Under the assumption that the variations of parameters of nature and the current acceleration of the universe are related and governed by the evolution of a single scalar field, we show how information can be obtained on the nature of dark energy fro
m observational detection of (or constraints on) cosmological variations of the fine structure constant and the proton-to-electron mass ratio. We also comment on the current observational status, and on the prospects for improvements with future spectrographs such as ESPRESSO and CODEX.
Non-local equations of motion contain an infinite number of derivatives and commonly appear in a number of string theory models. We review how these equations can be rewritten in the form of a diffusion-like equation with non-linear boundary conditio
ns. Moreover, we show that this equation can be solved as an initial value problem once a set of non-trivial initial conditions that satisfy the boundary conditions is found. We find these initial conditions by looking at the linear approximation to the boundary conditions. We then numerically solve the diffusion-like equation, and hence the non-local equations, as an initial value problem for the full non-linear potential and subsequently identify the cases when inflation is attained.
We investigate the behaviour of tensor fluctuations in Loop Quantum Cosmology, focusing on a class of scaling solutions which admit a near scale-invariant scalar field power spectrum. We obtain the spectral index of the gravitational field perturbati
ons, and find a strong blue tilt in the power spectrum with $n_t approx 2$. The amplitude of tensor modes are, therefore, suppressed by many orders of magnitude on large scales compared to those predicted by the standard inflationary scenario where $n_t approx 0$.
There has been considerable recent interest in solving non-local equations of motion which contain an infinite number of derivatives. Here, focusing on inflation, we review how the problem can be reformulated as the question of finding solutions to a
diffusion-like partial differential equation with non-linear boundary conditions. Moreover, we show that this diffusion-like equation, and hence the non-local equations, can be solved as an initial value problem once non-trivial initial data consistent with the boundary conditions is found. This is done by considering linearised equations about any field value, for which we show that obtaining solutions using the diffusion-like equation is equivalent to solving a local but infinite field cosmology. These local fields are shown to consist of at most two canonically normalized or phantom fields together with an infinite number of quintoms. We then numerically solve the diffusion-like equation for the full non-linear case for two string field theory motivated models.
We investigate the dynamics of super-inflation in t
