Cosmology of a Friedmann-Lama\^itre-Robertson-Walker 3-brane, Late-Time Cosmic Acceleration, and the Cosmic Coincidence

Understand

A late epoch cosmic acceleration may be naturally entangled with cosmic coincidence -- the observation that at the onset of acceleration the vacuum energy density fraction nearly coincides with the matter density fraction.

• In this Letter we show that this is indeed the case with the cosmology of a Friedmann-Lama\^itre-Robertson-Walker (FLRW) 3-brane in a five-dimensional anti-de Sitter spacetime.
• We derive the four-dimensional effective action on a FLRW 3-brane, which helps define a general reduction formula, namely, $M_P^{2}=\rho_{b}/|\Lambda_5|$, where $M_{P}$ is the effective Planck mass, $\Lambda_5$ is the 5-dimensional cosmological constant, and $\rho_b$ is the sum of the 3-brane tension $V$ and the matter density $\rho$.
• The behavior of the background solution is consistent with the results based on the form of the 4D effective potential.