only too small, but also conflicts with the thermal history of the universe. Several ways to solve the problem have been proposed.

For example, Firouzjahi, Sarangi and Tye [1, 2] brought the decoherence effect to the quantum creation of universe, and found the preferred classical universe is born at string scale, which is good for inflationary cosmology. As another approach, Hartle, Hawking and Hertog [3, 4] argued that from the Bayesian point of view, the quantum creation probability should multiply the spatial volume factor to get the observed probability. Again, inflation after the born of the universe is preferred.

These approaches on the one hand bring the Hartle–Hawking wave function back to be consistent with observations, but on the other hand make the whole subject more relevant to inflation, and less relevant to dark energy.

Nevertheless, dark energy is very probably an effect from quantum gravity. Indeed a lot of attempts on dark energy are related to quantum theories. Here in this chapter by quantum cosmology we shall restrict our attention to approaches closely related to the wave function of the universe. Other quantum approaches are reviewed in other related chapters.

The following sections are included:

• The Holographic Principle
• Holographic Dark Energy
• Complementary Motivations
• Agegraphic Dark Energy
• Ricci Dark Energy
• References

A universe without nonlinearity is simple and simply dull. Physicists like to start their calculation from the linear case because it is mathematically easy and often solvable. However, nobody likes to live in such a universe where two waves always propagate through each other without any impact…

In this chapter we introduce phenomenological models for dark energy, focusing on modification for known matter components.

Before getting to the part of experiments and fitting, it is helpful to pause and revisit the theoretical challenge. We are having too many dark energy models. On the other hand, are we close to a solution to the dark energy problem?…

As is known, theories and observations are connected by statistics. In this chapter, we will introduce some basic knowledge of statistics.

The most common approach to probe dark energy is through its effect on the expansion history of the universe. This effect can be detected via the luminosity distance d_L(z) and the angular diameter distance D_A(z). In addition, the growth of large-scale structure can also provide useful constraints on dark energy. In this chapter, we will review some mainstream cosmological observations, introduce the basic principles of these observations, and describe how they are introduced into the χ² statistics.

Here we provide a brief overview of present and future projects to probe dark energy. Although some high energy physics experiments (such as LHC [1]) might shed light on dark energy through discoveries about supersymmetry or dark matter, here we only introduce the projects involving cosmological observations. According to the DETF report [2], the dark energy projects can be classified into four stages: completed projects are Stage I; on-going projects, either taking data or soon to be taking data, are Stage II; intermediate-scale, near-future projects belong to Stage III; larger-scale, longer-term future projects belong to Stage IV…

In this chapter we will briefly review some research works concerning the cosmological constraints on the specific theoretical models. These models can be classified into three classes: (i) Models that modify the energymomentum tensor on the R.H.S. of the Einstein equation, i.e. dark energy models. We will briefly introduce some numerical results of scalar field models, Chaplygin gas models, and holographic models. (ii) Models that modify the L.H.S. of the Einstein equation, i.e. modified gravity models. We will briefly introduce some numerical results of the DGP braneworld model, the gravity, the Gauss–Bonnet gravity, the Brans–Dicke theory and the gravity. (iii) Models that attempt to explain the apparent cosmic acceleration by assuring the inhomogeneities in the distribution of matter. We will briefly introduce some numerical works on the inhomogeneous Lemaître–Tolman–Bondi model and back-reaction model. Lastly, we will summarize and compare these theoretical models.

In the last chapter, we have introduced some representative numerical works on the specific dark energy models. Due to the lack of a compelling fundamental theory to explain the dark energy, another route, the model-independent dark energy reconstructions, have drawn more and more attentions [1–9]…

The following section is included:

• Index