Cosmologically Viable Solutions in Geometric Modified Gravity

TL;DR

This work analyzes the cosmological viability and Solar System compatibility of gravity theories built on the geometric trinity: General Relativity, Teleparallel Gravity, and Symmetric Teleparallel Gravity. It surveys $f(R)$, $f(\mathbb{T})$, $f(\mathbb{Q})$ and extends to boundary-term theories $f(\mathbb{T},B)$ and $f(\mathbb{Q},C)$, demonstrating that ΛCDM-like expansion generally requires a cosmological constant in single-variable cases, while boundary-term extensions can mimic it without an explicit constant under suitable reconstruction. A key contribution is the introduction of de Sitter compatible connections to assess physical viability in static, spherically symmetric spacetimes, showing that TG/ STG with such connections tend to yield SdS with $γ=1$, whereas certain reconstructed boundary-term models can yield $γ=1/2$, conflicting with solar system constraints. The results emphasize the need for a unified testing framework across cosmological and local scales and highlight STG's richer connection freedom as a promising but constrained route for modified gravity.

Abstract

The discovery of the accelerated expansion of the universe highlighted General Relativity's inability to naturally account for dark energy without invoking a finely tuned cosmological constant. In response, a wide range of alternative paradigms have been proposed. Among these, Teleparallel Gravity and Symmetric Teleparallel Gravity, which depart from the Riemannian framework of General Relativity and instead rely on torsion or non-metricity to describe gravitational interactions, have gained increasing attention in recent years. We explore extensions of these non-Riemannian approaches, aiming to replicate the observed late-time acceleration of the universe by emulating the cosmological constant's role. We also evaluate the consistency of these theories with local gravity constraints by studying their static, spherically symmetric solutions. We show that although some models can reproduce the desired cosmological behavior, they often fail to meet Solar System observational bounds, particularly through deviations in the predicted Eddington parameter. Our findings underscore the need for a unified approach that tests modified gravity theories across both cosmological and local scales.

Theorems & Definitions (6)

• Proposition 1
• proof
• Proposition 2
• proof
• Theorem 1
• proof