Stability of the flat FLRW metric in $f(T)$ gravity

Abstract

In this paper, we investigate the stability of the flat FLRW metric in $f(T)$ gravity. This is achieved by analysing the small perturbations, $\delta$ about the Hubble parameter and the matter energy density, ${\delta }_{\text{m}}$. We find that $\delta \propto \dot{H}/H$ and ${\delta }_{\text{m}}\propto H$. Since the Hubble parameter depends on the function $f(T)$, two models were considered (A) the power-law model $f(T)=\alpha (-T{)}^n$, and (B) the exponential model $f(T)=\alpha T_0\left(1-\exp \left[-p\sqrt{\frac{T}{T_0}}\right]\right)$, where the parameters $n$ and $p$ were chosen to give comparable physical results. For the parameters considered, it was found that the solutions are stable with vanishing $\delta$ and decaying then constant ${\delta }_{\text{m}}$, meaning that the matter perturbations persist during late times.

arXiv comment14 pages, 14 figures

References in corpus (28)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Planck 2013 results. XVI. Cosmological parameters
• The Cosmological Constant and Dark Energy
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
• f(R) theories
• 4D Gravity on a Brane in 5D Minkowski Space
• Exploring the Expansion History of the Universe
• Accelerating Universes with Scaling Dark Matter
• f(T) teleparallel gravity and cosmology
• Dark torsion as the cosmic speed-up
• Einstein's Other Gravity and the Acceleration of the Universe
• Cosmological implications of baryon acoustic oscillation (BAO) measurements
• The teleparallel equivalent of general relativity
• The covariant formulation of f(T) gravity
• $f(T,\mathcal{T})$ gravity and cosmology
• Good and bad tetrads in f(T) gravity
• Torsion Gravity: a Reappraisal
• Viable f(T) models are practically indistinguishable from LCDM
• On the stability of the cosmological solutions in f(R,G) gravity
• Cosmographic Constraints and Cosmic Fluids
• Observational constraints on variable equation of state parameters of dark matter and dark energy after Planck
• Covariance properties and regularization of conserved currents in tetrad gravity
• Cosmic slowing down of acceleration for several dark energy parametrizations
• Interacting Dark Energy in f(T) cosmology : A Dynamical System analysis
• LCDM Model in f(T) Gravity: Reconstruction, Thermodynamics and Stability
• Reconstruction, Thermodynamics and Stability of $\Lambda$CDM Model in $f(T,\mathcal{T})$ Gravity
• Constraining $f(T,\mathcal{T})$ gravity models using type Ia supernovae

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