Speaker
Description
Cosmological inflation provides a mechanism to explain the origin of primordial fluctuations that give rise to anisotropies in the cosmic microwave background and the formation of large-scale structures in the Universe. In this work, we study primordial perturbations within the framework of modified teleparallel gravity $f(T,\phi,X)$, where $T$ is the torsion scalar, $\phi$ is a scalar field, and $X$ is its kinetic term. First, we derive the field equations and specialize them to a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker cosmological background, obtaining the modified Friedmann and Klein-Gordon equations. Subsequently, using cosmological perturbation theory, we derive the second-order action for the scalar and tensor sectors, whose variation leads to the corresponding Mukhanov-Sasaki-type evolution equations. Through canonical quantization of the variables describing the physical degrees of freedom of the perturbations, we obtain theoretical expressions for the primordial power spectra and their corresponding spectral indices, establishing a framework for analyzing the cosmological predictions of this class of theories.