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In this paper we investigate the cosmological dynamics of geometric inflation by means of the tools of the dynamical systems theory. We focus in the study of two explicit models where it is possible to sum the infinite series of higher curvature corrections that arises in the formalism. These would be very interesting possibilities since, if regard gravity as a quantum effective theory, a key feature is that higher powers of the curvature invariants are involved at higher loops. Hence, naively, consideration of the whole infinite tower of curvature invariants amounts to consideration of all of the higher order loops. The global dynamics of these toy models in the phase space is discussed and the quantum origin of primordial inflation is exposed.
The primordial power spectra of scalar and tensor perturbations during slow-roll inflation are usually calculated with the method of Bessel function approximation. For constant-roll or ultra slow-roll inflation, the method of Bessel function approxim
We examine the effect of the thermal vacuum on the power spectrum of inflation by using the thermal field dynamics. We find that the thermal effect influences the CMB anisotropy at large length scale. After removing the divergence by using the hologr
We discuss the constant-roll inflation with constant $epsilon_2$ and constant $bareta$. By using the method of Bessel function approximation, the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts, an
We consider the space-condensate inflation model to study the primordial gravitational waves generated in the early Universe. We calculate the energy spectrum of gravitational waves induced by the space-condensate inflation model for full frequency r
We study inflationary solution in an extension of mimetic gravity with the higher derivative interactions coupled to gravity. Because of the higher derivative interactions, the setup is free from the ghost and gradient instabilities while it hosts a