We propose an idea in spectroscopy to search for extra spatial dimensions as well as to detect the possible deviation from Newton’s inverse-square law at small scale,and we take high-Z hydro-genic systems and muonic atoms as illustrations.The relevant experiments might help to explore more than two extra dimensions scenario in ADD’s brane world model and to set constraints for fundamental parameters such as the size of extra dimensions.

The classical tests of general relativity-light deflection, time delay and perihelion shift-are applied,along with the geodetic precession test,to the five-dimensional extension of the theory known as Kaluza-Klein gravity,using an analogue of the four-dimensional Schwarzschild metric.The perihelion advance and geodetic precession calculations are generalized for the first time to situations in which the components of momentum and spin along the extra coordinate do not vanish. Existing data on light-bending around the Sun using long-baseline radio interferometry,ranging to Mars using the Viking lander,and the perihelion precession of Mercury all constrain a small parameter b associated with the extra part of the metric to be less than |b| < 0.07 in the solar system.An order-of-magnitude increase in sensitivity is possible from perihelion precession,if better limits on solar oblateness become available.Measurement of geodetic precession by the Gravity Probe B satellite will improve this significantly,probing values of b with an accuracy of one part in 104 or more.

Recent observations of Type Ia supernovae provide evidence for the acceleration of our universe,which leads to the possibility that the universe is entering an inflationary epoch.We simulate it under a “big bounce” model,which contains a time variable cosmological “constant” that is derived from a higher dimension and manifests itself in 4D spacetime as dark energy.By properly choosing the two arbitrary functions contained in the model,we obtain a simple exact solution in which the evolution of the universe is divided into several stages.Before the big bounce, the universe contracts from a Λ-dominated vacuum,and after the bounce,the universe expands.In the early time after the bounce,the expansion of the universe is decelerating.In the late time after the bounce,dark energy (i.e., the variable cosmological “constant”) overtakes dark matter and baryons,and the expansion enters an accelerating stage.When time tends to infinity,the contribution of dark energy tends to two third of the total energy density of the universe,qualitatively in agreement with observations.

Exact global solutions of five-dimensional cosmological models compactified on a S1/Z2 orbifold with two 3-branes are presented,and evolution of a simple model is studied.It is found that on all 4D spacetime hypersurfaces,except a singular one,the expanding universe was started not from a big bang but from a big bounce,and before the bounce the universe was in a deflationary contracting phase.It is also found that whether the energy density on the second brane is positive,zero,or negative depends on the size of the fifth dimension.

We extend the classical general relativistic theory of measurement to include the possibility of existence of higher dimensions.The intrusion of these dimensions in the spacetime interval implies that the inertial mass of a particle in general varies along its worldline if the observations are analyzed assuming the existence of only the four spacetime dimensions.The variations of mass and spin are explored in a simple 5D Kaluza-Klein model.