### 3.1 Dark Energy ()

In CDM, dark energy is a non-vanishing vacuum energy represented by the cosmological constant
in the field equations of general relativity. Einstein’s cosmological constant is equivalent to vacuum
energy with equation of state . In principle, the equation of state could be merely close to,
but not exactly . In this case, the dark energy could evolve and clump, depending on the value of
and its evolution . However, to date, there is no compelling observational reason to require
any form of dark energy more complex than the simple cosmological constant introduced by
Einstein.
The various observational datasets discussed above constrain the ratio of the dark energy density to
the critical density to be , where is Hubble’s constant and is
expressed in . This value, together with the matter density (see below), leads to a total
, i.e., a spatially-flat Euclidean geometry in the Robertson–Walker sense
that is nicely consistent with the expectations of inflation. It is important to stress that this
model relies on the cosmological principle, i.e., that our observational location in the Universe is
not special, and on the fact that on large scales, the Universe is isotropic and homogeneous.
For possible challenges to these assumptions and their consequences, we refer the reader to,
e.g., [83, 487, 488].