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Dark energy is theorized to be responsible for the acceleration of the universe's expansion. Explanations include the cosmological constant ($\Lambda$), quintessence, and modified gravity theories. Evidence includes supernovae observations, measurements of the CMB, and baryon acoustic oscillations.

Galactic rotation curves show that stars at the edges of galaxies rotate at similar speeds to those closer to the center, differing from Newtonian predictions. This suggests the presence of dark matter. The theoretical framework involves non-baryonic dark matter that does not emit electromagnetic radiation.

The CMB is the remnant radiation from the Big Bang. Observations of its anisotropies provide evidence for dark matter and dark energy. Theoretical understanding includes the Sachs-Wolfe effect, which explains large-scale anisotropies, and Silk damping, which involves the interaction of photons and baryons in the early universe.

Gravitational lensing occurs when light from a distant object is warped by the gravity of an intervening object. Dark matter's presence is revealed by lensing effects that can't be accounted for by visible matter alone. Theoretical models often incorporate mass in the form of a dark matter halo surrounding galaxies.