Limits on the Time Evolution of Space Dimensions from Newton's Constant

Limits are imposed upon the possible rate of change of extra spatial dimensions in a decrumpling model Universe with time variable spatial dimensions (TVSD) by considering the time variation of (1+3)-dimensional Newton's constant. Previous studies on the time variation of (1+3)-dimensional Newton's constant in TVSD theory had not been included the effects of the volume of the extra dimensions and the effects of the surface area of the unit sphere in D-space dimensions. Our main result is that the absolute value of the present rate of change of spatial dimensions to be less than about 10^{-14}yr^{-1}. Our results would appear to provide a prima facie case for ruling the TVSD model out. We show that based on observational bounds on the present-day variation of Newton's constant, one would have to conclude that the spatial dimension of the Universe when the Universe was at the Planck scale to be less than or equal to 3.09. If the dimension of space when the Universe was at the Planck scale is constrained to be fractional and very close to 3, then the whole edifice of TVSD model loses credibility.Comment: 22 pages, accepted for publication in Int.J.Mod.Phys.

A note on light velocity anisotropy

It is proved that in experiments on or near the Earth, no anisotropy in the one-way velocity of light may be detected. The very accurate experiments which have been performed to detect such an effect are to be considered significant tests of both special relativity and the equivalence principleComment: 8 pages, LaTex, Gen. Relat. Grav. accepte

Chaotic Inflation with Time-Variable Space Dimensions

Assuming the space dimension is not constant but decreases during the expansion of the Universe, we study chaotic inflation with the potential $m^2\phi^2/2$. Our investigations are based on a model Universe with variable space dimensions. We write down field equations in the slow-roll approximation, and define slow-roll parameters by assuming the number of space dimensions decreases continuously as the Universe expands. The dynamical character of the space dimension shifts the initial and final value of the inflaton field to larger values. We obtain an upper limit for the space dimension at the Planck length. This result is in agreement with previous works for the effective time variation of the Newtonian gravitational constant in a model Universe with variable space dimensions.Comment: 19 pages, To be published in Int.J.Mod.Phys.D. Minor changes to match accepted versio

Power-law Parameterized Quintessence Model

We introduce a power-law parameterized quintessence model for the dark energy which accelerate universe at the low redshifts while behaves as an ordinary matter for the early universe. We construct a unique scalar potential for this parameterized quintessence model. As the observational test, the Supernova Type Ia (SNIa) Gold sample data, size of baryonic acoustic peak from Sloan Digital Sky Survey (SDSS), the position of the acoustic peak from the CMB observations and structure formation from the 2dFGRS survey are used to constrain the parameters of the quintessence model. The best fit parameters indicates that the equation of state of this model at the present time is less than one $(w_0<-1)$ which violates the energy condition in General Relativity. Finally we compare the age of old objects with age of universe in this model.Comment: 11 pages, 17 figures, submitted to Phys. Rev.

Radiation from the LTB black hole

Does a dynamical black hole embedded in a cosmological FRW background emit Hawking radiation where a globally defined event horizon does not exist? What are the differences to the Schwarzschild black hole? What about the first law of black hole mechanics? We face these questions using the LTB cosmological black hole model recently published. Using the Hamilton-Jacobi and radial null geodesic-methods suitable for dynamical cases, we show that it is the apparent horizon which contributes to the Hawking radiation and not the event horizon. The Hawking temperature is calculated using the two different methods giving the same result. The first law of LTB black hole dynamics and the thermal character of the radiation is also dealt with.Comment: 9 pages, revised version, Europhysics Letter 2012 97 2900