Infrared divergences in scattering amplitudes arise when a loop momentum becomes collinear with a massless external momentum p. In gauge theories, it is known that the L-loop logarithm of a planar amplitude has much softer infrared singularities than the L-loop amplitude itself. We argue that planar amplitudes in N = 4 super-Yang-Mills theory enjoy softer than expected behavior as p already at the level of the integrand. Moreover, we conjecture that the four-point integrand can be uniquely determined, to any loop-order, by imposing the correct soft-behavior of the logarithm together with dual conformal invariance and dihedral symmetry. We use these simple criteria to determine explicit formulae for the four-point integrand through seven-loops, finding perfect agreement with previously known results through five-loops. As an input to this calculation, we enumerate all four-point dual conformally invariant (DCI) integrands through seven-loops, an analysis which is aided by several graph-theoretic theorems we prove about general DCI integrands at arbitrary looporder. The six-and seven-loop amplitudes receive non-zero contributions from 229 and 1873 individual DCI diagrams respectively. PDF and Mathematica files with all of our results are provided at

The exact solutions of the field equations are obtained by using the gamma law equation of state p = (γ − 1)ρ in which the parameter γ depends on scale factor R. The fundamental form of γ (R) is used to analyze a wide range of phases in cosmic history: inflationary phase and radiation-dominated phase. The corresponding physical interpretations of cosmological solutions are also discussed in the framework of (n + 2) dimensional space time.

We have investigated cosmological model with strange quark matter attached to the string cloud in general theory of gravitation for Axially Symmetric space time. The model is obtained with the help of special law of variation for Hubble parameter proposed by Bermann (Nuovo Cimento B 74:182, 1983). Also, some physical and kinematics properties of the model are discussed.

An exact higher dimensional LRS Bianchi type-I cosmological model is obtained in presence of thick domain walls in a scalar tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A113:467, 1985). Some physical and kinematical properties of the models are also discussed.