Testing Cosmological Models with Negative Pressure

There is now strong evidence that the main contribution to the cosmic energy density is not due to matter, but to another component with negative pressure. Its nature is still unknown: it could be the vacuum energy, manifesting itself as a positive cosmological constant with $w \equiv P/ρc^2 = -1$ ($Λ$CDM model), a spatially inhomogeneous and dynamically evolving form of energy with $-1 < w < 0$ (quintessence, QCDM model), or a dark energy component with $w < -1$, such as a quantized free scalar field (VCDM model). After presenting simple redshift--distance formulae, which are useful for comparing observations with theoretical predictions without numerical integration, I discuss the behaviour of different $w < 0$ models in the context of the Alcock--Paczyński geometric test and the statistics of gravitational lensing.