Description
The General Relativity (GR) presents limitations that have been observed in the power spectrum of the Cosmic Microwave Background (CMB). For instance, there are issues like the horizon problem, flatness problem and superhorizon correlations. In this work we study inflation, a theory proposed as an extension to the standard cosmological scenario to address these issues, which is characterized by a primordial exponential accelerated expansion. We present the parameters $\varepsilon$ and $\eta$ that guarantee that inflation can last long enough to provide a region of causality and stretching of the curvature of space-time. Subsequently, we study the dynamics of the scalar field $\phi$ by calculating the specific equation of motion that governs it, based on the FLRW metric. Besides that, with the pressure derived from the continuity equation, we have the condition that allows for the inflationary potential to act as a cosmological constant. Furthermore, we present the slow-roll mechanism for the scalar field and its respective approximations for the parameters $\varepsilon_{V}$ and $\eta_{V}$. Finally, we exemplify the theory with a quadratic potential and analyze under which conditions such potential leads to inflation.
