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A number of scalar field models proposed as alternatives to the standard inflationary scenario involve contracting phases which precede the universes present phase of expansion. An important question concerning such models is whether there are effects which could potentially distinguish them from purely expanding cosmologies. Vector perturbations have recently been considered in this context. At first order such perturbations are not supported by a scalar field. In this paper, therefore, we consider second order vector perturbations. We show that such perturbations are generated by first order scalar mode-mode couplings, and give an explicit expression for them. We compare the magnitude of vector perturbations produced in collapsing models with the corresponding amplitudes produced during inflation, using a number of suitable power-law solutions to model the inflationary and collapsing scenarios. We conclude that the ratios of the magnitudes of these perturbations depend on the details of the collapsing scenario as well as on how the hot big bang is recovered, but for certain cases could be large, growing with the duration of the collapse.
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An old question surrounding bouncing models concerns their stability under vector perturbations. Considering perfect fluids or scalar fields, vector perturbations evolve kinematically as $a^{-2}$, where $a$ is the scale factor. Consequently, a definite answer concerning the bounce stability depends on an arbitrary constant, therefore, there is no definitive answer. In this paper, we consider a more general situation where the primeval material medium is a non-ideal fluid, and its shear viscosity is capable of producing torque oscillations, which can create and dynamically sustain vector perturbations along cosmic evolution. In this framework, one can set that vector perturbations have a quantum mechanical origin, coming from quantum vacuum fluctuations in the far past of the bouncing model, as it is done with scalar and tensor perturbations. Under this prescription, one can calculate their evolution during the whole history of the bouncing model, and precisely infer the conditions under which they remain linear before the expanding phase. It is shown that such linearity conditions impose constraints on the free parameters of bouncing models, which are mild, although not trivial, allowing a large class of possibilities. Such conditions impose that vector perturbations are also not observationally relevant in the expanding phase. The conclusion is that bouncing models are generally stable under vector perturbations. As they are also stable under scalar and tensor perturbations, we conclude that bouncing models are generally stable under perturbations originated from quantum vacuum perturbations in the far past of their contracting phase.
We investigate the tensor and the scalar perturbations in the symmetric bouncing universe driven by one ordinary field and its Lee-Wick partner field which is a ghost. We obtain the even- and the odd-mode functions of the tensor perturbation in the matter-dominated regime. The tensor perturbation grows in time during the contracting phase of the Universe, and decays during the expanding phase. The power spectrum for the tensor perturbation is evaluated and the spectral index is given by $n_{rm T} =6$. We add the analysis on the scalar perturbation by inspecting the even- and the odd-mode functions in the matter-dominated regime, which was studied numerically in our previous work. We conclude that the comoving curvature by the scalar perturbation is constant in the super-horizon scale and starts to decay in the far sub-horizon scale while the Universe expands.
We study the tensor modes of linear metric perturbations within an effective framework of loop quantum cosmology. After a review of inverse-volume and holonomy corrections in the background equations of motion, we solve the linearized tensor modes equations and extract their spectrum. Ignoring holonomy corrections, the tensor spectrum is blue tilted in the near-Planckian superinflationary regime and may be observationally disfavoured. However, in this case background dynamics is highly nonperturbative, hence the use of standard perturbative techniques may not be very reliable. On the other hand, in the quasi-classical regime the tensor index receives a small negative quantum correction, slightly enhancing the standard red tilt in slow-roll inflation. We discuss possible interpretations of this correction, which depends on the choice of semiclassical state.
We discuss scalar-tensor realizations of the Anamorphic cosmological scenario recently proposed by Ijjas and Steinhardt. Through an analysis of the dynamics of cosmological perturbations we obtain constraints on the parameters of the model. We also study gravitational Parker particle production in the contracting Anamorphic phase and we compute the fraction between the energy density of created particles at the end of the phase and the background energy density. We find that, as in the case of inflation, a new mechanism is required to reheat the universe.
In this thesis, we discuss several instances in which non-linear behaviour affects cosmological evolution in the early Universe. We begin by reviewing the standard cosmological model and the tools used to understand it theoretically and to compute its observational consequences. This includes a detailed exposition of cosmological perturbation theory and the theory of inflation. We then describe the results in this thesis, starting with the non-linear evolution of the curvature perturbation in the presence of vector and tensor fluctuations, in which we identify the version of that variable that is conserved in the most general situation. Next, we use second order perturbation theory to describe the most general initial conditions for the evolution of scalar perturbations at second order in the standard cosmological model. We compute approximate solutions valid in the initial stages of the evolution, which can be used to initialize second order Boltzmann codes, and to compute many observables taking isocurvature modes into account. We then move on to the study of the inflationary Universe. We start by analysing a new way to compute the consequences of a sudden transition in the evolution of a scalar during inflation. We use the formalism of quantum quenches to compute the effect of those transitions on the spectral index of perturbations. Finally, we detail the results of the exploration of a multi-field model of inflation with a non-minimal coupling to gravity. We study popular attractor models in this regime in both the metric and the Palatini formulations of gravity and find all results for both the power spectrum and bispectrum of fluctuations to closely resemble those of the single-field case. In all systems under study we discuss the effects of non-linear dynamics and their importance for the resolution of problems in cosmology.
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