International Journal of Modern Physics D

Using the instanton representation method, we re-construct graviton solutions about de Sitter spacetime. We have used this example as a testing arena to expose the internal structure of the method and to establish that it works for known solutions. This paper is a precursor for its application to the construction of new General Relativity solutions in future work.

We present the "classical" Nielsen–Olesen vortex solution on a warped 5-dimensional spacetime, where we solved the effective 4-dimensional equations from the 5-dimensional equations together with the junction and boundary conditions. 4-dimensional cosmic strings show some serious problems concerning the mechanism of string smoothing related to the string mass per unit length, Gμ ≤ 10^-6. Moreover, there is no observational evidence of axially symmetric lensing effect caused by cosmic strings. Also super-massive cosmic strings (Gμ ≳ 1), predicted by superstring theory, possess some problems. They are studied because the universe may have undergone phase transitions at scales much higher than the GUT scale. But Gμ ≳ 1 is far above observational bounds, so one needs an inflationary scenario to smooth them out. Further, it is believed that these super-massive strings never extended to macroscopic size. Brane world models could overcome these problems. Gμ could be warped down to GUT scale, even if its value was at the Planck scale.

In our warped cosmic string model, where the string mass per unit length in the bulk can be of order of the Planck scale, we find that the 4-dimensional brane spacetime is exponential warped down. Moreover, asymptotically the induced 4-dimensional spacetime does not show conical behavior. So there is no angle deficit compared to its value in the bulk and the spacetime seems to be unphysical, at least under fairly weak assumptions on the stress–energy tensor and without a positive brane tension. The results are confirmed by numerical solutions of the field equations.

Based on Baumgarte–Shapiro–Shibata–Nakamura formalism and moving puncture method, we demonstrate the first numerical evolutions of the interaction between positive and negative mass objects. Using the causal property of general relativity, we set our computational domain around the positive mass black hole while excluding the region around the naked singularity introduced by the negative mass object. Besides the usual Sommerfeld numerical boundary condition, an approximate boundary condition is proposed for this nonasymptotically-flat computational domain. Careful checks show that either boundary condition introduces smaller error than the numerical truncation errors. This is consistent with the causal property of general relativity. Except for the numerical truncation error and round-off error, our method gives an exact solution to the full Einstein's equation for a portion of spacetime with two objects whose masses have opposite signs. So our method opens the door for numerical explorations with negative mass objects. Based on this method, we investigate the Newtonian limit of spacetime with two objects whose masses have opposite sign. Our result implies that this spacetime does have a Newtonian limit which corresponds to a negative mass particle chasing a positive mass particle. This result sheds some light on an interesting debate about the Newtonian limit of a spacetime with positive and negative point masses.

We examine the inflationary modes in the cubic curvature theories in the context of asymptotically safe gravity. On the phase space of the Hubble parameter, there exists a critical point which corresponds to the slow-roll inflation in Einstein frame. Most of the e-foldings are attained around the critical point for each inflationary trajectories. If the coupling constants g_i have the parametric relations generated as the power of the relative energy scale of inflation H₀ to the cutoff Λ, a successful inflation with more than 60 e-foldings occurs near the critical point.

We have studied a DGP-inspired braneworld scenario where the idea of Lorentz invariance violation has been combined into a specifying preferred frame that embed a dynamical normal vector field to brane. We propose the Lorentz violating DGP brane models with enough parameters can explain crossing of phantom divide line. Also we have considered the model for proper cosmological evolution that is according to the observed behavior of the equation of state. In other view point, we have described a Rip singularity solution of model that occur in this model.

We re-examine the growth index of the concordance Λ cosmology in the light of the latest 6dF and WiggleZ data. In particular, we investigate five different models for the growth index γ, by comparing their cosmological evolution using observational data of the growth rate of structure formation at different redshifts. Performing a joint likelihood analysis of the recent supernovae type Ia data, the Cosmic Microwave Background shift parameter, Baryonic Acoustic Oscillations and the growth rate data, we determine the free parameters of the γ(z) parametrizations and we statistically quantify their ability to represent the observations. We find that the addition of the 6dF and WiggleZ growth data in the likelihood analysis improves significantly the statistical results. As an example, considering a constant growth index we find Ω_m0 = 0.273 ± 0.011 and .

Motivated by some earlier works [G. Izquierdo and D. Pavon, Phys. Lett. B 639 (2006) 1; H. M. Sadjadi, Phys. Lett. B 645 (2007) 108.] dealing with the study of generalized second law (GSL) of thermodynamics for a system comprising of a Schwarzschild black hole accreting a test nonself-gravitating fluid namely phantom energy in FRW universe, we extend them when the entropy of horizons of black hole and the cosmological undergo quantum corrections. Two types of such corrections are relevant here including logarithmic and power-law, while both are motivated from different theoretical backgrounds. We obtain general mathematical conditions for the validity of GSL in each case. Further we find that GSL restricts the mass of black hole for accretion of phantom energy. As such we obtain upper bounds on the mass of black hole above which the black hole cannot accrete the phantom fluid, otherwise the GSL is violated.