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Einstein's Other Gravity and the Acceleration of the Universe

Eric V. Linder

TL;DR

The paper investigates curvature-free teleparallel gravity by promoting the torsion scalar $T$ to a general function $f(T)$, yielding second-order field equations and modified Friedmann dynamics $T=-6H^2$. It demonstrates how an effective dark-energy sector arises from $f(T)$ and presents two concrete models—power-law and exponential—that can drive late-time acceleration while reproducing GR at early times; a de Sitter fate is achievable in both cases, with parameter constraints ensuring observational viability. The work reveals connections to $f(R)$ gravity, higher-dimensional models like DGP, and scalar-tensor theories, and emphasizes the framework's ability to explain cosmic acceleration without curvature-based pathologies. Overall, $f(T)$ gravity offers a flexible, curvature-free route to modified gravity that preserves second-order dynamics and links to several broader gravity theories, making it a compelling alternative to explain the universe's acceleration.

Abstract

Spacetime curvature plays the primary role in general relativity but Einstein later considered a theory where torsion was the central quantity. Just as the Einstein-Hilbert action in the Ricci curvature scalar R can be generalized to f(R) gravity, we consider extensions of teleparallel, or torsion scalar T, gravity to f(T) theories. The field equations are naturally second order, avoiding pathologies, and can give rise to cosmic acceleration with unique features.

Einstein's Other Gravity and the Acceleration of the Universe

TL;DR

The paper investigates curvature-free teleparallel gravity by promoting the torsion scalar to a general function , yielding second-order field equations and modified Friedmann dynamics . It demonstrates how an effective dark-energy sector arises from and presents two concrete models—power-law and exponential—that can drive late-time acceleration while reproducing GR at early times; a de Sitter fate is achievable in both cases, with parameter constraints ensuring observational viability. The work reveals connections to gravity, higher-dimensional models like DGP, and scalar-tensor theories, and emphasizes the framework's ability to explain cosmic acceleration without curvature-based pathologies. Overall, gravity offers a flexible, curvature-free route to modified gravity that preserves second-order dynamics and links to several broader gravity theories, making it a compelling alternative to explain the universe's acceleration.

Abstract

Spacetime curvature plays the primary role in general relativity but Einstein later considered a theory where torsion was the central quantity. Just as the Einstein-Hilbert action in the Ricci curvature scalar R can be generalized to f(R) gravity, we consider extensions of teleparallel, or torsion scalar T, gravity to f(T) theories. The field equations are naturally second order, avoiding pathologies, and can give rise to cosmic acceleration with unique features.

Paper Structure

This paper contains 4 sections, 13 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Cosmological Equations
  3. Results for Cosmic Acceleration
  4. Summary and Conclusions

Figures (1)

  • Figure 1: Effective dark energy equation of state is plotted vs. scale factor for the exponential $f(T)$ model of Eq. (\ref{['eq:ftexp']}). Curves are labeled with the value of the one free parameter $p$. The model acts like a cosmological constant at high redshift and in the future, except for $p<0.51$ it behaves as Einstein-de Sitter in the future.