We shortly review the metric formalism for the f(R) gravity. Based on the metric formalism, we study the spherically symmetric static empty space solutions with the gravity Lagrangian L = R+λR 2 . We found the general metric that described the static empty space with the spherically symmetry. Our result is more general than Schwarzschild solution, specially the predicted metric is perturbed Schwarzschild metric of the Einstein theory. | Communications in Physics, Vol. 24, No. 3S2 (2014), pp. 23-28 DOI: A SPHERICALLY SYMMETRIC SOLUTION OF R + λ R2 GRAVITY BUI QUYET THANG Post graduate department, Institute of Physics, Vietnam Academy of Science and Technology DO THI HUONG Institute of Physics, Vietnam Academy of Science and Technology E-mail: dthuong@ Received 20 June 2014 Accepted for publication 20 August 2014 Abstract. We shortly review the metric formalism for the f (R) gravity. Based on the metric formalism, we study the spherically symmetric static empty space solutions with the gravity Lagrangian L = R+λ R2 . We found the general metric that described the static empty space with the spherically symmetry. Our result is more general than Schwarzschild solution, specially the predicted metric is perturbed Schwarzschild metric of the Einstein theory. Keywords: Einstein theory, Extended Einstein theory, Schwarzschild metric, Extended Schwarzschild metric I. INTRODUCTION Early time inflation is a very attractive idea in order to solve many serious problems of the Hot Big Bang cosmological model originating in the mystery of the initial conditions of our Universe such as flatness, horizon, monopole problems [1]. The inflation can be created by only one scalar field. In particular, many simplest models give different predictions about the scalar perturbation spectrum ns and the ratio r of squared amplitudes of tensor and scalar perturbations. Thus the predicted results can be distinguished experimentally by CMB observations [2]. On the contrary, if predictions for (ns , r) coincide with experimental results, it is very difficult to determine which model is realized in Nature. We would like to emphasize that the scalar-field models of inflation correspond to a modification of the energy-momentum tensor in Einstein equations. However there is another approach to explain the acceleration of the universe. This can be done by modifying gravitational .
