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Nelson Nunes Dynamical systems in Cosmology Scalar fields play a central role both in particle physics and in cosmology. Typical examples are the moduli, the inflaton and the quintessence fields. Considering these and other examples, it is important to understand the features that the potentials for these scalar fields can take. In an early article [1] I developed a framework to study the phase space of a system consisting of a minimally coupled scalar field rolling down an arbitrary potential with varying logarithmic slope and a background fluid, in a cosmological setting. In the search for viable models of inflation, it has been shown that exponential potentials lead to power law inflation for sufficiently flat potentials. In [2] I have obtained a new class of exact cosmological solutions for multi-scalar fields with exponential potentials. I have generalised the assisted inflation solutions previously obtained in the literature and demonstrated how they are modified when there exist cross-couplings between the fields, such as occur in supergravity inspired cosmological models. In a recent project I revised the assisted inflation properties for potentials that incorporate both power law and exponential terms [3]. Dark energy and structure formation After my observational and data analysis work as a member of the Supernova Cosmology Project in 1998 [4], I started my PhD studies at University of Sussex, working on the theories of ``dark energy'' that can drive the Universe to an accelerated expansion as suggested by the SnIa data. In particular, a scalar field (the ``quintessence'' field) rolling down a potential can act as an effective dynamical cosmological constant. The advantage of dealing with a dynamical scalar field is that there exist attractor solutions for certain classes of potentials that allow for a low value of the energy density of the quintessence field today regardless of its initial value at the Planck time, thus, relieving the fine-tuning issue associated with the bare cosmological constant. I have contributed to this area of research, with two models of quintessence [5,6] in my search for phenomenologically viable and well motivated models. A natural question to ask is whether the quintessence field and the inflaton can be the same field, however dominant at two different epochs. Several attempts were made in this direction and one of the most elegant forms is in the context of brane world, Randal-Sundrum II scenario. The high energy correction in the Friedmann equation allows steep potentials to inflate the Universe, and offers a ``graceful exit'' when it becomes negligible. I have shown in one publication that there are viable models of quintessence for which the field can track before it becomes dominant today [7], implying that the late time dynamics is independent of the position of the field at the end of inflation. I have analised both in theoretical and numerical terms, the effect of considering different types of energy contributions in the formation of large scale structure in the Universe. I have quantified, using the spherical collapse model, the departures of the mass functions and number counts with redshift of a number of dark energy models, from the familiar cosmological constant model in two possible scenarios: when dark energy is homogeneous; and when dark energy collapses with the dark matter -- inhomogeneous dark energy [8,9]. More recently, I and collaborators investigated the effect of dark energy on the X-ray and Sunyaev-Zel'dovich scaling relations. We generated N-body/hydrodynamic simulations that include radiative cooling with the public version of the Hydra code, modified to consider an arbitrary dark energy component. We produced cluster catalogs for four models of dark energy and derived the associated X-ray and SZ scaling relations. We found that dark energy has little effect on scaling laws making it safe to use the LCDM scalings for conversion of observed quantities into temperature and masses [10]. The growing neutrino scenario solves the coincidence problem of dark energy by a growing cosmological value of the neutrino mass which emerges from an interaction between a scalar field and the neutrino. The field mediated attraction between neutrinos induces the formation of large scale neutrino lumps in a recent cosmological epoch. I have shown in that the non-linearities in the scalar field equation of motion stop the further increase of the neutrino mass when sufficiently dense and large lumps are formed [11]. Consequently, the neutrino induced gravitational potential is substantially reduced when compared to linear estimates. I have also demonstrated that inside a lump, the possible time variation of fundamental constants is much smaller than their cosmological evolution. This feature may reconcile current geophysical bounds with claimed cosmological variations of the fine structure constant. Variation of fundamental parameters Recent observations of a number of quasar absorption lines indicate that the fine structure constant, was smaller than its present value at redshifts in the range z =1-3. Since this redshift range coincides with the epoch when the Universe underwent a transition from matter domination to dark energy domination, it is of interest to consider the possibility that this change in the effective fine structure constant arises as a direct result of a non trivial gauge coupling between the dark energy and the electromagnetic field strength. I have placed constraints on this coupling for generic scalar field potentials that exhibit tracking behaviour at present and for quintessence models [12]. In two follow up articles [13,14], I have considered the possibility of reconstructing the dark energy equation of state using quasar data only, in particular, I determined how accurate the reconstruction can be given data sets from the spectrographs ESPRESSO (for the VLT) and CODEX (for the E-ELT). The advantage of a reconstruction of this type is that it yields information on the equation of state at redshifts significantly higher than the range accessible by supernova searches. The variation of fundamental parameters can also have an important effect on the Big Bang Nucleosynthesis processes. In particular, I and collaborators have shown that a departure of the Yukawa coupling of the order 1e-5 can reconcile the Li7 abundance deduced from the WMAP analysis with its spectroscopically determined value while maintaining concordance with D and He4 abundances [15]. Inflation in Gauss-Bonnet brane cosmology Brane world scenarios have risen a great deal of attention. Some of these models regard our observable Universe as a four dimensional hyper-surface (brane) embedded in a five dimensional anti-de Sitter spacetime (bulk) and only gravity propagates into the bulk. As matter is confined to the brane, the equations of motion for any matter fields are unaltered. The Friedmann equation, however, is modified at high energies. In order to study the brane world scenario in a more string theoretic motivated setting, I have considered the effect of including higher order curvature invariants in the bulk action. I have shown in a publication [16] how the Friedmann equation is modified and how the slow roll parameters and the density perturbations are calculated when a Gauss-Bonnet term is present. When inflation is driven by an exponential potential, this term allows the spectral index of the scalar perturbation spectrum to take values in the range 0.944 and 0.989, thereby bringing the scenario in good agreement with the WMAP observations. Moduli stabilisation Scalar fields (called moduli) are abundant is string/M-theory and their vacuum expectation values (vev) are related to the size of the internal dimensions, the gauge coupling constants and the strength of the gravitational interactions. Interesting models, however, have exponentially steep potentials in the strong coupling regime and the barrier separating the vev from the the weak coupling is typically small, leading to a runaway problem. One of my early works [17] consisted of studying the cosmological evolution of moduli fields in heterotic string/M-theory scenarios. I examined in detail how the moduli evolve naturally to their minima when a dominant background fluid is present instead of rolling past them when the background is absent. Later [18] I have shown that this mechanism is also successful in stabilising the moduli fields with associated vev generated through flux compactifications. More recently we extended this project to take into account thermal corrections. One might think that these corrections are potentially dangerous as they modify the structure of the potential when the temperature is sufficiently high, however, my results showed that thermal corrections behave like a background fluid and instead favour the stabilisation of the moduli fields [19]. More recently I have performed a detailed numerical analysis of inflationary solutions in Kahler moduli of type IIB flux compactifications [20]. I have showed that there are inflationary solutions even when all the fields play an important role in the overall shape of the scalar potential. I gave explicit examples of these solutions, computed the corresponding tilt of the density perturbations power spectrum and showed that they provide a robust prediction of n_s ~ 0.96 for 60 e-folds of inflation. Inflation and super-inflation in LQC Dynamical scalar fields in the framework of loop quantum cosmology have recently risen a considerable amount of attention, mainly due to their interesting properties in setting the initial conditions for inflation, avoidance of a big crunch in a closed Universe and non-singular bounces in the cyclic scenario. My research in this topic started by studying the effects of the loop quantum corrections on the Friedmann equation in a positively curved Universe. It was found that the curvature term, rather than provoking a big crunch, plays an important role in moving the field up the inflationary potential as the Universe goes through a period of expanding and contracting phases. When the potential energy becomes important this behaviour ceases and inflation follows [21,22]. In a later publication [23] I have extended this work by including a background fluid in the dynamics of the Universe. It was concluded that also in this set up it is possible for the scalar field to become dominant and drive inflation, even if it has its initial position at the minimum of the potential. More recently I have computed the spectrum of primordial perturbations generated by a scalar field during the super-inflationary phase for a generic scalar potential [24,25]. In a follow up project, we calculated the power spectrum of tensor perturbations in these models. We found that, for both type of corrections, the abundance of gravitational waves is strongly suppressed with respect to standard inflation and that the tensor power spectrum is strongly blue tilted [26]. Non-local cosmology Non-local equations of motion contain an infinite number of derivatives and commonly appear in a number of string theory toy models such as the p-adic string and the cubic (super-)string field theory (CSSFT). In my first article on this topic [27] I reviewed how these equations can be rewritten in the form of a diffusion-like equation with non-linear boundary conditions. Moreover, I showed 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. These initial conditions are established by looking at the linear approximation to the boundary conditions. One can 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. In a follow up article [28], I and collaborators extended this work by studying the dynamics of the light-like tachyon condensation with a linear dilaton and found that the evolution is stable, even in the presence of ghost-like fields, for generic choices of initial data. 3-forms Although scalar fields are abundant in fundamental theories, they have not been observed yet. It is, therefore, important to test the robusteness of scalar fields as candidates for dark energy and inflation and understand how strict are the theoretical and phenomenological limits on the role of higher spin fields in cosmology. A thorough analysis on n-forms concluded that two-form inflation resembles much the vector inflation, having similar possibilities and problems, and that four-form becomes equivalent to scalar field or a higher order gravity theory. Three-forms, however, can naturally generate a variety of isotropic background dynamics, including scaling, possibly transient acceleration and phantom crossing. They can, therefore, naturally support either inflation or be responsible for the current acceleration of the universe and present feaures that can help us to observationally distinguish them from standard scalar field solutions [29,30]. Chameleon mechanism Certain scalar-tensor theories exhibit the so-called chameleon mechanism, whereby observational signatures of scalar fields are hidden by a combination of self-interactions and interactions with ambient matter. Not all scalar-tensor theories exhibit such a chameleon mechanism, which has been originally found in models with inverse power run-away potentials and field independent couplings to matter. In a recent work [31] I and a group of collaborators investigated field-theories with field-dependent couplings and a power-law potential for the scalar field. We proved that the theory indeed is a chameleon field theory. We found the thin-shell solution for a spherical body and investigate the consequences for Eot-Wash experiments, fifth-force searches and Casimir force experiments.

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