Search Results (15)

In this paper, we systematically study the evolution of the Universe within the framework of a modified loop quantum cosmological model (mLQC-I) using various inflationary potentials, including chaotic, Starobinsky, generalized Starobinsky, polynomials of the first and second kinds, generalized T-models and natural inflation. In all these models, the big bang singularity is replaced by a quantum bounce, and the evolution of the Universe, both before and after the bounce, is universal and weakly dependent on the inflationary potentials, as long as the evolution is dominated by the kinetic energy of the inflaton at the bounce. In particular, the pre-bounce evolution can be universally divided into three different phases: pre-bouncing, pre-transition, and pre-de Sitter. The pre-bouncing phase occurs immediately before the quantum bounce, during which the evolution of the Universe is dominated by the kinetic energy of the inflaton. Thus, the equation of state of the inflaton is about one, $w\left(\varphi \right)\simeq 1$. Soon, the inflation potential takes over, so $w\left(\varphi \right)$ rapidly falls from one to negative one. This pre-transition phase is very short and quickly turns into the pre-de Sitter phase, whereby the effective cosmological constant of Planck size takes over and dominates the rest of the contracting phase. Throughout the entire pre-bounce regime, the evolution of both the expansion factor and the inflaton can be approximated by universal analytical solutions, independent of the specific inflation potentials. Full article

A new (improved) model of inflation and primordial black hole (PBH) formation is proposed by combining the Starobinsky model of inflation, Appleby–Battye–Starobinsky (ABS) model of dark energy, and a quantum correction in the modified $F\left(R\right)$ gravity. The energy scale parameter in the ABS model is taken to be close to the inflationary scale, in order to describe double inflation instead of dark energy. The quantum correction is given by the term quartic in the spacetime scalar curvature R with a negative coefficient $(-\delta )$ in the $F\left(R\right)$ function. It is demonstrated that very good agreement (within $1\sigma$) with current measurements of the cosmic microwave background (CMB) radiation can be achieved by choosing the proper value of $\delta$, thus solving the problem of low values of the tilt of CMB scalar perturbations in the earlier proposed model in arXiv:2205.00603. A large (by a factor of ${10}^7$ against CMB) enhancement in the power spectrum of scalar perturbations is achieved by fine tuning the parameters of the model. It is found by numerical analysis that it can lead to formation of asteroid-size PBHs with masses up to ${10}^{20}$ g, which may form dark matter in the current universe. Full article

We propose inflationary models that are one-parametric generalizations of the Starobinsky $R+R^2$ model. Using the conformal transformation, we obtain scalar field potentials in the Einstein frame that are one-parametric generalizations of the potential for the Starobinsky inflationary model. We restrict the form of the potentials by demanding that the corresponding function $F\left(R\right)$ is an elementary function. We obtain the inflationary parameters of the models proposed and show that the predictions of these models agree with current observational data. Full article

This paper presents a noncommutative (NC) version of an extended Sáez–Ballester (SB) theory. Concretely, considering the spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) metric, we propose an appropriate dynamical deformation between the conjugate momenta and, applying the Hamiltonian formalism, obtain deformed equations of motion. In our model, the NC parameter appears linearly in the deformed Poisson bracket and the equations of the NC SB cosmology. When it goes to zero, we get the corresponding commutative counterparts. Even by restricting our attention to a particular case, where there is neither an ordinary matter nor a scalar potential, we show that the effects of the noncommutativity provide interesting results: applying numerical endeavors for very small values of the NC parameter, we show that (i) at the early times of the universe, there is an inflationary phase with a graceful exit, for which the relevant nominal condition is satisfied; (ii) for the late times, there is a zero acceleration epoch. By establishing an appropriate dynamical framework, we show that the results (i) and (ii) can be obtained for many sets of the initial conditions and the parameters of the model. Finally, we indicate that, at the level of the field equations, one may find a close resemblance between our NC model and the Starobinsky inflationary model. Full article

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. Full article

It is shown that the inflationary model is the result of the symmetry of the generalized $F(R,T,X,\phi )$-cosmological model using the Noether symmetry. It leads to a solution, a particular case of which is Starobinsky’s cosmological model. It is shown that even in the more particular case of cosmological models $F(R,X,\phi )$ and $F(T,X,\phi )$ the Monge–Ampère equation is still obtained, one of the solutions including the Starobinsky model. For these models, it is shown that one can obtain both power-law and exponential solutions for the scale factor from the Euler–Lagrange equations. In this case, the scalar field $\phi$ has similar time dependences, exponential and exponential. The resulting form of the Lagrangian of the model allows us to consider it as a model with $R^2$ or $X^2$. However, it is also shown that previously less studied models with a non-minimal relationship between R and X are important, as one of the possible models. It is shown that in this case the power-law model can have a limited evolutionary period with a negative value of the kinetic term. Full article

We calculate the baryon asymmetry value generated in the Scalar Field Condensate (SCF) baryogenesis model obtained in several inflationary scenarios and different reheating models. We provide analysis of the baryon asymmetry value obtained for more than 70 sets of parameters of the SCF model and the following inflationary scenarios, namely: new inflation, chaotic inflation, Starobinsky inflation, MSSM inflation, quintessential inflation. We considered both cases of efficient thermalization after inflation and delayed thermalization. We have found that the SFC baryogenesis model produces baryon asymmetry orders of magnitude bigger than the observed one for the following inflationary models: new inflation, new inflation model by Shafi and Vilenkin, MSSM inflation, chaotic inflation with high reheating temperature and the simplest Shafi–Vilenkin chaotic inflationary model. Strong diluting mechanisms are needed for these models to reduce the resultant baryon excess at low energies to its observational value today. We have found that a successful generation of the observed baryon asymmetry is possible by the SCF baryogenesis model in Modified Starobinsky inflation, chaotic inflation with low reheating temperature, chaotic inflation in SUGRA, and Quintessential inflation. Full article

In this work, the use of a calibration satellite (L2-CalSat) flying in formation with a Cosmic Microwave Background (CMB) polarization mission in an orbit located at the second Lagrange point, is proposed. The new generation of CMB telescopes are expected to reach unprecedented levels of sensitivity to allow a very precise measurement of the B-mode of polarization, the curl-like polarization component expected from gravitational waves coming from Starobinski inflationary models. Due to the CMB polarized signal weakness, the instruments must be subjected to very precise calibration processes before and after launching. Celestial sources are often used as external references for calibration after launch, but these sources are not perfectly characterized. As a baseline option, L2-CalSat is based on the CubeSat standard and serves as a perfectly known source of a reference signal to reduce polarization measurements uncertainty. A preliminary design of L2-CalSat is described and, according to the scanning strategy followed by the telescope, the influence of the relative position between the spacecrafts in the calibration process is studied. This new calibration element will have a huge impact on the performance of CMB space missions, providing a significant improvement in the measurements accuracy without requiring new and costly technological developments. Full article

We review the models unifying inflation and Primordial Black Hole (PBH) formation, which are based on the modified (Starobinsky-type) supergravity. We begin with the basic (Starobinsky) inflationary model of modified gravity and its alpha-attractor-type generalizations for PBH production, and recall how all those single-field models can be embedded into the minimal supergravity. Then, we focus on the effective two-field models arising from the modified (Starobinsky-type) supergravity and compare them to the single-field models under review. Those two-field models describe double inflation whose first stage is driven by Starobinsky’s scalaron and whose second stage is driven by another scalar belonging to the supergravity multiplet. The power spectra are numerically computed, and it is found that the ultra-slow-roll regime gives rise to the enhancement (peak) in the scalar power spectrum leading to an efficient PBH formation. The resulting PBH masses and their density fraction (as part of dark matter) are found to be in agreement with cosmological observations. The PBH-induced gravitational waves, if any, are shown to be detectable by the ground-based and space-based gravitational interferometers under construction. Full article

An extremely fast exponential expansion of the Universe is typical for the stable version of the inflationary model, based on the anomaly-induced action of gravity. The total amount of exponential e-folds could be very large, before the transition to the unstable version and the beginning of the Starobinsky inflation. Thus, the stable exponential expansion can be seen as a pre-inflationary semiclassical cosmological solution. We explore whether this stable phase could follow after the bounce, subsequent to the contraction of the Universe. Extending the previous consideration of the bounce, we explore both stable expansion and the bounce solutions in the models with non-zero cosmological constant and the presence of background radiation. The critical part of the analysis concerns stability for small perturbations of the Hubble parameter. It is shown that the stability is possible for the variations in the bounce region, but not in the sufficiently distant past in the contraction phase. Full article

Supergravity (SUGRA) theories are specified by a few functions, most notably the real Kähler function denoted by $G(T_i,{\overline{T}}_i)=K+log{\left|W\right|}^2$ , where K is a real Kähler potential, and W is a holomorphic superpotential. A field redefinition $T_i\to f_1\left(T_i\right)$ changes neither the theory nor the Kähler geometry. Similarly, the Kähler transformation, $K\to K+f_2+{\overline{f}}_2,W\to e^{-f_2}W$ where $f_2$ is holomorphic and leaves G and hence the theory and the geometry invariant. However, if we perform a field redefinition only in $K(T_i,{\overline{T}}_i)\to K(f\left(T_i\right),f\left({\overline{T}}_i\right))$ , while keeping the same superpotential $W\left(T_i\right)$ , we get a different theory, as G is not invariant under such a transformation while maintaining the same Kähler geometry. This freedom of choosing $f\left(T_i\right)$ allows construction of an infinite number of new theories given a fixed Kähler geometry and a predetermined superpotential W. Our construction generalizes previous ones that were limited by the holomorphic property of W. In particular, it allows for novel inflationary SUGRA models and particle phenomenology model building, where the different models correspond to different choices of field redefinitions. We demonstrate this possibility by constructing several prototypes of inflationary models (hilltop, Starobinsky-like, plateau, log-squared and bell-curve) all in flat Kähler geometry and an originally renormalizable superpotential W. The models are in accord with current observations and predict $r\in [{10}^{-6},0.06]$ spanning several decades that can be easily obtained. In the bell-curve model, there also exists a built-in gravitational reheating mechanism with $T_R\sim \mathcal{O}\left({10}^{7}GeV\right)$ . Full article

We review a possible origin of cosmological inflation from higher $\left(D\right)$ spacetime dimensions in the context of modified gravity theory. It is demonstrated that it requires a spontaneous warped compactification of higher $\left(D\right)$ spacetime dimensions together with the stabilization of extra $(D-4)$ dimensions by Freund–Rubin mechanism. The relevant tools include an extra gauge $(D/2-1)$ -form field with a non-vanishing flux in compact dimensions and a positive cosmological constant in D dimensions. Those features are illustrated on the specific example in eight spacetime dimensions compactified on a four-sphere with a warped factor and a flux, which leads to a viable Starobinsky-like inflationary model in four (non-compact) spacetime dimensions. Full article

We describe the primeval inflationary phase of the early Universe within a quantum field theoretical (QFT) framework that can be viewed as the effective action of vacuum decay in the early times. Interestingly enough, the model accounts for the “graceful exit” of the inflationary phase into the standard radiation regime. The underlying QFT framework considered here is supergravity (SUGRA), more specifically an existing formulation in which the Starobinsky-type inflation (de Sitter background) emerges from the quantum corrections to the effective action after integrating out the gravitino fields in their (dynamically induced) massive phase. We also demonstrate that the structure of the effective action in this model is consistent with the generic idea of re-normalization group (RG) running of the cosmological parameters; specifically, it follows from the corresponding RG equation for the vacuum energy density as a function of the Hubble rate, ${\rho }_{\Lambda }\left(H\right)$ . Overall, our combined approach amounts to a concrete-model realization of inflation triggered by vacuum decay in a fundamental physics context, which, as it turns out, can also be extended for the remaining epochs of the cosmological evolution until the current dark energy era. Full article

We review inflationary cosmology in modified gravity such as R² gravity with its extensions in order to generalize the Starobinsky inflation model. In particular, we explore inflation realized by three kinds of effects: modification of gravity, the quantum anomaly, and the R² term in loop quantum cosmology. It is explicitly demonstrated that in these inflationary models, the spectral index of scalar modes of the density perturbations and the tensor-to-scalar ratio can be consistent with the Planck results. Bounce cosmology in F(R) gravity is also explained. Full article