We study the null geodesics in a static circularly symmetric (SCS) black hole spacetime which is a solution in the (2 + 1)-dimensional massive gravity proposed by Bergshoeff, Hohm and Townsend (BHT massive gravity). We obtain analytic solutions for the null geodesic equation in the SCS black hole background and find the explicit form of deflection angles. We see that for various values of the impact parameter, the deflection angle can be positive, negative or even zero in this black hole spacetime. The negative deflection angle indicates the repulsive behavior of the gravity which comes from the gravitational hair parameter that is the most characteristic quantity of the BHT massive gravity.

We investigated the cosmology in a higher-curvature gravity where the dimensionality of spacetime gives rise to only quantitative difference, contrary to Einstein gravity. We found exponential type solutions for flat isotropic and homogeneous vacuum universe for the case in which the higher-curvature term in the Lagrangian density is quadratic in the scalar curvature, ξR 2 . The solutions are classified according to the sign of the cosmological constant, Λ, and the magnitude of Λξ. For these solutions 3-dimensional space has a specific feature in that the solutions are independent of the higher curvature term. For the universe filled with perfect fluid, numerical solutions are investigated for various values of the parameter ξ. Evolutions of the universes in different dimensionality of spacetime are compared.