Comparing $f(R)$ modified gravity and noncommutative geometry in the context of dark matter and traversable wormholes: a survey

TL;DR

This survey compares $f(R)$ modified gravity and noncommutative geometry, showing they produce similar predictions for dark matter and traversable wormholes, suggesting both are viable models in these contexts.

Contribution

It highlights the conceptual connection between $f(R)$ gravity and noncommutative geometry, demonstrating their similar predictions in dark matter and wormhole physics.

Findings

Both theories can be derived from similar principles.

They make comparable predictions for dark matter phenomena.

They support the viability of traversable wormholes.

Abstract

Noncommutative geometry, as conceptualized by Nicolini, Smailagic, and Spallucci, may be viewed as a slight modification of Einstein's theory. The same can be said for $f(R)$ modified gravity for an appropriate choice of the function $f(R)$. Since such an $f(R)$ could be determined from the noncommutative-geometry background, these gravitational theories make very similar predictions in the discussion of (a) dark matter and (b) traversable wormholes; they can therefore be taken as equally viable models.