# The cosmological nature of the dark Universe

## Abstract

This paper deals with the cancellation mechanism, which identifies the energy density of space-time expansion in an empty universe with the zero-point energy density and avoids the scale discrepancy with the observed energy density (cosmological constant problem). Using an intrinsic degree of freedom which describes the coupling of a variable cosmological term \(\varLambda \) with non-relativistic matter and radiation, the following consequences are demonstrated by coupling only a small contribution of \(\varLambda \) with non-relativistic matter. First, the standard model of cosmology with a positive cosmological constant can be generalised such that the missing mass problem of dark matter is solved by an overall negative variable cosmological term. Second, the model under consideration is compatible with constraints from the standard model of particle physics. Third, an equation of state parameter of dark matter is derived which agrees with observations of rotational curves of galaxies. Moreover, the creation and annihilation process of dark matter is presented.

## 1 Introduction

In the recent paper [1], the author has demonstrated that the variable cosmological term \(\varLambda (a)=\varLambda _0+\varLambda _1 a^{-r},\) \(r=4-\epsilon ,\) \(\epsilon =9.151 \times 10^{-122}\) solves the fine-tuning of the cosmological constant problem (see [2, 3, 4, 5, 6]) and generates the missing mass of dark matter which constitutes \(26\%\) of the matter-energy density. The remaining matter-energy constraints of the universe such as \(69\%\) dark energy and \(5\%\) ordinary matter as well as the initial singularity are also satisfied by the theory.

The remainder of the paper is organised as follows. In section 2 we review the Friedmann equations where the cosmological term \(\varLambda \) is a function of the scale factor *a*. Section 3 is devoted to the dark sector and states the basic ideas behind the derivation of the cancellation mechanism of the cosmological constant problem from [1]. Then, it is demonstrated that the attractive force of dark matter is a consequence of a positive energy density of the cosmological term. Finally, we show that our solution of the cosmological constant problem explains the already mentioned cosmological observations and how dark matter is created/destroyed by the interaction of non-relativistic matter/radiation.

## 2 A time-dependent cosmological term

*a*(

*t*)

*k*denotes the curvature parameter of unit \(\text {length}^{-2}.\) Moreover, the variable cosmological term is defined by

*r*, the presence of the variable cosmological term can completely change the dynamical behavior of \(\rho _m\) and \(\rho _r.\)

## 3 The dark sector

*r*such that an initial singularity is guaranteed. Using the settings

From (8) and (9) we can conclude that dark matter doesn’t interact with ordinary matter and radiation (\(\rho _{m,0}\) and \(\rho _{r,0}\) are independent of \(\varLambda _1\)). The interaction takes place between the three components of dark matter (self-interacting dark matter) which can be classified by their equation of state parameter \(w=-1, w=0\) and \(w=1/3.\)

## 4 Cosmological constraints

Now, some consequences of the value \(0<\alpha <10^{-5}\) are investigated. The low production \((\rho _{m\varLambda }>0)\) with respect to \(\alpha \) of non-relativistic (dark) matter particles by the coupling process between non-relativistic matter and the cosmological term is in agreement to the results of [7]: the limitation of baryon/antibaryon pair annihilations, the isotropy of the microwave background and Eq. (5) lead to a scale factor which is nearly indistinguishable to the scale factor in the matter dominated epoch. Hence, the term \(\frac{d}{da} (\rho _m a^3)\) is only a small perturbation of Eq. (5), which is equivalent to the case \(0 < \alpha \ll 1.\)

In contrast to the standard \(\varLambda \text {CDM}\) model with 6 parameters, the equation of state parameter \(w_\text {dm}\) extends this model to the \(\varLambda \text {wDM}\) model from [11]. The above constraint for \(w_\text {dm}\) increases the Hubble constant by a maximum of 0.007% and decreases \(\varOmega _\text {dm}\) by a maximum of 0.02% (cf. [11, Figure 7]) which is within the specified accuracies of the parameters. Moreover, the derived equation of state parameter \(w_\text {dm}\) meets the constraint \(-0.000896< w_\text {dm}<0.00238\) from cosmic microwave background observations [11].

The structure formation of the universe for the \(\varLambda \text {wDM}\) model was investigated in [12]. The main result is that the clustering scale of the large-scale structure is independent of the equation of state parameter.

## 5 Concluding remarks

In this paper, the variable cosmological term \(\varLambda (a)=\varLambda _0 + \varLambda _1 a^{-r}, r >0\) has been applied and it has been confirmed that the total energy density of an empty Friedmann universe is related to the cosmological term such that the fine-tuning problem was avoided by setting \(\varLambda _1=r-4/2 \pi r l_p^2, r \ne 4.\) As a consequence, the dynamical part of the cosmological term generates the attractive force of dark matter.

Moreover, it has been demonstrated that the accepted age of our universe requires that only a small fraction of the cosmological term couples with non-relativistic matter. More precisely, the cosmological term creates/destroys dark matter with the interaction of non-relativistic matter/radiation. Similar to black holes, the decrease of the density by radiation is caused by the vacuum energy density. This could be a further argument that dark matter consists of black holes and that \(\rho _{\text {dm}}\) represents the spatially averaged densities of black holes. On the other hand, the results of this paper cannot exclude that dark matter is made of particles. The range \(3<r<3.0000075\) is compatible with constraints from baryon/antibaryon pair annihilation [7].

Furthermore, the parameter range of *r* produces a non-zero equation of state parameter of dark matter \(w_{\text {dm}} \le 2.5 \times 10^{-6}\) which agrees with observational data of rotational curves of galaxies [8], generates the missing mass of dark matter, describes the present-day composition of the universe and realises a negative cosmological term. Living in an universe with a negative cosmological term will completely change our understanding of cosmology. This could have important consequences for holographic correspondence-theories which are mainly formulated on space-times with a negative cosmological constant (cf. [13]).

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