Testar os acoplamentos da energia escura

Tese de mestrado em Física (Astrofísica e Cosmologia), Universidade de Lisboa, Faculdade de Ciências, 2020Our dissertation aims to examine possible extensions of the standard ΛCDM2 model by generalizing the cosmological constant with quintessence, i.e. a scalar field φ whose equation of state w = p/ρ varies as time goes on. Rather than trying to elucidate the very nature of dark energy, we adopt a phenomeno-logical approach to construct different models in the form of a simple parametrisation of a scalar field, that could also be coupled to dark matter. The ambition is to propose viable alternatives to the standard model, limiting the number of additional parameters to the strict minimum as more complex models cannot usually be constrained by observations because of the degeneracies that increase with the number of parameters. Our work endeavours to cover the classical steps of model building and testing in cosmology. We begin with seeking suitable parametrisations from which we can extract analytic expressions. They enable us to theoretically study the asymptotic performance of the models in terms of both background and perturbations evolution. We modify an existing Einstein-Boltzmann code to numerically confirm the viability of the scenarios and compute related observable quantities such as luminosity distances and power spectra. The numerical results allow us to assess the sensitivity of the predicted observables to the extra degrees of freedom. We finally carry-out Markov Chain Monte Carlo analyses to estimate the parameters values and constrain the models considered with astronomical observations. While relying on previous works, particularly those studying dynamical systems in cosmology, we review key concepts across the dissertation whenever required to interpret cosmological features. We believe that this hands on approach is pedagogically invaluable in that it permits learning and presenting this complex domain by doing a concrete and comprehensive study. We hope the dissertation is also convincingly offering promising models whose originality mainly lies in the simplicity of the parametrisation which is though able to cover a wide range of evolutions with only one additional parameter. We aim in Chapter 1 to introduce the standard ΛCDM model that notably speculates the existence of a cosmological constant accelerating the expansion of the Universe. It is the benchmark against which we will be testing the dynamical dark energy models considered in this work. The standard model is built on the theoretical foundations of modern cosmology that we describe in Appendix A for convenience. Additionally, we are briefly reviewing how the equation of state of dark energy can be parametrised as the simplest means to address the cosmological constant problem. In Chapter 2, as an alternative to the usual parametrisation of the equation of state, we examine in detail a linear parametrisation of quintessence in the form of a logarithmic dependence on the scale factor: φ = λ ln a. Following the presentation of quintessence as a scalar field responsible for dark energy, we will be phenomenologically constructing a parametrised model we called λCDM to extend the standard one with just one single parameter λ. We will see that it provides for scaling solutions in the universe background that alleviate the problem of the initial conditions fine-tuning, while at the same time allows for the late-time cosmic acceleration. In order to appreciate the behaviour of our λCDM model in the perturbed universe, we also pay regard to the evolution of matter fluctuations. We will be describing the linear perturbation theory in the synchronous gauge, and later apply it to compare the scalar field parametrisation with the ΛCDM model as regards the dynamical evolution of the cold dark matter perturbations. Now that we are confident our scalar field λCDM parametrisation is a theoretically credible model of dynamical dark energy, we want in Chapter 3 to estimate the best-fit values of the parameters that ensure the model satisfies observational datasets. We first assess the sensitivity of observable quantities predicted by the model to the relevant parameter λ. We will broadly describe the Einstein-Boltzmann code called CLASS that we have modified to accommodate the analytic expression of the self-interacting potential of the parametrised scalar field. We will also be presenting the different datasets of cosmological and astrophysical observations we have chosen as probe of either background or perturbation evolution. We will finally be discussing the results of the Markov Chain Monte Carlo analyses we are carrying out with the Bayesian inference package called MontePython. We figure out that the parametrisation repro duces remarkably well the observations and is at the same time indistinguishable from a cosmological constant, which cannot be discarded. In Chapter 4, we are testing dark energy couplings with dark matter by considering a constant coupling strength β that parametrises the interaction between cold dark matter and the quintessence field. First of all, we will be building our model λβCDM to assess the effects of the coupling on the theoretical background evolution of the universe. We will also be addressing the evolution of the cosmological perturbations to identify the impact of the coupling on the corresponding predicted observables. To this end, we have again modified the CLASS code to notably adapt the perturbations module to the coupling. We will finish with a MCMC analysis to estimate and constrain the parameters of the model we are considering. Our last Chapter 5 wraps up the dissertation by offering concluding remarks, as well as prospects for future development of our work. They especially concern the necessity to complement the statistical analysis and to explore supplementary couplings, for instance with mixed dark matter and the electromagnetic sector. The latter would be useful to help constrain λ and β with the variation of the fine structure constant α