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

2PI Effective Action and Evolution Equations of N = 4 super Yang-Mills

We employ nPI effective action techniques to study N = 4 super Yang-Mills, and write down the 2PI effective action of the theory. We also supply the evolution equations of two-point correlators within the theory.Comment: 16 pages, 6 figures. Figure 2 replaced, approximation scheme clarified, references adde

Saturation and Universality in QCD at small x

We find approximate solutions to the renormalization group equation which governs the quantum evolution of the effective theory for the Color Glass Condensate. This is a functional Fokker-Planck equation which generates in particular the non-linear evolution equations previously derived by Balitsky and Kovchegov within perturbative QCD. In the limit where the transverse momentum of the external probe is large compared to the saturation momentum, our approximations yield the Gaussian Ansatz for the effective action of the McLerran-Venugopalan model. In the opposite limit, of a small external momentum, we find that the effective theory is governed by a scale-invariant universal action which has the correct properties to describe gluon saturation.Comment: 14 pages; further clarifications and new material in the discussion of the saturation regim

History of cosmic evolution with modified Gauss-Bonnet-dilatonic coupled term

Gauss-Bonnet-dilatonic coupling in four dimension plays an important role to explain late time cosmic evolution. However, this term is an outcome of low energy string effective action and thus ought to be important in the early universe too. Unfortunately, phase-space formulation of such a theory does not exist in the literature due to branching. We therefore consider a modified theory of gravity, which contains a nonminimally coupled scalar-tensor sector in addition to higher order scalar curvature invariant term with Gauss-Bonnet-dilatonic coupling. Such an action unifies early inflation with late-time cosmic acceleration. Quantum version of the theory is also well-behaved.Comment: 13 pages, 5 figures, To appear in EPJC (2017