A Renormalisation Group Study of Three Dimensional Turbulence

We study the three dimensional Navier-Stokes equation with a random Gaussian force acting on large wavelengths. Our work has been inspired by Polyakov's analysis of steady states of two dimensional turbulence. We investigate the time evolution of the probability law of the velocity potential. Assuming that this probability law is initially defined by a statistical field theory in the basin of attraction of a renormalisation fixed point, we show that its time evolution is obtained by averaging over small scale features of the velocity potential. The probability law of the velocity potential converges to the fixed point in the long time regime. At the fixed point, the scaling dimension of the velocity potential is determined to be ${-{4\over 3}}$. We give conditions for the existence of such a fixed point of the renormalisation group describing the long time behaviour of the velocity potential. At this fixed point, the energy spectrum of three dimensional turbulence coincides with a Kolmogorov spectrum.Comment: 8 pages , tex fil

Screening fifth forces in k-essence and DBI models

New fifth forces have not yet been detected in the laboratory or in the solar system, hence it is typically difficult to introduce new light scalar fields that would mediate such forces. In recent years it has been shown that a number of non-linear scalar field theories allow for a dynamical mechanism, such as the Vainshtein and chameleon ones, that suppresses the strength of the scalar fifth force in experimental environments. This is known as screening, however it is unclear how common screening is within non-linear scalar field theories. k-essence models are commonly studied examples of non-linear models, with DBI as the best motivated example, and so we ask whether these non-linearities are able to screen a scalar fifth force. We find that a Vainshtein-like screening mechanism exists for such models although with limited applicability. For instance, we cannot find a screening mechanism for DBI models. On the other hand, we construct a large class of k-essence models which lead to the acceleration of the Universe in the recent past for which the fifth force mediated by the scalar can be screened.Comment: 26 page

Brane World Cosmology, the CMB and the Radion

Recent developments in the theory of extra dimensions have opened up avenues to confront such theories with cosmological tests. We discuss a brane-world model with a bulk scalar field, motivated by supergravity. The low-energy effective action is derived and physical constraints on the parameters of the model discussed. The cosmological evolution of the brane-world moduli is investigated and it is shown that one of the moduli is a quintessence field. The CMB predictions are computed. Finally, the possibility that the radion field in brane-worlds could be a chameleon field is investigated.Comment: 11 pages, 6 figures, to appear in the proceedings of the DPU Workshop: The Density Fluctuations in the Universe: Beyond the Inflaton Paradigm (Athens, June 2004

An Environmental Variation of Constants

Models of modified gravity, whereby local tests of gravity are evaded thanks to a screening mechanism of the chameleon or Damour-Polyakov types, lead to a spatial variation of the particle masses and the fine structure constant. This is triggered by the environmental dependence of the value of the scalar field whose presence modifies gravity. In dense media, the field settles at a density dependent value while in sparse environments it takes the background cosmological value. We estimate that the maximal deviation of constants from their present values is constrained by local tests of gravity, and must be less than $10^{-6}$.Comment: 14 pages, 7 figures, published versio

The Supermoduli Space of Matrix String Theory

We study matrix string scattering amplitudes and matrix string instantons on a marked Riemann surface in the limit of a vanishing string coupling constant. We give an explicit parameterization of the moduli space of such instantons. We also give a description of the set of fermionic supermoduli. The integration over the supermoduli leads to the inclusion of picture changing operators at the interaction points. Finally we investigate the large N limit of the measure on the instanton moduli space and show its convergence to the Weil-Petersson measure on the moduli space of marked Riemann surfaces.Comment: 30 Pages, Latex, 2 Postscript figure

Lorentz Invariance Violation in Modified Gravity

We consider an environmentally dependent violation of Lorentz invariance in scalar-tensor models of modified gravity where General Relativity is retrieved locally thanks to a screening mechanism. We find that fermions have a modified dispersion relation and would go faster than light in an anisotropic and space-dependent way along the scalar field lines of force. Phenomenologically, these models are tightly restricted by the amount of Cerenkov radiation emitted by the superluminal particles, a constraint which is only satisfied by chameleons. Measuring the speed of neutrinos emitted radially from the surface of the earth and observed on the other side of the earth would probe the scalar field profile of modified gravity models in dense environments. We argue that the test of the equivalence principle provided by the Lunar ranging experiment implies that a deviation from the speed of light, for natural values of the coupling scale between the scalar field and fermions, would be below detectable levels, unless gravity is modified by camouflaged chameleons where the field normalisation is environmentally dependent.Comment: 8 pages, extended discussio

On Brane Cosmology and Naked Singularities

Brane-world singularities are analysed, emphasizing the case of supergravity in singular spaces where the singularity puzzle is naturally resolved. These naked singularities are either time-like or null, corresponding to the finite or infinite amount of conformal time that massless particles take in order to reach them. Quantum mechanically we show that the brane-world naked singularities are inconsistent. Indeed we find that time-like singularities are not wave-regular, so the time-evolution of wave packets is not uniquely defined in their vicinity, while null singularities absorb incoming radiation. Finally we stress that for supergravity in singular spaces there is a topological obstruction, whereby naked singularities are necessarily screened off by the second boundary brane.Comment: 12 page