[Paper Review] Dark energy as a cosmological consequence of existence of the Dirac scalar field

O. V. Babourova, V. Frolov|arXiv (Cornell University)|Oct 7, 2014

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper proposes that dark energy arises dynamically from the evolution of a Dirac scalar field in a conformal gravity framework with Cartan–Weyl spacetime. The field decreases exponentially in the early universe, driving the effective cosmological constant toward the observed small value today, offering a solution to the cosmological constant problem via field dynamics rather than fine-tuning.

ABSTRACT

The solution of the field equations of the conformal theory of gravitation with Dirac scalar field in Cartan-Weyl spacetime at the very early Universe is obtained. In this theory dark energy (describing by an effective cosmological constant) is a function of the Dirac scalar field $β$. This solution describes the exponential decreasing of $β$ at the inflation stage and has a limit to a constant value of the dark energy at large time. This can give a way to solving the fundamental cosmological constant problem as a consequence of the fields dynamics in the early Universe.

Motivation & Objective

• To address the cosmological constant problem—why the observed vacuum energy is 120 orders of magnitude smaller than quantum field theory predictions—by exploring field dynamics in the early universe.
• To investigate whether the Dirac scalar field in a conformal theory of gravitation can dynamically generate the observed small effective cosmological constant.
• To derive solutions for the Dirac scalar field and effective dark energy in a spatially flat, homogeneous, isotropic early universe model.
• To show that the effective cosmological constant approaches the observed value asymptotically, avoiding fine-tuning.
• To propose that the Dirac scalar field may also contribute to dark matter via condensation near massive objects.

Proposed method

• Formulate a conformal gravity theory in Cartan–Weyl spacetime using an external form formalism with a Lagrangian density including the Dirac scalar field β and a Weyl nonmetricity term.
• Derive field equations via exterior calculus and variational principles, treating β, the tetrad θᵃ, connection Γᵃᵇ, and Lagrange multipliers Λᵃᵇ as independent variables.
• Assume a Friedmann-like metric ansatz with scale factor a(t) and define u(t) = ln a(t), v(t) = ln β(t) to reduce the system to a set of ODEs.
• Solve the resulting system of equations (13) and (14) under the condition B = 3A, leading to a solution with exponential decay of β(t).
• Use the solution β(t) = 1 / (1 − e⁻ˡ⁽ᵗ⁺ᵗ⁰⁾) to show that β(t) → 1 and Λ_eff = β²Λ → Λ as t → ∞.
• Demonstrate that the effective cosmological constant asymptotically approaches the observed value of the Einstein cosmological constant, resolving the hierarchy problem dynamically.

Experimental results

Research questions

• RQ1 Can the cosmological constant problem be resolved through dynamical evolution of the Dirac scalar field in the early universe?
• RQ2 Does the effective cosmological constant, arising as β²Λ, naturally evolve toward the small observed value over time?
• RQ3 What is the functional behavior of the Dirac scalar field β(t) in the early universe within a conformal gravity framework?
• RQ4 How does the solution for β(t) lead to a transition from a high-energy vacuum to the current accelerated expansion phase?
• RQ5 Could the Dirac scalar field also contribute to dark matter via condensation near massive objects?

Key findings

• The solution β(t) = 1 / (1 − e⁻ˡ⁽ᵗ⁺ᵗ⁰⁾) shows exponential decay of the Dirac scalar field, with β(t) → 1 as t → ∞.
• The effective cosmological constant Λ_eff = β²Λ asymptotically approaches the observed value Λ, avoiding the need for fine-tuning.
• For t ≫ t₀, the scale factor behaves as a(t) ≈ a₀₁ e^(λt/3), indicating exponential expansion consistent with inflation.
• The solution realizes a sharp exponential decrease in physical vacuum energy (dark energy) in the early universe, reducing it by many orders of magnitude.
• The model predicts that the effective cosmological constant stabilizes at the modern observed value, enabling the transition to the current epoch of accelerated expansion.
• The Dirac scalar field may condense near massive objects, suggesting a dual role in both dark energy and dark matter.