**Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes**

We develop techniques to compute higher loop string amplitudes for twisted*N*=2 theories with*ĉ*=3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. [1]

**Reconstruction of a Scalar-Tensor Theory of Gravity in an Accelerating Universe**

The present acceleration of the Universe strongly indicated by recent observational data can be modeled in the scope of a scalar-tensor theory of gravity. We show that it is possible to determine the structure of this theory along with the present density of dustlike matter from two observable cosmological functions: the luminosity distance and the linear density perturbation in the dustlike matter component as functions of redshift. [2]

**Eddington’s Theory of Gravity and Its Progeny**

We resurrect Eddington’s proposal for the gravitational action in the presence of a cosmological constant and extend it to include matter fields. We show that the Newton-Poisson equation is modified in the presence of sources and that charged black holes show great similarities with those arising in Born-Infeld electrodynamics coupled to gravity. [3]

**Bianchi Type-IX Cosmological Model with a Perfect Fluid in f(R) Theory of Gravity**

Bianchi type-IX space-time is considered in the framework of the ƒ(*R*) theory of gravity when the source of the energy momentum tensor is a perfect fluid. The cosmological model is obtained by using the condition that the expansion scalar (*θ*) is proportional to the shear scalar (*σ)*. The physical and geometrical properties of the model are also discussed. [4]

**Plane Symmetric Vacuum Cosmological Model with a Special form of Deceleration Parameter in ƒ(R) Theory of Gravity**

In this paper we have obtained vacuum solutions of the plane symmetric space-time in ƒ(*R*) gravity. The general solutions of the field equations of plane symmetric space-time have been obtained under the assumption of special form of deceleration parameter. The physical and geometrical aspect of the model is also discussed. [5]

Reference

[1] Bershadsky, M., Cecotti, S., Ooguri, H. and Vafa, C., 1994. Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes. *Communications in Mathematical Physics*, *165*(2), pp.311-427.

[2] Boisseau, B., Esposito-Farese, G., Polarski, D. and Starobinsky, A.A., 2000. Reconstruction of a scalar-tensor theory of gravity in an accelerating universe. *Physical Review Letters*, *85*(11), p.2236.

[3] Banados, M. and Ferreira, P.G., 2010. Eddington’s theory of gravity and its progeny. *Physical review letters*, *105*(1), p.011101.

[4] R. Ghate, H. and S. Sontakke, A. (2015) “Bianchi Type-IX Cosmological Model with a Perfect Fluid in f(R) Theory of Gravity”, *Physical Science International Journal*, 7(3), pp. 214-222. doi: 10.9734/PSIJ/2015/18515.

[5] B. Raut, V., S. Adhav, K. and K. Joshi, D. (2014) “Plane Symmetric Vacuum Cosmological Model with a Special form of Deceleration Parameter in ƒ(R) Theory of Gravity”, *Physical Science International Journal*, 5(1), pp. 74-80. doi: 10.9734/PSIJ/2015/13999.