ETD

• CMB
• cosmology
• ModMax
• non-linear electrodynamics
• primordial gravitational waves

Inflation has become a crucial paradigm of the standard cosmological model, since it has received great support from the latest observational data by the Planck satellite. According to this scenario, the early Universe underwent an accelerated expansion that could solve some cosmological shortcomings such as the horizon, flatness and entropy problems, and it provides a mechanism to generate primordial cosmological perturbations. The most common way to describe the inflationary era is to use a canonical scalar field with a self-interacting potential, i.e., the inflaton. A variety of inflationary models have been proposed; many of these are based on scalar field(s); however, in the past, also models of non-linear electrodynamics (NED) have been proposed to sustain the inflationary period and to explain the generation of cosmological perturbations. Since Born and Infeld constructed the first non-linear generalization of Maxwell’s electrodynamics in 1933-1934, a wide variety of other models of non-linear electrodynamics have been studied and used in many areas of theoretical physics. In the thesis, we study the general features of non-linear electrodynamics and then, we focus on ModMax, the unique non-linear extension of Maxwell electrodynamics that is both conformally invariant and electromagnetic-duality invariant (Bandos et al. 2020). The ModMax Lagrangian depends on a positive real parameter γ and reduces to Maxwell theory in the limit γ → 0. Such a model, has never been studied in a cosmological setup and, in particular, in the gravitational sector. Dilaton-Maxwell theories include a coupling of the type φF_{μν} F^{μν}, where φ is a scalar field and F_{μν} is the electromagnetic tensor, while axion electrodynamics theories predict a coupling of the type ψF_{μν} \Tilde{F}^{μν}, with ψ being a pseudoscalar field and \Tilde{F}^{μν} the dual of the electromagnetic tensor. ModMax Lagrangian can be written in an alternative form using an auxiliary pseudoscalar field χ. In this way, ModMax presents both the dilaton-Maxwell and axion electrodynamics features, that is, it has the structure of an axion-dilaton electrodynamics model. However, the χ field, being auxiliary, must be subject to constraints. It is therefore decided to promote χ to a dynamic field and to study only the behavior of axion electrodynamics. We have studied this theory in an inflationary context: a model of inflation including the inflaton and the ModMax Lagrangian density with this new degree of freedom, i.e., the pseudo-scalar field χ, which is an axion-like particle. In this setup, the electromagnetic four-potential A_μ, only gravitationally coupled to the inflaton, sources scalar and tensor metric perturbations. We focus on the tensor perturbations of the metric, which, through the Einstein equation, are generated by the stress-energy tensor of the gauge field. Due to the parity-violating nature of the system, the right- and the left-handed tensor modes show different amplitudes. Consequently, the tensor power spectrum has different amplitudes for the two polarizations, with P_+ = H^2/(π^2 M_P^2) [1 + 8.6 × 10^{−7} H^2/M_P^2 e^{4πα}/α^6 (cosh γ + sinh γ)^2] and P_− = H^2/(π^2 M_P^2) [1 + 1.8 × 10^{−9} H^2/M_P^2 e^{4πα}/α^6 (cosh γ + sinh γ)^2], where α is a parameter depending on \Dot{χ}, H is the Hubble constant and M_P the Planck mass. This asymmetry also manifests itself through non-vanishing correlation functions in the Cosmic Microwave Background (CMB). The CMB preserves the imprint of cosmological perturbations in the early universe. After having introduced the main effects that affect the CMB and its temperature anisotropies, we analyze the effect of the sourced tensor modes on the two-points function of the temperature fluctuation, i.e., on the temperature angular power spectrum C^{TT}_ℓ . The ModMax contribution to the C_ℓ is computed before analytically in the flat-sky approximation: we consider scales that enter the horizon during matter domination since at smaller scales tensors are suppressed and do not give a sizable contribution to temperature fluctuations. This analysis is therefore valid for 1 ≪ ℓ ≲ 100, and we have found a contribution to C^{TT}_ℓ proportional to the tensor power spectrum P_+. Then, by relaxing such an approximation, we have performed the full computation numerically, using the Cosmic Linear Anisotropy Solving System (CLASS) Boltzmann code (http://class-code.net). We choose suitable values for the model parameters, based on the most recent experimental bound on the tensor-to-scalar ratio r to obtain the C^{TT}_ℓ spectrum. The result is obtained by adding the contribution given by ModMax to the tensor power spectrum. We have then generated a map of the CMB from the C^{TT}_ℓ spectrum using the HEALPix software (Gorski et al. 2005), which is widely used for the representation and analysis of data on celestial spheres. Since, at first order, CMB B-mode polarization is sourced only by transverse (tensor) perturbations, the ModMax model also affects the angular power spectrum C^{BB}_ℓ . We compute the B-mode angular spectrum including the ModMax contribution and we generate the corresponding CMB maps. Past and next-generation experiments—e.g., LiteBIRD—with sensitivity to the tensor-to-scalar ratio r ≲ 10^{−3} will enable direct tests of ModMax and, by comparison with CMB data, will allow us to constrain the parameters of the model.