11

Dark Energy

TheFriedmann–Lemaitre universewhich we met in Chapter 5 has become the gener-
ally accepted description of the Universe, theFLRW concordance model.InChapter8
we learned the reason for this: all observations show that the Universe is expanding
and characterized by a positivecosmological constant휆and a large density parameter,
훺휆; see Equations (5.20), (8.50). This is also clear from Figure 8.7.
What휆stands for is not known. Dark energy came as a complete surprise. Nothing
in big bang or inflationary cosmology predicted its existence. Is the Universe domi-
nated by some new form of dark energy or does Einstein’s theory of gravity break down
on cosmological scales? In the first case휆belongs to the energy-momentum tensor on
the right side of the Einstein Equation (3.29), in the second case it is a modification of
the geometry described by the left side of Equation (3.29). The introduction in Section
11.2 of a new single field could be a modification of the geometry or a fluid added to
the energy-momentum tensor. We spend most time on quintessence here.
In Section 11.3 we introduce푓(푅)models which are modifications of the geome-
try of spacetime. Even more exotic modifications of the geometry of spacetime are
models defined in extra dimensions in Section 11.4. We also list a number of other
models here.

11.1 The Cosmological Constant

The introduction of the cosmological constant into our description of the Universe
is problematic for at least three reasons. First, as we noted in Equation (5.22), its
present value is extremely small, in fact some 122 orders of magnitude smaller than
theoretical expectations. The density is about

휌휆≈^2.^9 ×^10 −^47 GeV^4.

Introduction to Cosmology, Fourth Edition. Matts Roos
© 2015 John Wiley & Sons, Ltd. Published 2015 by John Wiley & Sons, Ltd.