Search Results (35)

Making use of the well-known renormalization group (RG) scale dependences of the gravitational couplings in the framework of the two-parameter Einstein–Hilbert (EH) theory of gravity, the single scalar field-driven cosmological inflation is discussed in a spatially homogeneous, isotropic, and flat model universe. The inflaton field is represented by a one-component real, non-self-interacting, massive scalar field minimally coupled to gravity. Cases without and with the incorporation of the RG scaling of the inflaton mass are compared with each other and with the corresponding classical case. It is shown that the quantum improvement drastically alters the timing of the slow-roll inflation with the desirable number $\underset{,}{\mathrm{N}}\approx 60$ e-foldings, as compared with the classical case. Furthermore, accounting for the RG flow of the inflaton mass has an enormous effect on the timing of the desirable slow roll, too. Although providing the desirable slow-roll inflation, none of the versions of the investigated quantum-improved toy models provide a realistic value of the amplitude of the scalar perturbations. Full article

In this work, we elaborate further on a (3+1)-dimensional cosmological Running-Vacuum-type-Model (RVM) of inflation based on string-inspired Chern-Simons(CS) gravity, involving axions coupled to gravitational-CS(gCS) anomalous terms. Inflation in such models is caused by primordial-gravitational-waves(GW)-induced condensation of the gCS terms, which leads to a linear-axion potential. We demonstrate that this inflationary phase may be metastable, due to the existence of imaginary parts of the gCS condensate. These are quantum effects, proportional to commutators of GW perturbations, hence vanishing in the classical theory. Their existence is quantum-ordering-scheme dependent. We argue in favor of a physical importance of such imaginary parts, which we compute to second order in the GW (tensor) perturbations in the framework of a gauge-fixed effective Lagrangian, within a (mean field) weak-quantum-gravity-path-integral approach. We thus provide estimates of the inflation lifetime. On matching our results with the inflationary phenomenology, we fix the quantum-ordering ambiguities, and obtain an order-of-magnitude constraint on the String-Mass-Scale-to-Planck-Mass ratio, consistent with previous estimates by the authors in the framework of a dynamical-system approach to linear-axion RVM inflation. Finally, we examine the role of periodic modulations in the axion potential induced by non-perturbative effects on the slow-roll inflationary parameters, and find compatibility with the cosmological data. Full article

We calculated the two-loop corrections in the primordial power spectrum in models of single-field inflation incorporating an intermediate USR phase employed for PBH formation. Among the overall eleven one-particle irreducible Feynman diagrams, we calculated the corrections from the “double scoop” two-loop diagram involving two vertices of quartic Hamiltonians. We demonstrate herein the fractional two-loop correction in power spectrum scales, like the square of the fractional one-loop correction. We confirm our previous findings that the loop corrections become arbitrarily large in the setup where the transition from the intermediate USR to the final slow-roll phase is very sharp. This suggests that in order for the analysis to be under perturbative control against loop corrections, one requires a mild transition with a long enough relaxation period towards the final attractor phase. Full article

In this review, a pedagogical introduction to the concepts of slow-roll inflationary universe and number of e-folds is provided. In particular, the differences between the basic notion of number of e-folds ($N_e$), total number of e-folds ($N_T$) and number of e-folds before the end of inflation (N) are outlined. The proper application of the number of e-folds before the end of inflation is discussed both as a time-like variable for the scalar field evolution and as a key parameter for computing inflationary predictions. Full article

The de-Sitter spacetime is a maximally symmetric Lorentzian manifold with constant positive scalar curvature that plays a fundamental role in modern cosmology. Here, we investigate bulk-viscosity-assisted quasi de-Sitter inflation, that is the period of accelerated expansion in the early universe during which $-\dot{H}\ll H^2$, with $H\left(t\right)$ being the Hubble expansion rate. We do so in the framework of a causal theory of relativistic hydrodynamics, which takes into account non-equilibrium effects associated with bulk viscosity, which may have been present as the early universe underwent an accelerated expansion. In this framework, the existence of a quasi de-Sitter universe emerges as a natural consequence of the presence of bulk viscosity, without requiring introducing additional scalar fields. As a result, the equation of state, determined by numerically solving the generalized momentum-conservation equation involving bulk viscosity pressure turns out to be time dependent. The transition timescale characterising its departure from an exact de-Sitter phase is intricately related to the magnitude of the bulk viscosity. We examine the properties of the new equation of state, as well as the transition timescale in the presence of bulk viscosity pressure. In addition, we construct a fluid description of inflation and demonstrate that, in the context of the causal formalism, it is equivalent to the scalar field theory of inflation. Our analysis also shows that the slow-roll conditions are realised in the bulk-viscosity-supported model of inflation. Finally, we examine the viability of our model by computing the inflationary observables, namely the spectral index and the tensor-to-scalar ratio of the curvature perturbations, and compare them with a number of different observations, finding good agreement in most cases. Full article

The expectation that the physical expansion of space occurs smoothly may be expressed mathematically as a requirement for continuity in the time derivative of the metric scale factor of the Friedmann–Robertson–Walker cosmology. We explore the consequences of imposing such a smoothness requirement, examining the forms of possible interpolating functions between the end of inflation and subsequent radiation- or matter-dominated eras, using a straightforward geometric model of the interpolating behavior. We quantify the magnitude of the cusp found in a direct transition from the end of slow-roll inflation to the subsequent era, analyze the validity of several smooth interpolator candidates, and investigate equation-of-state and thermodynamic constraints. We find an order-of-magnitude increase in the size of the universe at the end of the transition to a single-component radiation or matter era. We also evaluate the interpolating functions in terms of the standard theory of preheating and determine the effect on the number of bosons produced. Full article

E-type $\alpha$-attractor models of single-field inflation were generalized further in order to accommodate production of primordial black holes (PBHs) via adding a near-inflection point to the inflaton scalar potential at smaller scales, in good agreement with measurements of cosmic microwave background (CMB) radiation. A minimal number of new parameters were used but their fine-tuning was maximized in order to increase the possible masses of PBHs formed during an ultra-slow-roll phase, leading to a large enhancement in the power spectrum of scalar (curvature) perturbations by 6 or 7 orders of magnitude against the power spectrum of perturbations observed in CMB. It was found that extreme fine-tuning of the parameters in our models can lead to the formation of moon-sized PBHs, with masses of up to ${10}^{26}$ g, still in agreement with CMB observations. Quantum corrections are known to lead to the perturbative upper bound on the amplitude of large scalar perturbations responsible for PBH production. The quantum (one-loop) corrections in our models were found to be suppressed by one order of magnitude for PBHs with masses of approximately ${10}^{19}$ g, which may form the whole dark matter in the Universe. Full article

We review conceptual aspects of inflationary scenarios able to produce primordial black holes by amplifying the size of curvature fluctuations to the level required to trigger black hole formation. We identify general mechanisms to do so, both for single- and multiple-field inflation. In single-field inflation, the spectrum of curvature fluctuations is enhanced by pronounced gradients of background quantities controlling the cosmological dynamics, which can induce brief phases of non-slow-roll inflationary evolution. In multiple-field inflation, the amplification occurs through appropriate couplings with additional sectors characterized by tachyonic instabilities that enhance the size of their fluctuations. As representative examples, we consider axion inflation and two-field models of inflation with rapid turns in field space. We develop our discussion in a pedagogical manner by including some of the most relevant calculations and by guiding the reader through the existing theoretical literature, emphasizing general themes common to several models. Full article

A simple phenomenological fit for the power spectrum of scalar (curvature) perturbations during inflation is proposed to analytically describe slow roll of inflaton and formation of primordial black holes (PBH) in the early universe, in the framework of single-field models. The fit is given by a sum of the power spectrum of slow-roll inflation, needed for a viable description of the cosmic microwave background (CMB) radiation in agreement with Planck/BICEP/Keck measurements, and the log-normal (Gaussian) fit for the power spectrum enhancement (peak) needed for efficient PBH production, in the leading (model-independent) approximation. The T-type $\alpha$-attractor models are used to get the simple CMB power spectrum depending upon the e-folds as the running variable. The location and height of the peak are chosen to yield the PBH masses in the asteroid-size window allowed for the whole (current) dark matter. We find the restrictions on the peak width. Full article

Single field inflationary models are investigated within Palatini quadratic gravity, represented by $R+\alpha R^2$, along with a non-minimal coupling of the form $f\left(\varphi \right)R$ between the inflaton field $\varphi$ and the gravity. The treatment is performed in the Einstein frame, where the minimal coupling to gravity is recovered through conformal transformation. We consider various limits of the model with different inflationary scenarios characterized as canonical slow-roll inflation in the limit $\alpha {\dot{\varphi }}^2\ll (1+f\left(\varphi \right))$, constant-roll k-inflation for $\alpha \ll 1$, and slow-roll K-inflation for $\alpha \gg 1$. A cosine and exponential potential are examined with the limits mentioned above and different well-motivated non-minimal couplings to gravity. We compare the theoretical results, exemplified by the tensor-to-scalar r ratio and spectral index $n_s$, with the recent observational results of Planck 2018 and BICEP/Keck. Furthermore, we include the results of a new study forecast precision with which $n_s$ and r can be constrained by currently envisaged observations, including CMB (Simons Observatory, CMB-S4, and LiteBIRD). Full article

We explore a feasible model that combines near-inflection point small-field slow roll inflationary scenario driven by single scalar inflaton with the production of non-thermal vector-like fermionic dark matter, $\chi$, during the reheating era. For the inflationary scenario, we consider two separate polynomial forms of the potential; one is symmetric about the origin, and the other is not. We fix the coefficients of the potentials satisfying current Planck-Bicep data. We calculate the permissible range of $y_{\chi }$ and $m_{\chi }$ for the production of enough dark matter to explain the total Cold Dark Matter (CDM) mass density of the present universe while satisfying Cosmic Background Radiation (CMBR) measurements and other cosmological bounds. Full article

The discovery of gravitational waves from merging binary black holes has generated considerable interest in examining whether these black holes could have a primordial origin. If a significant number of black holes have to be produced in the early universe, the primordial scalar power spectrum should have an enhanced amplitude on small scales, when compared to the COBE normalized values on the large scales that is strongly constrained by the anisotropies in the cosmic microwave background. In the inflationary scenario driven by a single, canonical scalar field, such power spectra can be achieved in models that permit a brief period of ultra slow roll inflation during which the first slow roll parameter decreases exponentially. In this review, we shall consider a handful of such inflationary models as well as a reconstructed scenario and examine the extent of formation of primordial black holes and the generation of secondary gravitational waves in these cases. We shall also discuss the strength and shape of the scalar bispectrum and the associated non-Gaussianity parameter that arise in such situations. We shall conclude with an outlook wherein we discuss the wider implications of the increased strengths of the non-Gaussianities on smaller scales. Full article

We investigate natural inflation with non-minimal coupling to gravity, characterized either by a quadratic or a periodic term, within the warm inflation paradigm during the slow-roll stage, in both strong and weak dissipation limits; and show that, in the case of a T-linearly dependent dissipative term, it can accommodate the spectral index $n_s$ and tensor-to-scalar ratio r observables given by Planck 2018 constraints, albeit with a too-small value of the e-folding number to solve the horizon problem, providing, thus, only a partial solution to natural inflation issues, assuming a T-cubically dependent dissipative term can provide a solution to this e-folding number issue. Full article

We study the constant-roll tachyon inflation with large and small $\eta$. In previous studies, only the constant-roll tachyon inflation with small $\eta$ is consistent with the observations. We find that the duality between the constant-roll tachyon inflation with large and small $\eta$ may exist. The apparent duality suggests that the constant-roll tachyon inflationary model with large $\eta$ may also be consistent with the observations. By fitting the spectral tilde $n_s$ and tensor to scalar ratio r, which is a measure of primordial gravitational waves with the observations, we get small and large $\eta$ in this range $-0.01629\le {\eta }_H\le -0.00079$ and $3.00081\le {\eta }_H\le 3.01621$ at the 2$\sigma$ C.L for $N=60$ efolds. 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