Abstract
Recent observations of the dark energy density have demonstrated the fine-tuning problem and the challenges faced by theoretical modeling. In this study, we apply the self-similar symmetry (SSS) model, describing the hierarchical structure of the universe based on the Dirac large numbers hypothesis, to Einstein’s cosmological term. We introduce a new similarity dimension, [Formula: see text], in the SSS model. Using the [Formula: see text] SSS model, the cosmological constant [Formula: see text] is simply expressed as a function of the cosmic microwave background (CMB) temperature. The result shows that both the gravitational constant [Formula: see text] and [Formula: see text] are coupled with the CMB temperature, which simplifies the solution of Einstein’s field equations for the variable [Formula: see text]–[Formula: see text] model.
Highlights
The cosmological constant problem, i.e. the dark energy problem, poses a formidable challenge in physics
The result in our earlier study [40], which explains the hierarchical structure of the universe based on the Dirac large numbers hypothesis (LNH) [41, 42], indicates that both G and me are coupled with the cosmic microwave background (CMB) temperature
Our result indicates that Λ and G are not independent functions, but are coupled with the CMB temperature
Summary
The cosmological constant problem, i.e. the dark energy problem, poses a formidable challenge in physics. Sonoda of nature), boundedness (Λ has a lower bound, 0 < Λ), simplicity (Λ is given by the simplest possible formula, consistent with the other axioms), and invariance (Λ values obtained using potentially different values of the fundamental parameters preserve the scale-invariance of the large-scale physics of the universe) Using these four axioms, Beck showed that Λ is given as follows: G2 Λ= 4 me. The result in our earlier study [40], which explains the hierarchical structure of the universe based on the Dirac large numbers hypothesis (LNH) [41, 42], indicates that both G and me are coupled with the cosmic microwave background (CMB) temperature. This means that we can simplify the solution of Einstein’s field equations for the variable Λ-G model, because we can unify the two independent variables Λ and G into one simple function of the CMB temperature
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