6
1 Einstein Gravity and the Need for Its Modification
while further de Sitter proved that the empty space with negative will expand
exponentially. Therefore, after discovery of the cosmic acceleration the idea of the
cosmological constant has been revitalized [8]. However, the cosmological constant,
by astronomical observations, should be extremely small (about 120 order less than a
natural scale for it given by M
4
Planck ), and this fact has no theoretical explanation (the
search for this explanation constitutes the famous cosmological constant problem).
Besides, the cosmological constant does not solve the problem of renormalizability
of gravity.
There are two manners how to extend the gravity in order to solve these problems.
Within the first approach, we modify the Einstein–Hilbert action through introducing
additive terms. Within the second approach, we suggest that the full description of
gravity involves, besides of the metric field, also some extra scalar or vector fields
which must not be confused with matter being treated as ingredients of the gravity
itself, so that usual results of Einstein gravity are recovered, for example, when
these fields are constant (the typical example is the Brans–Dicke gravity which we
discuss further). In this review, we give a description of these approaches. It should be
noted that among these approaches, an important role is played by adding new terms
(and/or fields) aimed either to break the Lorentz/CPT symmetry or to introduce
a supersymmetric extension of gravity. Within this review we also discuss these
approaches.
The structure of this review looks like follows. In the Chap. 2, we present various models obtained through modifications of the purely gravitational sector. In the
Chap. 3, we consider various scalar-tensor gravity models, such as Chern–Simons
and Brans–Dicke gravities, and galileons. In the Chap. 4, we discuss vector-tensor
gravity models and problem of Lorentz symmetry breaking in gravity. In the Chap. 5,
we review most interesting results in Horava–Lifshitz gravity. In the Chap. 6, we discuss some results for nonlocal gravity. The Chap. 7 represents conclusions of our
course.
1 Einstein Gravity and the Need for Its Modification
while further de Sitter proved that the empty space with negative will expand
exponentially. Therefore, after discovery of the cosmic acceleration the idea of the
cosmological constant has been revitalized [8]. However, the cosmological constant,
by astronomical observations, should be extremely small (about 120 order less than a
natural scale for it given by M
4
Planck ), and this fact has no theoretical explanation (the
search for this explanation constitutes the famous cosmological constant problem).
Besides, the cosmological constant does not solve the problem of renormalizability
of gravity.
There are two manners how to extend the gravity in order to solve these problems.
Within the first approach, we modify the Einstein–Hilbert action through introducing
additive terms. Within the second approach, we suggest that the full description of
gravity involves, besides of the metric field, also some extra scalar or vector fields
which must not be confused with matter being treated as ingredients of the gravity
itself, so that usual results of Einstein gravity are recovered, for example, when
these fields are constant (the typical example is the Brans–Dicke gravity which we
discuss further). In this review, we give a description of these approaches. It should be
noted that among these approaches, an important role is played by adding new terms
(and/or fields) aimed either to break the Lorentz/CPT symmetry or to introduce
a supersymmetric extension of gravity. Within this review we also discuss these
approaches.
The structure of this review looks like follows. In the Chap. 2, we present various models obtained through modifications of the purely gravitational sector. In the
Chap. 3, we consider various scalar-tensor gravity models, such as Chern–Simons
and Brans–Dicke gravities, and galileons. In the Chap. 4, we discuss vector-tensor
gravity models and problem of Lorentz symmetry breaking in gravity. In the Chap. 5,
we review most interesting results in Horava–Lifshitz gravity. In the Chap. 6, we discuss some results for nonlocal gravity. The Chap. 7 represents conclusions of our
course.