Loop inflection-point inflation

In this paper, we present a review of some recent results concerning the thermal corrections to the Casimir energy of massless scalar, electromagnetic, and massless spinor fields in the Einstein and closed Friedmann universes with a cosmic string. In the case of a massless scalar field, it is shown that the Casimir energy can be written as a simple sum of two terms; the first one corresponds to the Casimir energy for the massless scalar field in the Einstein and Friedmann universes without a cosmic string, whereas the second one is simply the Casimir energy of the electromagnetic field in these backgrounds, multiplied by a parameter λ=(1/α)−1, where α is a constant that codifies the presence of the cosmic string, and is related to its linear mass density, μ, by the expression α=1−Gμ. The Casimir free energy and the internal energy at a temperature different from zero, as well as the Casimir entropy, are given by similar sums. In the cases of the electromagnetic and massless spinor fields, the Casimir energy, free energy, internal energy, and Casimir entropy are also given by the sum of two terms, similarly to the previous cases, but now with both terms related to the same field. Using the results obtained concerning the mentioned thermodynamic quantities, their behavior at high and low temperatures limits are studied. All these results are particularized to the scenario in which the cosmic string is absent. Some discussions concerning the validity of the Nernst heat theorem are included as well.

We investigate for viable models of inflation that can successfully produce dark matter (DM) from inflaton decay process, satisfying all the constraints from Cosmic Microwave Background (CMB) and from some other observations. In particular, we analyze near-inflection-point small field inflationary scenario with non-thermal production of fermionic DM from the decaying inflaton field during the reheating era. To this end, we propose two different models of inflation with polynomial potential. The potential of Model I contains terms proportional to linear, quadratic, and quartic in inflaton; whereas in Model II, the potential contains only even power of inflaton and the highest term is sextic in inflaton. For both the models, we find out possible constraints on the model parameters which lead to proper inflationary parameters from CMB data with a very small tensor-to-scalar ratio, as expected from a small-field model. With the allowed parameter space from CMB, we then search for satisfactory relic abundance for DM, that can be produced from inflaton via reheating, to match with the present-day cold dark matter (CDM) relic density for the parameter spaces of the DM $χ$ mass and Yukawa couplings in the range $10^{-9} \gtrsim y_χ \gtrsim 10^{-15}$ and $10^3 \text{GeV} \lesssim m_χ \lesssim 10^9 \text{GeV}$. The DM relic is associated with the inflection-points in each model via maximum temperature reached in the early universe during its production. Finally, we find out allowed parameter space coming out of combined constraints from stability analysis for both SM Higgs and DM decays from inflaton as well as from BBN and Lyman-$α$ bounds.

Recently, considerable progress has been made in understanding the early universe by loop quantum cosmology. Modesto et al. investigated the loop quantum black hole (LQBH)using improved semiclassical analysis and they found that the LQBH has two horizons, an event horizon and a Cauchy horizon, just like the Reissner—Nordström black hole. This paper focuses on the dynamical evolution of a massless scalar wave in the LQBH background. By investigating the relation between the complex frequencies of the massless scalar field and the LQBH parameters using the numerical method, we find that the polymeric parameter P makes the massless scalar field decay more quickly and makes the ground scalar wave oscillate slowly. However, the polymeric parameter P causes the frequency of the high harmonic massless scalar wave to shift according to its value. We also find that the loop quantum gravity area gap parameter α0 causes the massless scalar field to decay more slowly and makes the period of the massless scalar field wave become longer. In the complex ω plane, the frequency curves move counterclockwise when the polymeric parameter P increases and this spiral effect is more obvious for a higher harmonic scalar wave.

Several models of inflection point inflation with the volumemodulus as the inflaton are investigated. Non-perturbativesuperpotentials containing two gaugino condensation terms orone such term with threshold corrections are considered.It is shown that the gravitino mass may be much smaller thanthe Hubble scale during inflation if at least one of thenon-perturbative terms has a positive exponent.Higher order corrections to the Kähler potential have to betaken into account in such models.Those corrections are used to stabilize the potential inthe axion direction in the vicinity of the inflection point.Models with only negative exponents require uplifting andin consequence have the supersymmetry breaking scale higherthan the inflation scale. Fine-tuning of parameters and initialconditions is analyzed in some detail for both types of models.It is found that fine-tuning of parametersin models with heavy gravitino is much stronger than in modelswith light gravitino.It is shown that recently proposed time dependent potentialscan provide a solution to the problem of the initial conditionsonly in models with heavy gravitino. Such potentials can not beused to relax fine tuning of parameters in any model becausethis would lead to values of the spectral index well outsidethe experimental bounds.

We construct a consistent quantum field theory of a free massless (pseudo)scalar field in 1+1-dimensional space-times free of infrared divergences. We show that in such a quantum field theory (i) a continuous symmetry of (pseudo)scalar field translations is spontaneously broken, (ii) Goldstone bosons appear as quanta of a free massless (pseudo)scalar field and (iii) there is a non-vanishing spontaneous {magnetization}. In spite of the existence of a spontaneous {magnetization} the main inequality between vacuum expectation values of certain operators which have been used for the derivation of the Mermin–Wagner–Hohenberg theorem (C. Itzykson and J.-M. Drouffe, {Statistical field theory}, Vol. I, 1989, pp. 219–224) is fulfilled.

We present higher-dimensional generalizations of the Buchdahl and Janis–Robinson–Winicour transformations which generate static solutions in the Einstein–Maxwell system with a massless scalar field. While the former adds a nontrivial scalar field to a vacuum solution, the latter generates a charged solution from a neutral one with the same scalar field. Applying these transformations to (i) a static solution with an Einstein base manifold, (ii) a multi-center solution, and (iii) a four-dimensional cylindrically symmetric solution, we construct several new exact solutions.

We explore whether generalised Brans -- Dicke theories, which have a scalar field $\Phi$ and a function $\omega(\Phi)$, can be the effective actions leading to the effective equations of motion of the LQC and the LQC--inspired models, which have a massless scalar field $\sigma$ and a function $f(m) \;$. We find that this is possible for isotropic cosmology. We relate the pairs $(\sigma, f)$ and $(\Phi, \omega)$ and, using examples, illustrate these relations. We find that near the bounce of the LQC evolutions for which $f(m) = sin \; m$, the corresponding field $\Phi \to 0$ and the function $\omega(\Phi) \propto \Phi^2 \;$. We also find that the class of generalised Brans -- Dicke theories, which we had found earlier to lead to non singular isotropic evolutions, may be written as an LQC--inspired model. The relations found here in the isotropic cases do not apply to the anisotropic cases, which perhaps require more general effective actions.

This investigation focuses on studying the dynamics of entropy disorder and quantum correlations between two detectors interacting with a scalar field in a four-dimensional Minkowski space-time using the Unruh-deWitt model. The aim is to gain insights into the evolution of quantum resources in uniformly accelerated detectors that interact with a massless scalar field. To achieve this, useful metrics such as local quantum Fisher information (LQFI), quantum consonance, and linear entropy are employed to analyze the quantum correlations and entropy disorder. The results indicate that the quantum correlations are heavily reliant on the choice of the initial state of the detectors. Interestingly, the quantum correlations exhibit a surprising resurgence as the Unruh temperature increases for specific initial state parameters. However, for other values, the Unruh temperature takes over and leads to a monotonic decrease in the quantum correlations. In addition, the degree of disorder is observed to increase as the Unruh temperature increases. Furthermore, the investigation delves into how the energy spacing of the detector affects quantum correlations across various initial state parameters. Further elucidating the behavior of quantum resources in curved space-time, we demonstrate that some initial state parameters can cause sudden changes in correlation measures as a function of energy spacing. These results highlight the relevance of choosing adequate initial state parameters, as they have a significant impact on the variation of quantum resources in two Unruh-deWitt detectors.

We present the general discussion on the inflection point inflation with small or large inflaton fields and show the effects of reheating dynamics on the inflationary predictions. In order to compare the model predictions with precisely measured CMB anisotropies and constrain the inflation models, the knowledge of the reheating dynamics is required. Inflection point inflation extended to the trans-Planckian regime can accommodate a sizable tensor-to-scalar ratio at the detectable level in the future CMB experiments.

In this paper we provide approximate analytical analysis of stability of nonsingular inflationary chaotic-type cosmological models. Initial conditions for nonsingular solutions at the bounce correspond to dominance of potential part of the energy density of the scalar field over its kinetic part both within general relativity and gauge theories of gravity. Moreover, scalar field at the bounce exceeds the Planckian value and on expansion stage these models correspond to chaotic inflation. Such solutions can be well approximated by explicitly solvable model with constant effective potential (cosmological term) and massless scalar field during the bounce and on stages of quasi-exponential contraction and expansion. Perturbative analysis shows that nonsingular inflationary solutions are exponentially unstable during contraction stage. This result is compared with numerical calculations.

We investigate the presence of massless scalar fields in a Kaluza—Klein theory based on a dimensionally continued Euler-form action. We show that massless scalar fields exist provided that the internal space is a direct product of two irreducible manifolds. The condition of a vanishing effective four-dimensional cosmological constant and the presence of a graviton, gauge fields and massless scalar fields can be satisfied if both irreducible manifolds have odd dimensions and the sum of these dimensions is equal to the dimension of the Euler form.

Several classes of conformally-flat and spherically symmetric exact solutions to the Einstein field equations coupled with either a massless scalar field or a radiation fluid are given, and their main properties are studied. It is found that some represent the formation of black holes due to the gravitational collapse of the matter fields. When the spacetimes have continuous self-similarity (CSS), the masses of black holes take a scaling form $M_{BH} \propto (P - P^{*})^{\gamma}$, where $\gamma = 0.5$ for massless scalar field and $\gamma = 1$ for radiation fluid. The reasons for the difference between the values of $\gamma$ obtained here and those obtained previously are discussed. When the spacetimes have neither CSS nor DSS (Discrete self-similarity), the masses of black holes always turn on with finite non-zero values.

A solution of the renormalised Thirring model constructed only from two scalar massless fields is studied. The representations of the conformal group for the solution as well as those for the scalar fields are obtained. It is proved that the renormalised Thirring equation is covariant with respect to the above representations.

The Tolman-Oppenheimer-Volkov (TOV) equation describes the interior properties of spherical static perfect fluid object as a relationship between two physical observables - pressure and density. For a fluid sphere object, which contains electric charge, magnetic field, and scalar field, the pressure becomes anisotropic. In the previous article [Phys. Rev. D 76 (2007) 044024; gr-qc/0607001], we deformed TOV in terms of δρC and δpC, and we found a new physical and mathematical interpretation for the TOV equation. In this work, we cannot use the perfect fluid constrains because of the electromagnetic field and the massless scalar field within this object. The TOV equation was thus generalized to involve the electromagnetic and the scalar fields. This model is close to the realistic objects in our universe such as a neutron star. In this paper, we consider the modified TOV equation for Schwarzschild coordinates in a special case. The density is considered as a constant and the scalar field is considered absent. On the general model of the TOV equation, the pressure is expressed in terms of radius. However, this model shows that pressure is affected by electric charge. Moreover, we also calculate the rigorous bound on the transmission probability for the Tolman-Bayin type of charged fluid sphere.

We show that a massless scalar field in a gravitational wave background can develop a non-zero vacuum expectation value. We draw comparisons to the generation of a non-zero vacuum expectation value for a scalar field in the Higgs mechanism and with the dynamical Casimir vacuum. We propose that this vacuum expectation value, generated by a gravitational wave, can be connected with particle production from gravitational waves and may have consequences for the early Universe where scalar fields are thought to play an important role.