**Current Issue**

# Special Issue "Modified Gravity: From Black Holes Entropy to Current Cosmology"

A special issue of *Entropy* (ISSN 1099-4300). This special issue belongs to the section "Astrophysics and Cosmology".

Deadline for manuscript submissions: **closed (20 September 2012)**

## Special Issue Editors

*Guest Editor*

**Prof. Dr. Sergei D. Odintsov**

Institució Catalana de Recerca i Estudis Avançats (ICREA) and Institut de Ciencies de l’Espai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans, s/n 08193 Cerdanyola del Valles, Barcelona, Spain

Website: http://www.ice.csic.es/en/view_staff.php?MID=41&ap=1

E-Mail: odintsov@ieec.uab.es

Phone: +34 93 5814368

Fax: +34 93 5814363 **Interests:** cosmology; dark energy and inflation; quantum gravity; modified gravity and beyond general relativity; quantum fields at external fields

*Guest Editor*

**Prof. Dr. Kazuharu Bamba**

Leading Graduate School Promotion Center, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan

E-Mail: bamba.kazuharu@ocha.ac.jp

Phone: +81 3 5978 5775

Fax: +81 3 5978 5776 **Interests:** modified theories of gravity; dark energy; cosmology; particle-theory and field-theory models of the early universe; electric and magnetic fields; quantum aspects of black holes, evaporation, thermodynamics

## Special Issue Information

Dear Colleagues,

Recent cosmological observations strongly support that the current expansion of the universe is accelerating. The origin of such a cosmic acceleration mechanism is one of the most significant problems in modern cosmology. Indeed, this is shown by the fact that the Nobel Prize in Physics 2011 was presented to the finding of the current cosmic acceleration by means of the observations of the Type Ia supernovae.

There are two representative approaches to explain the current accelerated expansion of the universe. One is to introduce “dark energy” in the framework of general relativity. The other is to modify a gravitational theory, such as *F(R)* gravity, so that we can obtain so-called geometrical dark energy. It is believed that a modified gravitational theory must pass cosmological bounds and solar system tests because it corresponds to an alternative theory of gravitation to general relativity. As another meaningful touchstone of modified gravity, it is important to examine whether the second law of thermodynamics can be satisfied in the models of modified gravity.

The fundamental connection between gravitation and thermodynamics has been suggested by the discovery of black hole thermodynamics with black hole entropy and Hawking temperature. In addition, it was shown that the Einstein equation can be derived from the proportionality of the entropy to the horizon area together with the Clausius relation in thermodynamics. This consequence has been applied to various cosmological settings as well as modified gravitational theories. In particular, the connections between thermodynamics and modified gravity have recently been discussed extensively.

In this special issue, we discuss the application of thermodynamics to the test of a successful alternative gravitational theory to general relativity. Through this procedure, we can obtain a clue to resolve the dark energy problem “geometrically”. It is considered that any successful modified gravity theory should obey the second law of thermodynamics. If the second law is violated in certain universes in a model, it is more likely to be due to an incorrect generalization of the second law or some inherent inconsistency of the model itself. For the latter case, the model should be abandoned. It is strongly expected that the considerations of this special issue can produce our new physical understanding on entropy in the context of the relation between thermodynamics and gravitation and shed light on novel ingredients as well as insights on modern cosmology, in particular new properties of dark energy.

Prof. Dr. Sergei D. Odintsov

Dr. Kazuharu Bamba*Guest Editors*

** **

## Keywords

- Quantum aspects of black holes, evaporation, thermodynamics
- Black hole entropy
- Modified theories of gravity
- Dark energy
- Cosmology

Last update: 3 December 2014