Why is the expansion rate of the universe accelerating?
I noticed that the FLRW metric closely follows the deceleration and acceleration trend, does it have anything to do with it?
The current understanding of the accelerating expansion of the universe is based on observations of distant supernovae and the cosmic microwave background radiation. The most widely accepted explanation for this phenomenon is the presence of dark energy, a mysterious form of energy that is thought to permeate all of space and exert a repulsive force, causing the expansion of the universe to accelerate.

The Friedmann-Lemaître-Robertson-Walker (FLRW) metric is a solution to the Einstein field equations of general relativity that describes a homogeneous, isotropic, and expanding universe. It provides a mathematical framework for understanding the large-scale structure and evolution of the universe. The FLRW metric itself doesn't directly cause the acceleration or deceleration of the universe's expansion, but rather, it allows us to model these behaviors based on the matter and energy content of the universe.

The expansion history of the universe is governed by the energy densities of its various components, such as matter (both ordinary and dark matter), radiation, and dark energy. The FLRW metric incorporates these components and their evolution over time. The acceleration or deceleration of the universe's expansion depends on the balance of attractive forces (due to gravity, from matter and radiation) and repulsive forces (due to dark energy).

Observations suggest that the energy density of dark energy remains nearly constant as the universe expands, while the energy densities of matter and radiation decrease over time. Consequently, as the universe continues to expand, the repulsive force from dark energy becomes dominant over the attractive gravitational forces, resulting in the observed accelerating expansion.

Although we have a working model to describe the accelerating expansion of the universe, dark energy itself remains one of the biggest mysteries in modern cosmology. Understanding its true nature and origin is an ongoing area of research.