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We study the matter density fluctuations in the running cosmological constant (RCC) model using linear perturbations in the longitudinal gauge. Using this observable we calculate the growth rate of structures and the matter power spectrum, and compare them with the $SDSS$ data and other available data of the linear growth rate. The distribution of collapsed structures may also constraints models of dark energy. It is shown that RCC model enhances departures from the $Lambda CDM$ model for both cluster number and cumulative cluster number predicted. In general increasing the characteristic parameter $ u$ leads to significant growth of the cluster number. In general, we found that the theory of perturbations provides a good tool to distinguish the new model $RCC$ of the standard cosmological model $Lambda CDM$.
Theoretically, the running of the cosmological constant in the IR region is not ruled out. On the other hand, from the QFT viewpoint, the energy released due to the variation of the cosmological constant in the late universe cannot go to the matter s
We probe the cosmological consequences of a recently proposed class of solutions to the cosmological constant problem. In these models, the universe undergoes a long period of inflation followed by a contraction and a bounce that sets the stage for t
We argue that the instability of Euclidean Einstein gravity is an indication that the vacuum is non perturbative and contains a condensate of the metric tensor in a manner reminiscent of Yang-Mills theories. As a simple step toward the characterizati
Calculations of the evolution of cosmological perturbations generally involve solution of a large number of coupled differential equations to describe the evolution of the multipole moments of the distribution of photon intensities and polarization.
It is well known that string theories naturally compactify on anti-de Sitter spaces, and yet cosmological observations show no evidence of a negative cosmological constant in the early Universes evolution. In this letter we present two simple nonloca