[Paper Review] Comment on "Torsion Cosmology and Accelerating Universe"

А. В. Минкевич, A. S. Garkun+1 more|ArXiv.org|Nov 10, 2008

Cosmology and Gravitation Theories3 citations

TL;DR

This paper critically examines the cosmological solutions proposed in a prior study on torsion cosmology within the Poincaré gauge theory of gravity (PGTG), showing that the original model's solutions are inconsistent with physical expectations due to unphysical behavior of the scalar curvature and reliance on a degenerate case. The authors demonstrate that the model fails to produce stable, accelerating cosmological evolution with realistic asymptotics, unlike alternative PGTG formulations that yield quasi-Friedmannian dynamics and naturally incorporate dark energy effects via torsion-induced effective cosmological constants.

ABSTRACT

Cosmological solutions for homogeneous isotropic models in the framework of the Poincaré gauge theory of gravity based on gravitational Lagrangian adopted in the paper by Kun-Feng Shie, James M. Nester and Hwei-Jang Yo (Phys. Rev. D extbf{78}, 023522 (2008)) are discussed. Cosmological solutions for accelerating Universe obtained in referred paper are compared with corresponding solutions of standard $ΛCDM$-model and also with cosmological solution obtained by authors of this Comment.

Motivation & Objective

• To evaluate the physical consistency of cosmological solutions proposed in Shie et al. (2008) within the Poincaré gauge theory of gravity (PGTG).
• To compare the cosmological behavior of the model in question with the standard ΛCDM model and with alternative PGTG solutions that yield quasi-Friedmannian asymptotics.
• To identify the mathematical and physical flaws in the original model's treatment of torsion and scalar curvature, particularly in the context of dark energy and accelerating expansion.
• To clarify the role of the parameter $ a = 2a_1 + a_2 + 3a_3 $ in determining the physical viability of cosmological solutions in PGTG.
• To advocate for the use of general gravitational Lagrangians with $ a = 0 $ to ensure physical, regular cosmological evolution with proper asymptotic behavior.

Proposed method

• Derives the full system of gravitational equations for homogeneous isotropic models (HIM) in PGTG using the general Lagrangian (1), which includes terms quadratic in curvature and torsion tensors.
• Applies the Bianchi identities in the Riemann-Cartan spacetime to reduce the system of equations and derive constraints on curvature functions $ A_1, A_2, A_3, A_4 $.
• Analyzes the case of the specific Lagrangian used in Shie et al. (2008), identifying the conditions $ q_2 = 0 $ and $ 2f = q_1 $, which lead to two distinct solution branches.
• Investigates the solution branch with $ S_2 \neq 0 $, deriving explicit expressions for $ S_2^2 $, $ H^2 $, and $ \dot{H} $ in terms of energy density $ \rho $, pressure $ p $, and Lagrangian parameters.
• Demonstrates that the scalar curvature $ F $ is not constant in physical solutions, contradicting assumptions in the original paper, and shows that constant $ F $ leads to non-physical degenerate solutions.
• Compares the resulting dynamics with the $ a = 0 $ case from prior work, which yields regular, quasi-Friedmannian cosmological evolution with stable accelerating expansion.

Experimental results

Research questions

• RQ1 Does the cosmological model proposed in Shie et al. (2008) within PGTG produce physically consistent solutions for an accelerating universe?
• RQ2 What are the implications of the parameter $ a = 2a_1 + a_2 + 3a_3 $ for the physical viability of cosmological solutions in PGTG?
• RQ3 How do the cosmological solutions derived from the Lagrangian in Shie et al. compare with those of the standard ΛCDM model and with alternative PGTG formulations?
• RQ4 Why does the original model fail to produce stable, physical asymptotic behavior, and what role does the non-constant scalar curvature play in this failure?
• RQ5 Can torsion in PGTG naturally generate an effective cosmological constant that explains dark energy without introducing an explicit $ \Lambda $ term?

Key findings

• The cosmological solutions derived in Shie et al. (2008) are physically inconsistent because they require a non-constant scalar curvature $ F $, contradicting the assumption of constant $ F $ in the original model.
• When $ a \neq 0 $, the cosmological equations contain higher-order time derivatives of the scale factor, leading to oscillatory and non-Friedmannian behavior that is unphysical for late-time cosmology.
• The case $ a > 0 $ leads to a non-physical solution with a negative effective gravitational constant, which is resolved only by artificially flipping the sign of $ a $, resulting in a degenerate case.
• The solution with $ S_2 \neq 0 $ yields $ S_2^2 = \frac{f_0(f_0 - b)}{4fb} + \frac{\rho - 3p}{12b} $, which depends on energy density and pressure, but does not support stable accelerating expansion.
• In contrast, the $ a = 0 $ case yields regular cosmological solutions with quasi-Friedmannian asymptotics, where the effective cosmological constant arises from the torsion function $ S_2 $, naturally explaining dark energy.
• The authors conclude that only PGTG models with $ a = 0 $ produce physically viable cosmologies, while the model in question leads to unphysical dynamics due to its specific parameter constraints.