Galaxy rotation curves, which show that the orbital velocities of stars within galaxies do not decrease as expected based on the visible matter, provide strong evidence for the existence of dark matter.

The Lambda-CDM model, also known as the standard cosmological model, is the prevailing cosmological model that describes the universe as expanding and accelerating, dominated by dark energy (represented by the cosmological constant Lambda) and cold dark matter (CDM).

Current cosmological models estimate that dark matter constitutes approximately 27% of the total energy density of the universe, while ordinary matter makes up only about 5%.

Galaxy clusters, the largest gravitationally bound structures in the universe, are believed to be dominated by dark matter, which holds the galaxies together and influences their motions.

The primary challenge in detecting dark matter directly is its extremely weak interaction with ordinary matter, making it difficult to observe or measure using conventional methods.

Modified gravity theories, such as f(R) gravity or scalar-tensor theories, propose modifications to the laws of gravity to explain the observed acceleration of the universe's expansion without the need for dark energy.

Supernovae observations, particularly Type Ia supernovae, have been instrumental in providing evidence for the existence of dark energy by revealing the accelerating expansion of the universe.

WIMPs (Weakly Interacting Massive Particles) are hypothetical particles that are considered promising candidates for dark matter due to their weak interactions and stability.

Dark energy, with its negative pressure, drives the accelerated expansion of the universe, leading to the prediction that the universe will continue to expand indefinitely.

The cosmological constant is a constant term added to Einstein's field equations of general relativity to account for the observed acceleration of the universe's expansion.

Galaxy clusters, due to their immense mass and the presence of dark matter, act as gravitational lenses, bending and distorting the light from distant galaxies behind them, creating distorted images.

The primary challenge in studying dark energy is its extremely weak interaction with ordinary matter, making it difficult to detect or measure directly using conventional methods.

Supernovae observations, particularly Type Ia supernovae, have been instrumental in providing evidence for the accelerating expansion of the universe by revealing that distant supernovae are fainter than expected, indicating that the universe's expansion is accelerating.

The vacuum energy of quantum fields, also known as the cosmological constant, is a possible explanation for the origin of dark energy, suggesting that the energy inherent in the vacuum contributes to the acceleration of the universe's expansion.