[Paper Review] Vacuum energy $f(T)$ decay: Inflation at the open universe

W. El Hanafy, G. L. Nashed|arXiv (Cornell University)|Oct 9, 2014

Cosmology and Gravitation Theories2 references3 citations

TL;DR

This paper proposes an exact $f(T)$ gravity formulation for the open universe that naturally explains the small present value of the cosmological constant through vacuum energy decay. By showing that torsion scalar $T$ does not vanish when the energy-momentum tensor vanishes—unlike in general relativity—it enables an exponential scale factor independent of curvature and provides a dynamical solution to the cosmological constant fine-tuning problem via a scalar field-driven inflationary scenario.

ABSTRACT

We derived a uniquely exact $f(T)$ formula of the lowest possible energy of an isotropic and homogeneous universe. We show that vanishing of the energy-momentum tensor $\mathcal{T}^{\mu u}$ of matter does not imply vanishing of the teleparallel torsion scalar $T$, in contrast to general relativity, where Ricci scalar vanishes. The theory provides an exponential scale factor independent of the choice of the sectional curvature. In addition, the obtained $f(T)$ of the open universe model shows a decaying form to the small present value of cosmological constant which contributes directly to solve the fine-tuning problem of the cosmological constant. The Equation of State (EoS) of the torsion fluid has been studied. We study the case when the torsion potential is made of a scalar field and its consequences on the inflationary description.

Motivation & Objective

• To derive an exact $f(T)$ formulation for the lowest possible energy state of an isotropic and homogeneous open universe.
• To address the cosmological constant fine-tuning problem by showing a decaying vacuum energy mechanism in teleparallel gravity.
• To investigate the Equation of State (EoS) of the torsion fluid in the context of inflationary cosmology.
• To explore the role of a scalar field as the torsion potential and its implications for early-universe inflation.

Proposed method

• Derives the exact $f(T)$ function for the open universe model under isotropy and homogeneity assumptions.
• Demonstrates that the vanishing of the energy-momentum tensor $\mathcal{T}^{\mu\nu}$ does not imply $T = 0$, contrasting with general relativity.
• Introduces a scale factor that evolves exponentially, independent of the spatial sectional curvature.
• Models the cosmological constant as a dynamically decaying vacuum energy term in the $f(T)$ framework.
• Analyzes the Equation of State (EoS) of the torsion fluid to assess its cosmological implications.
• Considers the scalar field as the source of torsion potential and studies its role in driving inflation.

Experimental results

Research questions

• RQ1 How does the torsion scalar $T$ behave when the energy-momentum tensor vanishes in teleparallel gravity, compared to general relativity?
• RQ2 Can an exact $f(T)$ formulation for the open universe yield a naturally decaying cosmological constant?
• RQ3 What is the role of the scalar field in generating torsion and enabling inflation in this framework?
• RQ4 How does the exponential scale factor in this model remain independent of the curvature of space?
• RQ5 What is the Equation of State (EoS) of the torsion fluid, and how does it support an inflationary phase?

Key findings

• The theory shows that $T$ does not vanish when $\mathcal{T}^{\mu\nu} = 0$, a key distinction from general relativity.
• An exact $f(T)$ formula is derived for the open universe that yields a scale factor evolving exponentially, independent of sectional curvature.
• The cosmological constant emerges as a small present-day value due to vacuum energy decay, directly addressing the fine-tuning problem.
• The Equation of State (EoS) of the torsion fluid is studied and found to support an inflationary phase.
• When the torsion potential is modeled as a scalar field, the framework naturally supports an inflationary description of the early universe.
• The model provides a dynamical mechanism for the cosmological constant, avoiding the need for arbitrary parameter tuning.