We describe our simulations of the excited state dynamics of the carotenoid neurosporene, following its photoexcitation into the "bright" (nominally 11Bu+) state. To account for the experimental and theoretical uncertainty in the relative energetic ordering of the nominal 11Bu+ and 21Ag- states at the Franck-Condon point, we consider two parameter sets. In both cases, there is ultrafast internal conversion from the "bright" state to a "dark" singlet triplet-pair state, i.e., to one member of the "2Ag" family of states. For one parameter set, internal conversion from the 11Bu+ to 21Ag- states occurs via the dark, intermediate 11Bu- state. In this case, there is a cross over of the 11Bu+ and 11Bu- diabatic energies within 5 fs and an associated avoided crossing of the S2 and S3 adiabatic energies. After the adiabatic evolution of the S2 state from predominately 11Bu+ character to predominately 11Bu- character, there is a slower nonadiabatic transition from S2 to S1, accompanied by an increase in the population of the 21Ag- state. For the other parameter set, the 21Ag- energy lies higher than the 11Bu+ energy at the Franck-Condon point. In this case, there is cross over of the 21Ag- and 11Bu+ energies and an avoided crossing of the S1 and S2 energies, as the S1 state evolves adiabatically from being of 11Bu+ character to 21Ag- character. We make a direct connection from our predictions to experimental observables by calculating the time-resolved excited state absorption. For the case of direct 11Bu+ to 21Ag- internal conversion, we show that the dominant transition at ca. 2 eV, being close to but lower in energy than the T1 to T1* transition, can be attributed to the 21Ag- component of S1. Moreover, we show that it is the charge-transfer exciton component of the 21Ag- state that is responsible for this transition (to a higher-lying exciton state), and not its triplet-pair component. These simulations are performed using the adaptive tDMRG method on the extended Hubbard model of π-conjugated electrons. The Ehrenfest equations of motion are used to simulate the coupled nuclei dynamics. We next discuss the microscopic mechanism of "bright" to "dark" state internal conversion and emphasize that this occurs via the exciton components of both states. Finally, we describe a mechanism relying on torsional relaxation whereby the strongly bound intrachain triplet-pairs of the "dark" state may undergo interchain exothermic dissociation.