30
P. K. Suresh
S =
d
D √
−g
m
2
pl
2
R + f (φ)F(R, R μν ) + g
μν
∂ μ φ∂ ν φ
+ V ren (φ) +
∞
n=5
c n
φ
n
m
n−4
pl
,
(29)
where V ren (φ) includes all renormalizable terms up to dimension four and c n are
Wilson coefficients of higher dimensional operators [13]. The second term in the
bracket corresponds to the non-minimal coupling between the gravity and the scalar
field. The present study assumes that the coupling of the scalar field to gravity is
minimal, and hence ignoring the second term. We also neglect the derivative term
like ∂ μ φ∂
ν
φ
n for simplicity. Further, it is assumed that the kinetic term of the graviton
is canonically normalizable.
In view of the effective theory approach to inflation, the potential for the inflaton
can be written as
V (φ) = V ren (φ) +
∞
n=5
c n
φ
n
m
n−4
pl
.
(30)
The term c n
φ
n
m
n−4
pl
present in the above potential is known as the higher dimension
operator (HDO). For a given inflationary model, usually one specific dominant term
of Wilson coefficients is only considered and other remaining terms are ignored. To
preserve the flatness of the inflationary potential, the value of Wilson coefficients
must be of the order of 10
−3 [4, 5, 23]. The origin of HDO depends on the nature of
the quantum gravity theory. For instance, in the extra-dimensional scenario it may
arise from the exchange of supermassive Kaluza–Klein mode or due to either real or
virtual quantum black holes in generic quantum gravity theory [24].
4.1 Quantum Gravity Effect on the Chaotic Inflation
Next, we consider the effect of quantum gravity on the two specific chaotic inflationary models, namely, quadratic and quartic chaotic inflation models through the
HDO effect. In the usual scenario, these inflationary models are disfavorable due to
the Planck result [25–28]. However, the study of the inflation model with the HDO
effect is encouraging to reconsider some of the disfavored models because it may
bring down the value of the associated parameters of the inflation compared to their
standard case.
4.1.1 Quadratic Chaotic Inflation
In the light of the effective theory, the potential for the quadratic chaotic inflation
can be written as [13]
P. K. Suresh
S =
d
D √
−g
m
2
pl
2
R + f (φ)F(R, R μν ) + g
μν
∂ μ φ∂ ν φ
+ V ren (φ) +
∞
n=5
c n
φ
n
m
n−4
pl
,
(29)
where V ren (φ) includes all renormalizable terms up to dimension four and c n are
Wilson coefficients of higher dimensional operators [13]. The second term in the
bracket corresponds to the non-minimal coupling between the gravity and the scalar
field. The present study assumes that the coupling of the scalar field to gravity is
minimal, and hence ignoring the second term. We also neglect the derivative term
like ∂ μ φ∂
ν
φ
n for simplicity. Further, it is assumed that the kinetic term of the graviton
is canonically normalizable.
In view of the effective theory approach to inflation, the potential for the inflaton
can be written as
V (φ) = V ren (φ) +
∞
n=5
c n
φ
n
m
n−4
pl
.
(30)
The term c n
φ
n
m
n−4
pl
present in the above potential is known as the higher dimension
operator (HDO). For a given inflationary model, usually one specific dominant term
of Wilson coefficients is only considered and other remaining terms are ignored. To
preserve the flatness of the inflationary potential, the value of Wilson coefficients
must be of the order of 10
−3 [4, 5, 23]. The origin of HDO depends on the nature of
the quantum gravity theory. For instance, in the extra-dimensional scenario it may
arise from the exchange of supermassive Kaluza–Klein mode or due to either real or
virtual quantum black holes in generic quantum gravity theory [24].
4.1 Quantum Gravity Effect on the Chaotic Inflation
Next, we consider the effect of quantum gravity on the two specific chaotic inflationary models, namely, quadratic and quartic chaotic inflation models through the
HDO effect. In the usual scenario, these inflationary models are disfavorable due to
the Planck result [25–28]. However, the study of the inflation model with the HDO
effect is encouraging to reconsider some of the disfavored models because it may
bring down the value of the associated parameters of the inflation compared to their
standard case.
4.1.1 Quadratic Chaotic Inflation
In the light of the effective theory, the potential for the quadratic chaotic inflation
can be written as [13]