Higher-dimensional theories imply that some constants, such as the gravitational constant and the strength of the gauge-couplings, are not fundamental constants. Instead they are related to the sizes of the extra-dimensional space, which are moduli fields in the fourdimensional effective theory. We study the cosmological evolution of the moduli fields appearing in brane world scenarios and discuss the implications for varying constants.

We study cosmological consequences of non-constant brane world moduli in five dimensional brane world models with bulk scalars and two boundary branes. We focus on the case where the brane tension is an exponential function of the bulk scalar field, U b ∝ exp (αφ). In the limit α → 0, the model reduces to the two-brane model of Randall-Sundrum, whereas larger values of α allow for a less warped bulk geometry. Using the moduli space approximation we derive the four-dimensional low-energy effective action from a supergravity-inspired five-dimensional theory.For arbitrary values of α, the resulting theory has the form of a bi-scalar-tensor theory. We show that, in order to be consistent with local gravitational observations, α has to be small (less than 10−2 ) and the separation of the branes must be large. We study the cosmological evolution of the interbrane distance and the bulk scalar field for different matter contents on each branes. Our findings indicate that attractor solutions exist which drive the moduli fields towards values consistent with observations. The efficiency of the attractor mechanism crucially depends on the matter content on each branes. In the five-dimensional description, the attractors correspond to the motion of the negative tension brane towards a bulk singularity, which signals the eventual breakdown of the four-dimensional description and the necessity of a better understanding of the bulk singularity.

We discuss the effect of the time evolution of extra dimensions on CMB anisotropies and largescale structure formation. We study the impact of scalar fields in a low-energy effective description of a general class of brane world models on the temperature anisotropy power spectrum. We show that when the coupling between these scalar fields and matter evolves over cosmological timescales, current observations of the CMB anisotropies can constrain primordial values of the fields in a manner complementary to local, late-time tests of gravity. We also present the effect of these fields on the polarization anisotropy spectra and the growth of large-scale structure, showing that future CMB observations will constrain theories of the Universe involving extra dimensions even further.

The interaction between the Earth's magnetic field and the solar wind plasma results in a natural plasma confinement system which stores energy. Dissipation of this energy through Joule heating in the ionosphere can be studied via the Auroral Electrojet (AE ) index. The apparent broken power law form of the frequency spectrum of this index has motivated investigation of whether it can be described as fractal coloured noise. One frequently-applied test for selfaffinity is to demonstrate linear scaling of the logarithm of the structure function of a time series with the logarithm of the dilation factor λ. We point out that, while this is conclusive when applied to signals that are self-affine over many decades in λ, such as Brownian motion, the slope deviates from exact linearity and the conclusions become ambiguous when the test is used over shorter ranges of λ. We demonstrate that non self-affine time series made up of random pulses can show near-linear scaling over a finite dynamic range such that they could be misinterpreted as being self-affine. In particular, we show that pulses with functional forms such as those identified by Weimer within the AL index, from which AE is partly derived, will exhibit nearly linear scaling over ranges similar to those previously shown for AE and AL. The value of the slope, related to the Hurst exponent for a self-affine fractal, seems to be a more robust discriminator for fractality, if other information is available.

The behaviour of the distance between two branes (the `radion') in a braneworld model with a bulk scalar field is investigated. We show that the BPS conditions of supergravity ensure that the dynamics of the scalar field and the radion are not independent; we derive the four-dimensional effective action, showing that the effective theory is of scalar--tensor nature, coupling the radion to four-dimensional gravity.Comment: 13 pages, LaTe