[Paper Review] Dark Energy: A Missing Physical Ingredient

M. I. Wanas|ArXiv.org|Sep 29, 2008

Cosmology and Gravitation Theories5 references3 citations

TL;DR

This paper proposes that dark energy arises not from an unknown form of matter or a cosmological constant, but from torsion-induced repulsive forces in a geometric framework with both curvature and torsion. By introducing a parameterized absolute parallelism (PAP) geometry, the authors show that torsion energy—generated by spin-torsion interactions—produces negative pressure and repulsive gravity, offering a geometric explanation for cosmic acceleration without invoking exotic matter or modifying general relativity's field equations.

ABSTRACT

Recent observation of supernovae type Ia show clearly that there is a large scale repulsive force in the Universe. Neither of the four known fundamental interactions can account for this repulsive force. Gravity is known to be the interaction responsible for the large scale structure and evolution of the Universe. The problem with gravity is that it gives rise to a force which is attractive only. Gravity theories, including General Relativity, deals with gravity as an attractive force. Although this is consistent with our experience in the solar system and other similar astrophysical systems, gravity theories fail to account for SN type Ia observation. So, we are in a real problem concerning the interpretation of these observation. This problem is only ten years old. In order to go out of this problematic situation, scientists have suggested the existence of a type of energy in the Universe that is responsible for the above mentioned repulsive force. They have given this type of energy the exotic term {\it "Dark Energy"}. Although this type of energy forms more than two thirds of the energetic contents of our Universe, its reasonable nature is missing in all gravity theories. The aim of the present work is to review the present status of the problem of dark energy. Also, to suggest a new geometric solution for this problem.

Motivation & Objective

• To resolve the discrepancy between observed cosmic acceleration (from Type Ia supernovae) and the predictions of general relativity, which only allows attractive gravity.
• To address the missing physical ingredient in gravity theories that could explain large-scale repulsive forces, such as those inferred from supernovae, flat rotation curves, and the Pioneer anomaly.
• To propose that torsion energy—arising from non-vanishing torsion in a parameterized absolute parallelism (PAP) space—acts as a geometric substitute for dark energy.
• To unify the interpretation of dark energy, electromagnetic fields, and gravity under a single geometric framework based on space-time with both curvature and torsion.
• To demonstrate that the repulsive force from torsion energy naturally leads to negative pressure, consistent with observations of accelerated expansion.

Proposed method

• Adopts a parameterized absolute parallelism (PAP) geometry, where the connection is non-symmetric and includes both curvature and torsion components.
• Introduces a geometric structure with a parameter $ b $, where $ b = 0 $ recovers Riemannian geometry (standard GR), and $ b = 1 $ recovers the conventional absolute parallelism (AP) geometry with vanishing curvature but non-zero torsion.
• Derives the PAP-path equation (14), which includes a term representing interaction between particle spin and space-time torsion, leading to a generalized potential $ \Phi = \Phi_N - b\Phi_N $.
• Identifies the torsion energy as a physical quantity arising from the anti-curvature tensor $ Q(\gamma) $, which is the additive inverse of the Riemann-Christoffel curvature tensor $ R(\{\}) $, and satisfies a conservation law via the Bianchi identity.
• Uses the contracted Bianchi identity to interpret $ R^{\mu\nu} - \frac{1}{2}g^{\mu\nu}R $ and $ Q^{\mu\nu} - \frac{1}{2}g^{\mu\nu}Q $ as geometric representatives of curvature and torsion energy, respectively.
• Shows that the linearized form of the PAP-path equation yields a potential $ \Phi_T = -b\Phi_N $, which generates a repulsive force opposite to Newtonian gravity, with $ b = 1 $ yielding maximal repulsion.

Experimental results

Research questions

• RQ1 What geometric ingredient is missing in general relativity that could explain the observed cosmic acceleration without introducing a cosmological constant or exotic matter?
• RQ2 Can torsion in a space-time with both curvature and torsion generate a repulsive force consistent with the negative pressure required by dark energy?
• RQ3 How does the interaction between particle spin and space-time torsion give rise to a physical energy source that behaves like dark energy?
• RQ4 Is the anti-curvature tensor $ Q(\gamma) $, which cancels the Riemann curvature in the AP limit, a viable geometric representation of a new form of energy with negative pressure?
• RQ5 Can the electromagnetic field be similarly interpreted as a geometric property of space-time, analogous to how torsion energy is derived from the PAP-geometry framework?

Key findings

• Torsion energy, arising from the non-vanishing contortion tensor in PAP-geometry, is shown to be a physical source of repulsive force, with a potential $ \Phi_T = -b\Phi_N $, which becomes fully repulsive when $ b = 1 $.
• The PAP-geometry framework allows the curvature and torsion tensors to coexist, with the anti-curvature tensor $ Q(\gamma) $ acting as the additive inverse of the Riemann curvature, ensuring $ B^{\alpha}_{\mu\nu\sigma} = R^{\alpha}_{\mu\nu\sigma} + Q^{\alpha}_{\mu\nu\sigma} \equiv 0 $ in the AP limit.
• The torsion energy tensor satisfies a conservation law via the Bianchi identity, analogous to energy-momentum conservation, and is interpreted as a geometric source of negative pressure.
• In the limit $ b = 1 $, the PAP-geometry reduces to the conventional AP-geometry, where the space is flat (vanishing Riemann curvature) but possesses non-zero torsion, and the torsion energy becomes dominant.
• The spin-torsion interaction term in the PAP-path equation (14) provides a geometric origin for the repulsive force, with the potential $ \Phi_T = -\Phi_N $, which directly explains the observed acceleration of the universe.
• The paper concludes that dark energy is not a separate form of matter but is geometrically equivalent to torsion energy, with the missing ingredient in gravity theories being the spin-torsion interaction.