Conformal relativity versus Brans-Dicke and superstring theories

Conformal relativity theory which is also known as Hoyle-Narlikar theory has recently been given some new interest. It is an extended relativity theory which is invariant with respect to conformal transformations of the metric. In this paper we show how conformal relativity is related to the Brans-Dicke theory and to the low-energy-effective superstring theory. We show that conformal relativity action is equaivalent to a transformed Brans-Dicke action for Brans-Dicke parameter $\omega = -3/2$ in contrast to a reduced (graviton-dilaton) low-energy-effective superstring action which corresponds to a Brans-Dicke action with Brans-Dicke parameter $\omega = -1$. In fact, Brans-Dicke parameter $\omega =-3/2$ gives a border between a standard scalar field evolution and a ghost. We also present basic cosmological solutions of conformal relativity in both Einstein and string frames. The Eintein limit for flat conformal cosmology solutions is unique and it is flat Minkowski space. This requires the scalar field/mass evolution instead of the scale factor evolution in order to explain cosmological redshift. It is interesting that like in ekpyrotic/cyclic models, a possible transition through a singularity in conformal cosmology in the string frame takes place in the weak coupling regime.Comment: REVTEX4, 12 pages, an improved version, references adde

Cosmic Microwave Background Temperature and Polarization Anisotropy in Brans-Dicke Cosmology

We develop a formalism for calculating cosmic microwave background (CMB) temperature and polarization anisotropies in cosmological models with Brans-Dicke gravity. We then modify publicly available Boltzmann codes to calculate numerically the temperature and polarization power spectra. Results are illustrated with a few representative models. Comparing with the general-relativistic model with the same cosmological parameters, both the amplitude and the width of the acoustic peaks are different in the Brans-Dicke models. We use a covariance-matrix calculation to investigate whether the effects of Brans-Dicke gravity are degenerate with those of variation in other cosmological parameters and to simultaneously determine whether forthcoming CMB maps might be able to distinguish Brans-Dicke and general-relativistic cosmology. Although the predicted power spectra for plausible Brans-Dicke models differ from those in general relativity only slightly, we find that MAP and/or the Planck Surveyor may in principle provide a test of Brans-Dicke theory that is competitive to solar-system tests. For example, if all other parameters except for the CMB normalization are fixed, a value of the Brans-Dicke parameter omega as large as 500 could be identified with MAP, and for Planck, values as large as omega \simeq3000 could be identified; these sensitivities are decreased roughly by a factor of 3 if we marginalize over the baryon density, Hubble constant, spectral index, and reionization optical depth. In more general scalar-tensor theories, omega may evolve with time, and in this case, the CMB probe would be complementary to that from solar-system tests.Comment: 27 pages, 10 figures, typeset using RevTe

Gravitational wave astronomy: the definitive test for the "Einstein frame versus Jordan frame" controversy

The potential realization of a gravitational wave (GW) astronomy in next years is a great challenge for the scientific community. By giving a significant amount of new information, GWs will be a cornerstone for a better understanding of the universe and of the gravitational physics. In this paper the author shows that the GW astronomy will permit to solve a captivating issue of gravitation as it will be the definitive test for the famous "Einstein frame versus Jordan frame" controversy. In fact, we show that the motion of the test masses, i.e. the beam splitter and the mirror in the case of an interferometer, which is due to the scalar component of a GW, is different in the two frames. Thus, if a consistent GW astronomy will be realized, an eventual detection of signals of scalar GWs will permit to discriminate among the two frames. In this way, a direct evidence from observations will solve in an ultimate way the famous and long history of the "Einstein frame versus Jordan frame" controversy.Comment: Corrected latest typos. This definitive version matches the version to be published in Astroparticle Physics 34 (2011) 412-419, 22 page

Collapse to Black Holes in Brans-Dicke Theory: II. Comparison with General Relativity

We discuss a number of long-standing theoretical questions about collapse to black holes in the Brans-Dicke theory of gravitation. Using a new numerical code, we show that Oppenheimer-Snyder collapse in this theory produces black holes that are identical to those of general relativity in final equilibrium, but are quite different from those of general relativity during dynamical evolution. We find that there are epochs during which the apparent horizon of such a black hole passes {\it outside\/} the event horizon, and that the surface area of the event horizon {\it decreases\/} with time. This behavior is possible because theorems which prove otherwise assume $R_{ab}l^al^b \ge 0$ for all null vectors $l^a$. We show that dynamical spacetimes in Brans-Dicke theory can violate this inequality, even in vacuum, for any value of $\omega$.Comment: 24 pages including figures, uuencoded gz-compressed postscript, Submitted to Phys Rev

Phase Transition of Black Holes in Brans–Dicke Born–Infeld Gravity through Geometrical Thermodynamics

Using the geometrical thermodynamic approach, we study phase transition of Brans–Dicke Born–Infeld black holes. We apply introduced methods and describe their shortcomings. We also use the recently proposed new method and compare its results with those of canonical ensemble. By considering the new method, we find that its Ricci scalar diverges in the places of phase transition and bound points. We also show that the bound point can be distinguished from the phase transition points through the sign of thermodynamical Ricci scalar around its divergencies

Dilatonic Dark Matter and Unified Cosmology -- a New Paradigm --

We study the possibility that the dilaton -- the fundamental scalar field which exists in all the existing unified field theories -- plays the role of the dark matter of the universe. We find that the condition for the dilaton to be the dark matter strongly restricts its mass to be around 0.5 keV or 270 MeV. For the other mass ranges, the dilaton either undercloses or overcloses the universe. The 0.5 keV dilaton has the free-streaming distance of about 1.4 Mpc and becomes an excellent candidate of a warm dark matter, while the 270 MeV one has the free-streaming distance of about 7.4 pc and becomes a cold dark matter. We discuss the possible ways to detect the dilaton experimentallyComment: 19 pages, 5 figure, Talk given at the IIth RESCEU International Symposium on Dark Matter in the Universe and its Direct Detections, 1996. Proceedings published by Academic Press, Tokyo, edited by K sat