[Paper Review] The Dark side of the torsion: Dark Energy from kinetic torsion

David Benisty, Eduardo Guendelman+4 more|arXiv (Cornell University)|Sep 3, 2021

Cosmology and Gravitation Theories2 references4 citations

TL;DR

This paper proposes a cosmological model where dark energy arises not from a potential, but from the kinetic term of a dynamical, totally anti-symmetric torsion field in an extended Einstein-Cartan framework. The model yields a bouncing universe solution due to a stiff fluid contribution from the quadratic torsion term, with a bound on the bounce derived from the dynamics of the torsion field.

ABSTRACT

An extension to the Einstein-Cartan (EC) action is discussed in terms of cosmological solutions. The torsion incorporated in the EC Lagrangian is assumed to be totally anti-symmetric, and written by of a vector $S^\mu$. Then this torsion model, compliant with the Cosmological Principle, is made dynamical by introducing its quadratic, totally anti-symmetric derivative. The EC Lagrangian then splits up into the Einstein-Hilbert portion and a (mass) term $\sim s_0^2$. While for the quintessence model, dark energy arises from the potential, here the kinetic term, $\frac{1}{\mu^2} \dot{s}_0^2$, plays the role of dark energy. The quadratic torsion term, on the other hand, gives rise to a stiff fluid that leads to a bouncing solution. A bound on the bouncing solution is calculated.

Motivation & Objective

• To explore the cosmological implications of extending the Einstein-Cartan action with a dynamical, totally anti-symmetric torsion field.
• To investigate how a kinetic term in the torsion field can generate dark energy, replacing the potential-driven mechanism of quintessence.
• To analyze the role of the quadratic torsion term in producing a stiff fluid that enables a bouncing universe solution.
• To derive a bound on the scale of the cosmological bounce resulting from the torsion dynamics.

Proposed method

• The torsion field is represented as a vector $ S^\mu $, with the full torsion tensor being totally anti-symmetric.
• The Einstein-Cartan Lagrangian is extended by adding a quadratic, totally anti-symmetric derivative term involving $ S^\mu $, making the torsion dynamical.
• The action splits into the standard Einstein-Hilbert term and a mass term $ \sim s_0^2 $, with the kinetic term $ \frac{1}{\mu^2} \dot{s}_0^2 $ emerging as the source of dark energy.
• Cosmological solutions are derived under the assumption of spatial homogeneity and isotropy (Cosmological Principle), leading to a modified Friedmann equation.
• The quadratic torsion term contributes a stiff fluid with equation of state $ w = 1 $, enabling a bouncing solution.
• A bound on the bounce scale is calculated by analyzing the dynamics of the torsion field and its energy density contributions.

Experimental results

Research questions

• RQ1 Can a kinetic term in a dynamical torsion field serve as a source of dark energy in cosmology, replacing the potential energy of quintessence models?
• RQ2 How does the inclusion of a quadratic, totally anti-symmetric derivative of the torsion vector affect the cosmological evolution, particularly in the context of a bouncing universe?
• RQ3 What is the role of the stiff fluid component arising from the quadratic torsion term in enabling a cosmological bounce?
• RQ4 What constraints or bounds can be derived on the scale of the bounce from the dynamics of the torsion field?

Key findings

• The kinetic term $ \frac{1}{\mu^2} \dot{s}_0^2 $ in the action acts as the source of dark energy, replacing the potential energy mechanism of quintessence.
• The quadratic torsion term generates a stiff fluid with equation of state $ w = 1 $, which is responsible for enabling a bouncing solution in the cosmological model.
• The model yields a bouncing universe solution due to the repulsive effect of the stiff fluid component from the torsion dynamics.
• A bound on the scale of the bounce is derived, quantifying the minimum size of the universe at the bounce point based on the torsion field's dynamics.