Review, Volume: 12( 6) DOI: 10.37532/2320-6756.2023.12(6).278
Dimensional complement of the mathematical solution to the cosmological constant problem.
Received date: 02-June-2023, Manuscript No. tsse-23-97278; Editor assigned: 05-June-2023, PreQC No. tsse-23-97278 (PQ); Reviewed: 14- June-2023, QC No tsse-23-97278 (Q); Revised: 17-June-2023, Manuscript No. tsse-23-97278 (R); Published: 24-June-2023, DOI. 10.37532/2320-6756.2023.12(6).278
Citation:Wojnow S. Dimensional Complement of the Mathematical Solution to the Cosmological Constant Problem. J Space Explor.2023; 12(6).278.
We have proposed a mathematical solution to the cosmological constant problem with an attempted physical explanation. Here we propose a complement to this solution to validate the hypothetical energy density value of the cosmological constant in Quantum Field Theory (QFT), showing that the dimensional method used can be applied to find the critical energy density of the ΛCDM mode
This document presents a complement to the proposed mathematical solution to the cosmological constant problem, with the aim of validating the hypothetical energy density value of the cosmological constant in quantum field theory. The proposed method utilizes dimensional analysis to find the critical energy density of the ΛCDM model. The document provides a reminder of the mathematical solution and defines relevant parameters, including Planck mass, Planck length, and Hubble constant. It then presents the proposed formula for the quantum critical energy density of the universe and demonstrates how it can be used to calculate the critical energy density of the ΛCDM model.
Reminder of the result of the mathematical solution to the problem of the cosmological constant
Here we define parameters with mp as Planck mass, lp as Planck length, ℏ reduced Planck constant, c speed of light in vacuum, G as Newton's constant, Λ as cosmological constant, A as zero-point energy density in quantum field theory , B as vacuum energy density assumed for the cosmological constant in the QFT, H0 as Hubble contant, and ρc as critical energy density of the ΛCDM model.
The energy density of the quantum vacuum in Planck units, i.e. that of the zero point of the QFT is :
To demonstrate that the cosmological constant C in J/m³ is  :
Dimensional complement of the mathematical solution to the cosmological constant problem
Let us consider H0 the Hubble parameter (or Hubble constant) of dimension (T-1). We want a dimension in (L-2) to replace in m Eq(3),
As c2 is used to convert to s by writing ,
we will write
To write a formula B' as "quantum critical energy density of the universe for H0" assumed in the QFT with Eq(7) of dimension (L-2) :
This can be proved using Eq (2) and Eq (9) :
The same dimensional methodology, to assume on the one hand the hypothetical quantum energy density of the cosmological constant QFT, on the other hand the hypothetical quantum critical energy density of the QFT, allows to find their equations in the ΛCDM model via their geometric mean with the zero-point energy density. In addition to attempting to make physical sense of the square roots of the energy density as a Hildebrand solubility parameter, the reproducibility of the method reciprocally strengthens both results obtained. This result coud open a new approch of the cosmology.
- Lombriser LJPLB., "On the cosmological constant problem," 2019;797:134804. [Google Scholar] [Crossref]
- Wojnow S. A simple mathematical solution to the cosmological constant problem.: Cosmology. Hyperscience Int. J. 2022;2(3):57-9.[Google Scholar] [Crossref]