[Paper Review] Adelic Universe and Cosmological Constant

Nugzar Makhaldiani|ArXiv.org|Dec 26, 2003

Quantum Mechanics and Applications7 references3 citations

TL;DR

This paper proposes that the cosmological constant (CC) problem—why vacuum energy is unnaturally small—can be resolved through adelic quantum field and string theory models, where the CC vanishes due to the global adelic structure of p-adic and real number spaces. The mechanism relies on the Euler product formula over primes and zeta function regularization, with additional insights into the fine-structure constant and prime numbers.

ABSTRACT

In the quantum adelic field (string) theory models, vacuum energy -- cosmological constant vanish. The other (alternative ?) mechanism is given by supersymmetric theories. Some observations on prime numbers, zeta -- function and fine structure constant are also considered.

Motivation & Objective

• To resolve the cosmological constant problem, where quantum field theory predicts a vacuum energy density vastly larger than observed.
• To explore whether the adelic structure of quantum field and string theories naturally cancels vacuum energy contributions.
• To investigate connections between prime numbers, the Riemann zeta function, and fundamental constants like the fine-structure constant.
• To propose an alternative to supersymmetry for CC cancellation, based on number-theoretic structures in quantum theory.
• To suggest that the absence of divergences in adelic QFT may stem from the global Euler product structure over primes.

Proposed method

• Utilizes the adelic framework, combining real and p-adic quantum field theories via the Euler product over all primes.
• Applies zeta function regularization to the vacuum energy density, using the functional equation of the Riemann zeta function.
• Employs the adelic trace formula and product formula to show that the total vacuum energy vanishes when summed over all places (real and p-adic).
• Uses the statistical mechanics of the partition function: in the adelic case, Z(β) = ∏_p Z_p, and Z(β) → 1 in the low-temperature limit, implying λ ∝ ln Z → 0.
• Analyzes the fine-structure constant α⁻¹ ≈ 137.036 as a sum of squares of Gaussian integers (11² + 4²), linking it to complex plane geometry and primes.
• Considers Dirac-Schwinger quantization and magnetic monopoles to relate α to prime numbers via g² = α⁻¹ ≈ 137.

Experimental results

Research questions

• RQ1 Can the cosmological constant problem be resolved through the adelic structure of quantum field theory?
• RQ2 Does the Euler product over p-adic and real spaces lead to cancellation of vacuum energy, resulting in a vanishing cosmological constant?
• RQ3 Is there a number-theoretic explanation for the fine-structure constant α⁻¹ ≈ 137.036 in terms of Gaussian integers and primes?
• RQ4 How does the adelic mechanism compare to supersymmetry in canceling vacuum energy?
• RQ5 Can the absence of ultraviolet divergences in quantum field theory be explained via adelic zeta regularization?

Key findings

• In adelic quantum field and string theory models, the cosmological constant vanishes due to the global adelic structure and zeta function regularization.
• The vacuum energy density is shown to cancel exactly when the Euler product over all places (real and p-adic) is applied, leading to <ρ> = 0.
• The fine-structure constant α⁻¹ ≈ 137.036 is numerically close to 11² + 4² = 137, suggesting a geometric interpretation in the complex plane.
• The paper notes that 137 + 887 = 1024 = 2¹⁰, and 887 is the neutron lifetime in seconds, hinting at a possible deep number-theoretic connection.
• The adelic partition function Z(β) → 1 in the low-temperature limit, implying λ ∝ ln Z → 0, providing a statistical mechanism for CC cancellation.
• The model suggests that quantum field theories without divergences may emerge from adelic structures, with the zeta function playing a central role in regularization.