This paper presents a new exact inflationary solution to the non-minimMly coupled scalar field. The inflation is driven by the evolution of a scalar field with inflation potential V（φ） = （λ/4）φ4 ＋ b1φ2 ＋ b2 ＋ b3φ-2 ＋ b4φ-4. The spectral index of the scalar density fluctuations ns is consistent with the result of WMAP3 （Wilkinson Microwave Anisotropy Probe 3） for ACDM （Lambda-Cold Dark Matter）. This model relaxes the constraint to the quartic coupling constant. And it can enter smoothly into a radiation-dominated stage when inflation ends.
Based on the anomaly cancellation method, initiated by Robinson and Wilczek, we investigates Hawking radiation from the modified Schwarzschild black hole from gravity＇s rainbow from the anomaly point of view. Unlike the general Schwarzschild space-time, the metric of this black hole depends on the energies of probes. The obtained result shows to restore the underlying general covariance at the quantum level in the effective field, the covariant compensating flux of energy-momentum tensor, which is related to the energies of the probes, should precisely equal to that of a （1 ＋ 1）-dimensional blackbody at the Hawking temperature.
This paper discusses Hawking radiation from the charged and magnetized Bafiados-Teitelboim-Zanelli （BTZ） black hole from the viewpoint of anomaly, initiated by Robinson and Wilczek recently. It reconstructs the electromagnetic field tensor and the Lagrangian of the field corresponding to the source with electric and magnetic charges to redefine an equivalent charge and gauge potential. It employs the covariant anomaly cancellation method to determine the compensating fluxes of charge flow and energy-momentum tensor, which are shown to match with those of the 2- dimensional blackbody radiation at the Hawking temperature exactly.
