Modified gravity and alternatives to single field inflation

Motivated by the need to understand the origin of inflation and address theoretical
limitations of general relativity, this thesis investigates four complementary directions
beyond standard single-field inflation. Each approach is rooted in well-motivated extensions of gravity and multifield inflationary dynamics, aiming to bridge fundamental
theory and cosmological observations. After introducing the theoretical foundations of
modified gravity and inflation, the thesis presents original research across four main
themes: multifield inflation with kinetic couplings, scale-invariant models, non-local
gravity, and cyclic cosmologies.

First, multifield models with non-trivial kinetic couplings are analysed. Arising from
conformal transformations in non-minimally coupled theories, these models exhibit rich
dynamics including adiabatic and isocurvature perturbations. Using our sampling algorithm, the thesis explores their predictions and compares them with cosmological data. Second, the R-squared scale-invariant inflationary model is studied, where mass scales emerge dynamically via spontaneous symmetry breaking. This model addresses the hierarchy problem and yields predictions consistent with current observations, offering an interesting alternative to Starobinsky and alpha-attractor scenarios.
Third, the thesis examines inflation in non-local hybrid metric-Palatini gravity, inspired by attempts to include quantum corrections through non-local operators. Reformulating the theory with auxiliary fields, we identify stable configurations and investigate how non-local terms deform the inflationary potential in observable ways.
Finally, a non-inflationary alternative is explored: the cyclic universe. A general
framework is developed to study the evolution of primordial gravitational waves across
cosmological cycles. The impact of initial conditions and vacuum choice is assessed,
with implications for the robustness of gravitational wave predictions.

Together, these results offer novel insight into early-universe cosmology, proposing
viable alternatives to standard inflation, and guiding future observational and theoretical
research.