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We propose a method to relate the holographic minimal information density to de Broglie’s wavelength at a given universe temperature

Almost two decades ago, the universe acceleration has been observed [

Among all, an enticing prospect is to postulate the validity of the holographic principle [

A consolidate conjecture states that general relativity may break down as it is applied to small distances in the regime of very high energies. The level of small distances and/or high energies may cause the breakdown of geometrical continuum as well. Examples are offered by lattice or grids in which the interactions are modified at either classical or quantum levels [

As stated above, the holographic principle certifies the existence of a further energy density, hereafter

For example, in the case of Chevallier-Polarski-Linder parametrization [

Together with the requirements of (

Clearly, we need the correct universe’s volume in order to characterize

This implies that (

Since, as stated, these choices are valid for classical and quantum regimes, respectively, we have

The two thermal lengths lead to approaches at different stages of the universe evolution. The first analysis can be performed by using the adiabatic volume at the small redshift regime. This epoch corresponds to our time, in which, making use of the thermal length for massive particles, one finds

The

In both cases, (

Inside the observational domains, predicted by model independent measurements of the deceleration parameter, that is,

(a) Behaviors of the deceleration parameters for our model (red line) and for the concordance paradigm (dashed line), with indicative values

It indicates discrepancies smaller than

Behaviors of our model and

Analogous considerations may be carried out by investigating the consequences of our recipe at higher redshift domains, so that, at early times, following (

In this case, using again the temperature parametrization but at the regime in which

With those considerations in mind, at a first approximation one can write the first-order perturbation equation approximating the sound speed with

When the redshift increases, the matter density influences the whole dynamics and so one can suppose checking how much the growth factor deviates from the concordance model. To do so, we can define the deviation parameter

In Figures

In (a) we obtain our model with an equidistant grid spacing, split by five steps with the same distance. (a) shows slight departures from our framework and the concordance model. This is even confirmed in (b). There, we report the behavior of the growth factor

In this paper, we assumed the validity of the holographic principle to characterize the dark energy evolution. To do so, we supposed that the cut-off scale, entering the minimal information density, is given by the well-consolidate de Broglie’s wavelength associated with massive and massless particles, that is, matter and photons, respectively. The corresponding cut-off scales become the thermal lengths which can be used at late and early times, respectively, for classical and quantum regimes. We built up two cosmological models parameterizing the temperature with respect to the redshift

The author declares that there are no conflicts of interest regarding the publication of this paper.