Inflationary cosmology in unimodular $F(T)$ gravity

Abstract

We investigate the inflationary realization in the context of unimodular $F(T)$ gravity, which is based on the $F(T)$ modification of teleparallel gravity, in which one imposes the unimodular condition through the use of Lagrange multipliers. We develop the general reconstruction procedure of the $F(T)$ form that can give rise to a given scale-factor evolution, and then we apply it in the inflationary regime. We extract the Hubble slow-roll parameters that allow us to calculate various inflation-related observables, such as the scalar spectral index and its running, the tensor-to-scalar ratio, and the tensor spectral index. Then, we examine the particular cases of de Sitter and power-law inflation, of Starobinsky inflation, as well as inflation in a specific model of unimodular $F(T)$ gravity. As we show, in all cases the predictions of our scenarios are in a very good agreement with Planck observational data. Finally, inflation in unimodular $F(T)$ gravity has the additional advantage that it always allows for a graceful exit for specific regions of the model parameters.

11 pages, 2 figures, published version

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• f(T) teleparallel gravity and cosmology
• Dark torsion as the cosmic speed-up
• Einstein's Other Gravity and the Acceleration of the Universe
• BICEP2 / Keck Array VI: Improved Constraints On Cosmology and Foregrounds When Adding 95 GHz Data From Keck Array
• The teleparallel equivalent of general relativity
• Degrees of freedom of $f(T)$ gravity
• Conformal transformation in $f(T)$ theories
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• Reconstruction of scalar field theories realizing inflation consistent with the Planck and BICEP2 results

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• Phase Portraits of general f(T) Cosmology
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• Einstein's cluster mimicking compact star in the teleparallel equivalent of general relativity
• Reconstructing inflation in scalar-torsion $f(T,\varphi )$ gravity
• Cosmological singularities in interacting dark energy models with an $\omega (q)$ parametrization
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• Diffusion in unimodular gravity: Analytical solutions, late-time acceleration, and cosmological constraints
• Lorenz Gauge Fixing of $f(T)$ Teleparallel Cosmology
• Solving the $H_0$ tension in $f(T)$ Gravity through Bayesian Machine Learning
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• Phase Space description of Nonlocal Teleparallel Gravity
• Dynamically Generated Inflation from Non-Riemannian Volume Forms
• A clarification on prevailing misconceptions in unimodular gravity
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• Dynamically Generated Inflationary Lambda-CDM
• A viable form of the metric Teleparallel F(T) theory of gravity
• Slow-roll inflation in $f(T,\mathcal{T})$ modified gravity
• Extension of unimodular gravity and the cosmological constant
• Reconstructing modified and alternative theories of gravity
• Cosmic expansion beyond $\Lambda$CDM: Investigating power-law and logarithmic corrections
• Unimodular Theory of Gravity in Light of the Latest Cosmological Data
• Inflation from a generalized exponential plateau: towards extra suppressed tensor-to-scalar ratios
• Reconciling the ACT Preference in $f(T)$ Gravity: Inflation and Reheating Constraints