24
P. K. Suresh
waves can not only provide ample evidence of its existence but also tells whether the
universe had an inflationary era or not. It is believed that the primordial gravitational
waves left its imprint on the CMB in the form of B-mode polarization [9, 10]. The
B-mode polarization of the CMB is a unique feature due to the primordial gravitational waves. A recent study indicates that the B-mode polarization of the CMB
is useful in exploring the effect of quantum gravity through inflation, provided the
energy scale of inflation field was much larger than the Planck scale. It is reasonable
to assume that such a high energy scale, the field that is responsible for inflation
necessarily be sensitive enough to quantum gravity. Therefore, the exploration of the
B-mode polarization of the CMB is very important in understanding inflation as well
as quantum gravity. Recent results of the B-mode polarization of the CMB [11] with
Lyth bound [12] indicate that the value of the inflation field could be much higher
than the Planck energy scale. This provides a novel and promising path to explore
quantum gravity experimentally through the B-mode polarization of the CMB.
As discussed, there is no consistent theory of quantum gravity existing at present.
Nevertheless, currently, several approaches available to it and one such approach
is the effective theory [13, 14]. The feasibility of the effective theory techniques
to inflation also has already been examined [15, 16]. Further, it is shown that the
effective theory scenario has the prospective to accommodate some of the disfavored
inflationary models because of the nature of the higher dimensional operator of the
theory [13]. As per the effective theory, the higher dimensional operator of inflation
potential can take only small value, but can play a key role in the inflation and
consequently on the BB mode spectrum of the CMB. The quantum gravity effect
may result in reducing the value of the slow-roll parameters and the tensor-to-scalar
ratio of an inflationary model compared to its predicted value. The consequence
of the lowering of the tensor-to-scalar ratio is expected to reflect on the BB mode
angular power spectrum of the CMB. Therefore, it is interesting to explore the imprint
of quantum gravity on the BB mode angular power spectrum of the CMB through
inflation with the measured B-mode polarization data of the CMB. The repercussion
of the lowering value of the tensor-to-scalar ratio of an inflation model on the BB
mode angular spectrum of the CMB is a potential probe to seek the signature of
quantum gravity. Therefore, the present study aims to explore the signature of the
quantum gravity that follows the effective theory approach via the chaotic inflationary
models in terms of the BB mode correlation angular power spectrum with the BK15
and Planck 2018 joint data of the CMB [17].
Throughout the study we follow the unit c = = 1.
2 Inflation and Power Spectra
In a simple inflationary scenario, a homogeneous scalar field, known as the inflation,
is considered as the candidate of inflaton. The equation of motion of the inflaton,
called the Klein–Gordon equation, in a flat Friedmann–Lemaître–Robertson–Walker
(FLRW) metric can be written as
P. K. Suresh
waves can not only provide ample evidence of its existence but also tells whether the
universe had an inflationary era or not. It is believed that the primordial gravitational
waves left its imprint on the CMB in the form of B-mode polarization [9, 10]. The
B-mode polarization of the CMB is a unique feature due to the primordial gravitational waves. A recent study indicates that the B-mode polarization of the CMB
is useful in exploring the effect of quantum gravity through inflation, provided the
energy scale of inflation field was much larger than the Planck scale. It is reasonable
to assume that such a high energy scale, the field that is responsible for inflation
necessarily be sensitive enough to quantum gravity. Therefore, the exploration of the
B-mode polarization of the CMB is very important in understanding inflation as well
as quantum gravity. Recent results of the B-mode polarization of the CMB [11] with
Lyth bound [12] indicate that the value of the inflation field could be much higher
than the Planck energy scale. This provides a novel and promising path to explore
quantum gravity experimentally through the B-mode polarization of the CMB.
As discussed, there is no consistent theory of quantum gravity existing at present.
Nevertheless, currently, several approaches available to it and one such approach
is the effective theory [13, 14]. The feasibility of the effective theory techniques
to inflation also has already been examined [15, 16]. Further, it is shown that the
effective theory scenario has the prospective to accommodate some of the disfavored
inflationary models because of the nature of the higher dimensional operator of the
theory [13]. As per the effective theory, the higher dimensional operator of inflation
potential can take only small value, but can play a key role in the inflation and
consequently on the BB mode spectrum of the CMB. The quantum gravity effect
may result in reducing the value of the slow-roll parameters and the tensor-to-scalar
ratio of an inflationary model compared to its predicted value. The consequence
of the lowering of the tensor-to-scalar ratio is expected to reflect on the BB mode
angular power spectrum of the CMB. Therefore, it is interesting to explore the imprint
of quantum gravity on the BB mode angular power spectrum of the CMB through
inflation with the measured B-mode polarization data of the CMB. The repercussion
of the lowering value of the tensor-to-scalar ratio of an inflation model on the BB
mode angular spectrum of the CMB is a potential probe to seek the signature of
quantum gravity. Therefore, the present study aims to explore the signature of the
quantum gravity that follows the effective theory approach via the chaotic inflationary
models in terms of the BB mode correlation angular power spectrum with the BK15
and Planck 2018 joint data of the CMB [17].
Throughout the study we follow the unit c = = 1.
2 Inflation and Power Spectra
In a simple inflationary scenario, a homogeneous scalar field, known as the inflation,
is considered as the candidate of inflaton. The equation of motion of the inflaton,
called the Klein–Gordon equation, in a flat Friedmann–Lemaître–Robertson–Walker
(FLRW) metric can be written as