Recently, in cosmology various modifications of gravity have been discussed partly motivated by the dark energy problem.
Many of such attempts are to construct effective theories at low energies,
but as we start thiniking about the quantum stability against radiation
correction, the necessary unnnatural tuning of the model parameters
threatens the validity of the model.
In particular, considering modified gravity theories in the infrared regime,
the theory tends to be strongly coupled and the prediction power is lost
at a relatively low energy scale compared to the Planck scale.
It would be extremely important to investigate the existence of an
example in which such models can be embedded in the framework of a
theory applicable to higher energy scales, to answer the question
about whether or not such models are meaningful as an effective theory
at low energies.
In the bi-gravity theories,
we focused on the parameter region of the model
in which we pointed out that graviton oscillation occurs.
If we focus on low energy phenomena, this model resembles
the low energy limit of a certain 5-dimensional braneworld model.
It is also interesting to develop a general discussion about
what kind of model is permitted as an effective theory at low energies.
Now we can use the data from gravitational wave interferometers.
Throught the gravitational wave data analysis, we can perform
various tests of gravity, which were out of scope before the era
of gravitational wave physics. So, it is also interesting to develope
new analysis techniques for gravitational wave signals
based on novel theoretical inputs. Prediction of wave form from
binary coalescences is still widely open in the context of modified gravity.
The use of machine learning also has a large possibility, since
the application of the current analysis method
is limited in various senses by the computational power.
The problem of infrared divergence in the inflation universe tends to be neglected because it is not a problem as far as loop corrections are ignored.
However, reflecting back in the 1980s when the idea of the inflationary universe was proposed, it seems that there was a similar situation.
In general, the problems of homogeneity and flatness were pointed out as a crack in the Big Bang cosmology, and it became a trigger for the idea of inflation.
However, at that time, many people thought that the initial condition of the universe had been appropriately chosen to solve the problems of homogeneity and flatness at the moment of the creation of the universe by some mechanism.
The apparent infrared divergences in the computation of quantum fluctuation generated during inflation are not a easily solved problem, once we recognize it as a problem. There are hand-waving prescriptions to obtain finite answers, but they are based on naive intuititive argument, and difficult to give a solid foundation.
I suspect that the problem of infrared divergence may provide
hints for a next leap of cosmology.
In our previous studies, as we had anticipated from the beginning,
it became clear that many of the problems of infrared divergence are caused
by not considering exactly what the actual observable quantities are.
On the other hand, unexpected conclusions have also been drawn such that
infrared divergence should not be excluded unless at least some constraint
is imposed on the choise of the quantum state of the universe.
As an example of extreme assertions, there have been arguments that
gravitational wave perturbation produces large infrared correction,
leading to dramatic modification of the scenario such as shielding
of the cosmological constant term and secular change of the coupling
constants. There are many weaknesses of logic that doubt the grounds
for such assertions, but it has not definitely been denied the possibility
of such a dramatic phenomenon. However, with regard to the presence or
absence of these phenomena, I am convinced that by steadily carrying out
research from the viewpoint of what the actual observable quatities are,
we will steadily reach a clear answer.
Recently, we noticed that these issues of IR divergences are closely connected to the
so-called large gauge transformation. Under this key word, many important
concepts such as the adiabatic modes, consistency relations, and IR divergences
turned out to be intimately related with each other.
String axions are a candidate of dark matter. For some mass range, axion clouds that develope around a rotating black hole can provide an evidence for the existence of such particles. There are several ways to probe axion clouds. One is to study the spin and mass distribution of black hole, another is the direct gravitational wave signal from the clouds. Indirectly, the binary inspiral waveform might be modified by the presence of such clouds. So far, many studies are restricted to non self-interactive axions. But the whole picture can change drastically, once the self-interaction is turned on. The growth of the axion cloud is rather slow compared with the dynamical time scale of a black hole and the perturbation around it. Therefore, it is difficult to trace the evolution of the cloud from the very beginning till the end by using the standard method for numerical simulation. This is the challenge that we are tackling with.
Theoretical studies towards the understanding of the orbital evolution
of binary systems are essential when trying to verify gravity theory
from gravitational wave observations, and research is progressing from
both post-Newton approximation and black hole perturbation.
Orbital evolution using black hole perturbation is an efficient
approximation method especially for a sattelite motion in a massive
black hole spacetime with a large mass ratio, and this system is
thought to be the most suitable system to measure black hole spacetime
by gravitational waves.
It can be said that research on the orbital evolution by means of black hole
perturbation started with our paper in 1996, but the subsequent progress
has never been linear. The difficulty is
in the technical aspect of regularizing and evaluating the
divergent self-field.
Many studies so far have been performed based on the idea of
directly evaluating the force by the self-field, that is,
self-force.
Because if one can directly evaluate the self-force, one
can always calculate the necessary physical quantities related to the
orbital evolution.
However, the self-force is actually a quantity that depends on the
gauge chose, and only the gauge invariant derived from an
appropriate long-term average is the physical quantity that we
intend to evaluate.
With this idea, you can see that, at the lowest order in the mass
ratio, the self-force can be evaluated by completely avoiding the
problem of regularization.
The expression for the secular change of the Carter constant
is obtained by the adiabatic approximation, also based on this idea.
The concise expression we got makes it possible to trace the
long-term evolution of orbits much more conveniently with higher
accuracy than directly evaluating the self-force.
This way of thinking has also succeessflly extended to
the resonance orbits, which becomes necessary to make the orbital
evolution be more precise.
Furthermore, by further developing this idea, the orbital evolution
can be described just by evaluating simple gauge invariant quantities
even for the next order in the mass ratio.
In fact, this order of accuracy is considered to be sufficent,
because higher order effects are indistinguishable from the observation
of the binary system with large mass ratio.
As clarified in the lowest order calculation, we expect that
building a calculation scheme by
considering what the observable quantity will significantly reduce
the amount of required computation. If so, I believe that it will
be a standard way to calculate theoretical templates for gravitational
waves in the future.
Braneworld is a relatively new scenario of compactification of extra-dimensions. In this scenario the extension of extra-dimensions is assumed to be relatively large compared with Planck scale. In the usual scheme of Kalza-Klein compactification large extra-dimensions mean presence of many light particles, which contradicts with experiments. However, recently people realized the possibility that ordinary matter fields can be localized on a low dimensional object called brane. In that case, directions orthogonal to the brane are not sensed by ordinary matter fields. Then even if we consider higher dimensional models with relatively large extra-dimensions, the models can be consistent with observations. On the other hand, since spacetime is extended, gravity propagates in a higher dimensional spacetime, which we call bulk. Fortunately or unfortunately, gravity is so weak. Hence, the deviation from the standard Newton's law has not been severely tested below sub-mm scale.
My collaborators and I studied
gravity in braneworld mainly in
RS II model,
and clarified how the prediction of braneworld
deviates from the standard general relativity.
Another aspect on which I'm working is quantum correction
to the brane dynamics. It is well known that
Casimir force arises between two parallel plates.
Analogous phenomena happens in the context of braneworld.
This force may play a role to stabilize the distance between branes.
We made a conjecture that black holes in RS-II braneworld would evaporate rapidly due to a large number of CFT degrees of freedom in the dual four dimensional CFT picture. This conjecture turned out to be too naive and the evaporation slows down dramatically owing to the strong coupling effects of CFT. This system would be interesting to investigate further as an extreme case of Hawking evaporation due to the emission of particles with self-interaction.