Chapter 3
Scalar-Tensor Gravities
3.1 General Review
In the previous chapter we demonstrated that modifications of the pure gravitational
sector allow for obtaining interesting results, in particular, for a consistent explanation
of the cosmic acceleration. At the same time, we noted that f (R) gravities are
dynamically equivalent to some gravity models whose action is given by the sum of
the usual Einstein term and a new term depending on the extra scalar field [15]. This
field, being related with the function of the curvature, evidently cannot be associated
with the matter, hence it is natural to suggest that the complete description of gravity is
given by composition of the dynamical metric tensor and this scalar field, so we have
the scalar-tensor gravity model. Another motivation for a scalar-tensor gravity arises
from quintessence models in cosmology which involve a very light scalar field called
the quintessence field and are known to explain accelerated expansion of the Universe
as well as the cosmological constant which therefore implied active application of
the quintessence field within the inflationary context [36]. The advantage of the
quintessence in comparison with the cosmological constant consists in the fact that
the very tiny mass of the quintessence field (estimated to be about 10
−33 eV [37]) is
much more reasonable from the theoretical viewpoint than the extremal smallness of
the cosmological constant giving the famous cosmological constant problem, since
even the massless scalar fields are physically consistent.
While the quintessence is well discussed now (see f.e. [37] and references therein),
there are other interesting manners to introduce new scalar fields in the gravity, moreover, while the quintessence field is treated as a matter, the scalar fields introduced
within these approaches are interpreted as ingredients of the complete description
of the gravity rather than the matter. One of these manners is the Brans–Dicke gravity where the gravitational constant whose negative dimension is responsible for a
non-renormalizability of the gravity is suggested to be not a fundamental constant
but a function of a some slowly varying fundamental scalar field. Another one is
the four-dimensional Chern–Simons modified gravity where the pseudoscalar field
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
A. Petrov, Introduction to Modified Gravity, SpringerBriefs in Physics,
https://doi.org/10.1007/978-3-030-52862-1_3
21
Scalar-Tensor Gravities
3.1 General Review
In the previous chapter we demonstrated that modifications of the pure gravitational
sector allow for obtaining interesting results, in particular, for a consistent explanation
of the cosmic acceleration. At the same time, we noted that f (R) gravities are
dynamically equivalent to some gravity models whose action is given by the sum of
the usual Einstein term and a new term depending on the extra scalar field [15]. This
field, being related with the function of the curvature, evidently cannot be associated
with the matter, hence it is natural to suggest that the complete description of gravity is
given by composition of the dynamical metric tensor and this scalar field, so we have
the scalar-tensor gravity model. Another motivation for a scalar-tensor gravity arises
from quintessence models in cosmology which involve a very light scalar field called
the quintessence field and are known to explain accelerated expansion of the Universe
as well as the cosmological constant which therefore implied active application of
the quintessence field within the inflationary context [36]. The advantage of the
quintessence in comparison with the cosmological constant consists in the fact that
the very tiny mass of the quintessence field (estimated to be about 10
−33 eV [37]) is
much more reasonable from the theoretical viewpoint than the extremal smallness of
the cosmological constant giving the famous cosmological constant problem, since
even the massless scalar fields are physically consistent.
While the quintessence is well discussed now (see f.e. [37] and references therein),
there are other interesting manners to introduce new scalar fields in the gravity, moreover, while the quintessence field is treated as a matter, the scalar fields introduced
within these approaches are interpreted as ingredients of the complete description
of the gravity rather than the matter. One of these manners is the Brans–Dicke gravity where the gravitational constant whose negative dimension is responsible for a
non-renormalizability of the gravity is suggested to be not a fundamental constant
but a function of a some slowly varying fundamental scalar field. Another one is
the four-dimensional Chern–Simons modified gravity where the pseudoscalar field
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
A. Petrov, Introduction to Modified Gravity, SpringerBriefs in Physics,
https://doi.org/10.1007/978-3-030-52862-1_3
21