Dark Matter in Modified Gravity?
Taishi Katsuragawa and Shinya Matsuzaki
Department of Physics, Nagoya University
Introduction
What is Modified Gravity?

F(R) Gravity= Broader class of gravitational theory
GeneralRelativity+Methods and Results

Modificationof GR

Modification leads to emergence of new DOF.
= Expressed in terms of new field(new gravitational force = the fifth force)

Why Modified Gravity?
New field can generate the late-timeaccelerated expansion of the Universe.

Chameleon Mechanism
EOM of Scalaron

ActionwhereWeyl transformation

Scalaron potential couples with 𝑇𝜇𝜈′′2The mass 𝑚𝜑= 𝑉eff(𝜑min ) depends
on the environment.

Scalaron field 𝜑(𝑥) appears.

For large 𝜌, the scalaron becomes heavy.

Scalaron Coupling with SMParticle Picture of Scalaron
Background= Dynamical dark energy

𝜑 𝑥 =When the new field is quantized,

new particle shows up from modified gravity.
Then, a question naturally arises“New particle derived from the modificationof gravity can be a Dark Matter?”

Dilatonic couplings show up.
= Suppressed by Planck mass𝜅𝜑e ∼ 1 + 𝜅𝜑Weak coupling with SM particles

Lifetime of Scalaron→whereViable modified gravity theories possess
screening mechanism.
It suppresses the fifth force in order to avoid
local tests of gravity although the new fieldacts as DE at cosmological scale.

Many constraints on DM are known(i.e. lifetime, relic abundance, direct search).
They can be converted into those on themodified gravity.
= To distinguish the modified gravities

1024

The scalaron mass is given by

1021
1018
1015

Finally, we obtain1012

𝛽 < 10−69 for n=1, 𝛽 < 10−59 for n=4

Thus, new field depends on environment;
it is dynamical DE at cosmological scale,
while it is a DM candidate at smaller scales.

New Constraint on Modified Gravity

0.0010.01

110

We studied the scalaron as a DM candidate derived from F(R) gravity.
We estimated the lifetime of scalaron based on QFT and obtained the constraint
on 𝛽 in the Starobinsky model.
𝛽 is extremely small although 𝛽 = 𝑂(1) for compatibility with DE.
= Scalaron is not DM. Or we need to reconsider assumptions in analysis.
𝝁Improvement of Environment 𝑻𝝁

SM particles
Scalaron

Ordinary
DE and DM have the same origin.
Matter= Answer to Coincidence problem? 4.9%

One may predict the ratio of DE to DM
w.r.t. current energy density.

0.1

Conclusions

Unification of DE and DM

DM 26.8%

DM (particle)

We assume that the environmentis described by the perfect fluid.

The Starobinsky model

New Dark Matter Candidate

DE 68.3%

𝜑min 𝑥DE (classical)

Constraint on F(R) Gravity

Motivations

Fluctuation+𝜑ො 𝑥Comptonwavelength−1𝑚𝜑ෝ ∼ distance btw. particles

We assumed perfect fluid
around the scalaron.
In large scale, perfect fluid
approximation is OK.

Literature Cited
1. T. Katsuragawa and S. Matsuzaki, “Modified GravityExplains Dark Matter?”, arXiv:1610.01016 [gr-qc].
2. S. Nojiri and S. D. Odintsov, “Can F(R)-gravity be a viable
model: the universal unication scenario for inflation, darkenergy and dark matter”, arXiv:0801.4843 [astro-ph].

In microscopic scale, the approximation is invalid.
The chameleon mechanism may be weakened
because the environment btw. particles is almostvacuum.

Acknowledgements
We are deeply grateful to Shin'ichi Nojiri for his constructive
advice and useful comments.
This research is supported by the Grant-in-Aid for JSPS Fellows#15J06973 (T.K.), and by the JSPS Grant-in-Aid for Young
Scientists (B) #15K17645 (S.M.).