Asymptotic Solutions of a Generalized Starobinski Model: Kinetic Dominance, Slow Roll and Separatrices

We consider a generalized Starobinski inflationary model. We present a method for computing solutions as generalized asymptotic expansions, both in the kinetic dominance stage (psi series solutions) and in the slow roll stage (asymptotic expansions of the separatrix solutions). These asymptotic expansions are derived in the framework of the Hamilton-Jacobi formalism where the Hubble parameter is written as a function of the inflaton field. They are applied to determine the values of the inflaton field when the inflation period starts and ends as well as to estimate the corresponding amount of inflation. As a consequence, they can be used to select the appropriate initial conditions for determining a solution with a previously fixed amount of inflation.

The very early universe

The universe at very early times, before the GUT era, is discussed. The entropy problem is described. The horizon and flatness problems are subsumed into the general problem of finding plausible models of the physics of the Planck era or the era immediately after it. An outline of inflationary cosmology is given, including quantitative treatment of a scalar inflaton field, treated in both a classical and quantum approach, in order to find the average dynamics and the spectrum of perturbations, respectively.

SU(2,1)/(SU(2) × U(1)) B − L Higgs Inflation

We present a realization of Higgs inflation within Supergravity which is largely tied to the existence of a pole of order two in the kinetic term of the inflaton field. This pole arises due to the selected Kaehler potential which parameterizes the SU(2,1)/(SU(2) × U(1)) manifold with scalar curvature R 21 = − 6 / N . The associated superpotential includes, in addition to the Higgs superfields, a stabilizer superfield, respects a B − L gauge and an R symmetries and contains the first allowed nonrenormalizable term. If the coefficient of this term is almost equal to that of the others within about 10−5 and N = 2, the inflationary observables can be done compatible with the present data. The tuning can be eluded if we modify the Kaehler potential associated with the manifold above. In this case, inflation can be realized with just renormalizable superpotential terms and results to higher tensor-to-scalar ratios as N approaches its maximum at N ≃80.

Were strong inflaton field fluctuations the cause of the big bang?

In this paper, I propose a model to describe the birth of the universe taking into account back reaction effects produced by the inflaton field fluctuations, with self-interactions included. These fluctuations [Formula: see text] would have been very important at the Planck scales and their self-interactions could have been the fuel to the primordial expansion of the universe.

Dark photon dark matter from charged inflaton

We present a scenario of vector dark matter production during inflation containing a complex inflaton field which is charged under a dark gauge field and which has a symmetry breaking potential. As the inflaton field rolls towards the global minimum of the potential the dark photons become massive with a mass which can be larger than the Hubble scale during inflation. The accumulated energy of the quantum fluctuations of the produced dark photons gives the observed relic density of the dark matter for a wide range of parameters. Depending on the parameters, either the transverse modes or the longitudinal mode or their combination can generate the observed dark matter relic energy density.

Axion monodromy inflation, trapping mechanisms and the swampland

We study the effects of particle production on the evolution of the inflaton field in an axion monodromy model with the goal of discovering in which situations the resulting dynamics will be consistent with the swampland constraints. In the presence of a modulated potential the evolving background field (solution of the inflaton homogeneous in space) induces the production of long wavelength inflaton fluctuation modes. However, this either has a negligible effect on the inflaton dynamics (if the field spacing between local minima of the modulated potential is large), or else it traps the inflaton in a local minimum and leads to a graceful exit problem. On the other hand, the production of moduli fields at enhanced symmetry points can lead to a realization of trapped inflation consistent with the swampland constraints, as long as the coupling between the inflaton and the moduli fields is sufficiently large.

Strengthening the de Sitter swampland conjecture in warm inflation

The de Sitter constraint on the space of effective scalar field theories consistent with superstring theory provides a lower bound on the slope of the potential of a scalar field which dominates the evolution of the Universe, e.g., a hypothetical inflaton field. Whereas models of single scalar field inflation with a canonically normalized field do not obey this constraint, it has been claimed recently in the literature that models of warm inflation can be made compatible with it in the case of large dissipation. The de Sitter constraint is known to be derived from entropy considerations. Since warm inflation necessary involves entropy production, it becomes necessary to determine how this entropy production will affect the constraints imposed by the swampland conditions. Here, we generalize these entropy considerations to the case of warm inflation and show that the condition on the slope of the potential remains essentially unchanged and is, hence, robust even in the warm inflation dynamics. We are then able to conclude that models of warm inflation indeed can be made consistent with the swampland criteria.

Pure natural quintessential inflation and dark energy

We propose the pure natural quintessential inflation model which is motivated by Witten’s conjecture, where the axion couples to pure Yang–Mills [Formula: see text] gauge field at large [Formula: see text] limit. This modifies the standard cosine potential which is presented in the natural inflation, making it compatible with current CMB data. Our model gives a successful inflation as well as acceleration at the late times by quintessence inflaton field ([Formula: see text]). Here the inflaton field is responsible for inflation, after that the field enters into peculiar type of reheating and then they act as dynamical dark energy field which follows the same inflation potential and same model parameters. The dynamical field slowly rolls until the Hubble drops to mass of the quintessence field and it reaches the current dark energy field value. Here the dark energy scale is field dependent. Our quintessence model follows thawing frozen approach, therefore the frozen quintessence field evolves with respect to cosmic time from initial field value [Formula: see text] to present nonzero minimum field value [Formula: see text]. The obtained field value turned into ultralight and it satisfies the present dark energy density which is [Formula: see text].

The Spectrum of Gravitational Waves, Their Overproduction in Quintessential Inflation and Its Influence in the Reheating Temperature

One of the most important issues in an inflationary theory as standard or quintessential inflation is the mechanism to reheat the universe after the end of the inflationary period in order to match with the Hot Big Bang universe. In quintessential inflation two mechanisms are frequently used, namely the reheating via gravitational particle production which is, as we will see, very efficient when the phase transition from the end of inflation to a kinetic regime (all the energy of the inflaton field is kinetic) is very abrupt, and the so-called instant preheating which is used for a very smooth phase transition because in that case the gravitational particle production is very inefficient. In the present work, a detailed study of these mechanisms is done, obtaining bounds for the reheating temperature and the range of the parameters involved in each reheating mechanism in order that the Gravitational Waves (GWs) produced at the beginning of kination do not disturb the Big Bang Nucleosynthesis (BBN) success.

Exploring the inflation of F(R) gravity

The early-time expansion of the spacetime, namely, inflation, is introduced to solve some cosmological problems. [Formula: see text] gravity is a simple extension of the general relativity to induce the inflationary expansion. The precise observation of the Cosmic Microwave Background gives us the information to inspect the model of the inflation. [Formula: see text] gravity can be transformed to the Einstein–Hilbert term with a scalar field that plays the role of the inflaton. The inflaton potential is described as an explicit function of the inflaton field with a noncanonical kinetic term. In this paper, we obtain general formulae to derive the inflationary parameters including the models with a noncanonical kinetic term. The inflationary parameters are described as functions of the inflaton potential and its derivatives. We evaluate a well-known model, [Formula: see text], to confirm the validity of our formulae. Then, we apply the procedure to a model, [Formula: see text], in which it is not possible to represent the potential as an explicit function of the inflaton field with a canonical kinetic term.