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We consider a cosmology with decaying metastable dark energy and assume that a decay process of this metastable dark energy is a quantum decay process. Such an assumption implies among others that the evolution of the Universe is irreversible and violates the time reversal symmetry. We show that if we replace the cosmological time

In the explanation of the Universe, we encounter the old problem of the cosmological constant, which is related to understanding why the measured value of the vacuum energy is so small in comparison with the value calculated using quantum field theory methods [

Both mentioned cosmological constant problems can be considered in the framework of the extension of the standard cosmological

Results of many recent observations lead to the conclusion that our Universe is in an accelerated expansion phase [

This is the place where one has to emphasize that the use of the assumption that dark energy depends on time and is decaying during time evolution leads to the conclusion that such a process is irreversible and violates a time reversal symmetry. (Consequences of this effect will be analysed in next sections of this paper) Note that the picture of the evolving Universe, which results from the solutions of the Einstein equations completed with quantum corrections appearing as the effect of treating the false vacuum decay as a quantum decay process, is consistent with the observational data. The evolution starts from the early time epoch with the running

The paper is organised as follows: In Section

In the quantum decay theory of unstable systems, properties of the survival amplitudes

This last property suggests that, in the case of the unstable states prepared at some instant

Note that canonical (that is a classical radioactive) decay law

Now let us focus the attention on the survival amplitude

As it is seen from (

In the general case the density

From decomposition (

The late time form of the integral

As was mentioned we consider the hypothesis that a dark energy depends on time,

The above described approach is self-consistent if we identify

Let us consider cosmological implications of the parameter

Szydlowski et al. [

The model with the radioactive (exponential) decay of dark energy was investigated by Shafieloo et al. [

The set of equations (

System (

System (

The phase portrait of system (

Szydlowski et al. [

It is interesting that, during this phase, the Universe violates the reflection symmetry of the time:

If we considered radioactivity (in which the time reversal symmetry is broken) then a direction of decaying vacuum is in accordance with the thermodynamical arrow of time. First, note that it is in some sense very natural that the dynamics of the Universe is in fact irreversible when the full quantum evolution is taken into account. Therefore, radioactive decay of vacuum irreversibility has a thermodynamic interpretation as far as the evolution of the Universe is concerned: in horizon thermodynamics the area of the cosmological horizon is interpreted as (beginning proportional to) the entropy, i.e., the Hawking entropy. In a system where

In the general parameterization (

In cosmology, especially in quantum cosmology, the analysis of the concept of time seems to be the key for the construction of an adequate quantum gravity theory, which we would like to apply to the description of early Universe.

The good approximation of (

The diagram of the evolution of the Hubble function with respect to the cosmological time

The diagram of the evolution of the Hubble function with respect to the cosmological time

This condition guarantees for us a consistency of our model with astronomical observations of the accelerating phase of the Universe [

If all parameters

Figure

The diagram of the evolution of the scale factor with respect to the cosmological time

In the extension of Friedmann equation (

The diagram of the evolution of the parameter

In the special case of radioactive decay of vacuum (

In the case of the interaction between matter and decaying dark energy, the natural consequence of conservation of the total energy-momentum tensor

Let

From our investigation of cosmological implications of effects of the quantum decay of metastable dark energy, one can derive following results:

The cosmological models with the running cosmological parameter can be included in the framework of some extension of Friedmann equation. The new ingredient in the comparison with the standard cosmological model (

We have found that the appearance of the universal exponential contribution in energy density of the decaying vacuum can explain the irreversibility of the cosmic evolution. While the reversibility

We have also compared the time evolution of the Hubble function in the model under consideration (where

No data were used to support this study.

The authors declare that they have no conflicts of interest.

The authors are very grateful to Dr. Tommi Markkanen for suggestion of conclusion of their paper and indication of important references in the context of irreversibility of quantum decay process and thermodynamic arrow of time.

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