| Crynodeb: | <p>The aim of this thesis is to question some of the basic assumptions that go into building the ΛCDM model of our universe. The assumptions we focus on are the initial conditions of the universe, the fundamental forces in the universe on large scales and the approximations made in analysing cosmological data.
For each of the assumptions we outline the theoretical understanding behind them, the current methods used to study them and how they can be improved and finally we also perform numerical analysis to quantify the novel solutions/methods we propose to extend the previous assumptions. </p>
<p>The work on the initial conditions of the universe focuses on understanding what the most general, gauge invariant, perturbations are present in the beginning of the universe and how they impact observables such as the CMB anisotropies.
We show that the most general set of initial conditions allows for a decaying adiabatic solution which can have a non-zero contribution to the perturbations in the early universe.
The decaying mode sourced during an inflationary phase would be highly suppressed and should have no observational effect, thus, if these modes are detected they could potentially rule out most models of inflation and would require a new framework to understand the early universe such as a bouncing/cyclic universe. </p>
<p>After studying the initial conditions of the universe, we focus on understanding the nature of gravity on the largest scales.
It is assumed that gravity is the only force that acts on large scales in the universe and we propose a novel test of this by cross-correlating two different types of galaxies that should be sensitive to fifth-force's in the universe.
By focusing on a general class of scalar-tensor theories that have a property of screening, where the effect of the fifth force depends on the local energy density, we show that future surveys will have the power to constrain screened fifth-forces using the method we propose.</p>
<p>Finally, to test theoretical models with observations a complete understanding of the statistical methods used to compare data with theory is required.
The goal of a statistical analysis in cosmology is usually to infer cosmological parameters that describe our theoretical model from observational data.
We focus on one particular aspect of cosmological parameter estimation which is the covariance matrix used during an inference procedure.
The usual assumption in modelling the covariance matrix is that it can be computed at a fiducial point in parameter space, however, this is not self-consistent.
We check this claim explicitly by calculating the effect of including the parameter dependence in the covariance matrix on the constraining power of cosmological parameters. </p>
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