Narrow Results

Motivated by brane cosmology, we solve the Einstein equations with a time-dependent cosmological constant. Assuming that at an early epoch the vacuum energy scales as 1/log t, we show that the universe passes from a fast growing phase (inflation) to an expanding phase in a natural way.

We discuss inflationary solutions of the coupled Einstein–Klein–Gordon equations for a complex field in a five-dimensional spacetime with a compact x⁵ dimension. As a new feature, the scalar field contains a dependence on the extra dimension of the form exp(imx⁵), corresponding to Kaluza–Klein excited modes. In a four-dimensional picture, a nonzero m implies the presence of a new term in the scalar field potential. An interesting feature of these solutions is the possible existence of several periods of oscillation of the scalar field around the equilibrium value at the minimum of the potential. These oscillations lead to cosmological periods of accelerated expansion of the universe.

We present aspects of a model which attempts to unify the creation of cold dark matter, a CP-violating baryon asymmetry, and also a small, residual vacuum energy density, in the early universe. The model contains a primary scalar (inflaton) field and a primary pseudoscalar field, which are initially related by a cosmological, chiral symmetry. The nonzero vacuum expectation value of the pseudoscalar field spontaneously breaks CP invariance.

We investigated a simple D-term inflation with taking account of higher order corrections in the Kähler potential. These terms may solve the cosmic string problem in D-term inflation model. The mass per unit length of cosmic strings formed after inflation can be suppressed enough. In addition, the change of the potential slope leads simultaneously a more tilted scalar spectral index n_s ≃ 0.96 – 0.97 than that in the model without these corrections.

We consider a small, metastable maximum vacuum expectation value b₀ of order of a few eV, for a pseudoscalar Goldstone-like field, which is related to the scalar inflaton field ϕ in an idealized model of a cosmological, spontaneously-broken chiral symmetry. The b field allows for relating semi-quantitatively three distinct quantities in a cosmological context.

(a) A very small, residual vacuum energy density or effective cosmological constant of , for λ ~ 3×10^-14, the same as an empirical inflaton self-coupling.

(b) A tiny neutrino mass, less than b₀.

(c) A possible small variation downward of the proton to electron mass ratio over cosmological time. The latter arises from the motion downward of the b field over cosmological time, toward a nonzero value. Such behavior is consistent with an equation of motion.

We argue that hypothetical b quanta, potentially inducing new long-range forces, are absent, because of negative, effective squared mass in an equation of motion for b-field fluctuations. The assumed flatness of a potential maximum involves a small inverse-time parameter μ ≪ 1/t₀, where t₀ is the present age of the universe.

In this paper we study closed inflationary universe models by means of a tachyonic field. We described a general treatment for created a universe with Ω > 1 in patch cosmology, which is able to represent General Relativity, Gauss–Bonnet or Randall–Sundrum patches. We use recent data from astronomical observations to constrain the parameters appearing in our model.

Recent detection of B-mode polarization induced from tensor perturbations by the BICEP2 experiment implies the so-called large field inflation, where an inflaton field takes super-Planckian expectation value during inflation, at a high energy scale. We show however, if another inflation follows hybrid inflation, the hybrid inflation can generate a large tensor perturbation with not super-Planckian but Planckian field value. This scenario would relax the tension between BICEP2 and Planck concerning the tensor-to-scalar ratio, because a negative large running can also be obtained for a certain number of e-fold of the hybrid inflation. A natural interpretation of a large gravitational wave mode with or without the scalar spectral running might be multiple inflation in the early Universe.

It is generally considered as self evident that the lifetime of our vacuum in the landscape of string theory cannot be much shorter than the current age of the universe. Here I show why this lower limit is invalid. A certain type of "parallel universes" is a necessary consequence of the string-landscape dynamics and might well allow us to "survive" vacuum decay. As a consequence our stringy vacuum's lifetime is empirically unconstrained and could be very short.

Based on this counterintuitive insight I propose a novel type of laboratory experiment that searches for an apparent violation of the quantum-mechanical Born rule by gravitational effects on vacuum decay. If the lifetime of our vacuum should turn out to be shorter than 6 ×10^-13 seconds such an experiment is sufficiently sensitive to determine its value with state-of-the-art equipment.

In part I of the foundation of the hyperunified field theory, we have shown the presence of entangled hyperqubit-spinor field as fundamental building block with appearance of Minkowski hyper-space–time as free-motion space–time and emergence of inhomogeneous hyperspin symmetry as fundamental symmetry. In this paper as part II, we demonstrate by following along gauge invariance principle and scaling invariance hypothesis that the inhomogeneous hyperspin gauge symmetry and scaling gauge symmetry govern fundamental interactions and reveal the nature of gravity and space–time. With the fiber bundle structure of biframe hyper-space–time and emergence of noncommutative geometry, we explore methodically the gauge-geometry duality and genesis of gravitational interaction in locally flat gravigauge hyper-space–time. A whole hyperunified field theory in 19-dimensional hyper-space–time is established to unify not only all discovered leptons and quarks into hyperunified qubit-spinor field but also all known basic forces into hyperunified interaction governed by inhomogeneous hyperspin gauge symmetry. We present a systematic investigation on the hyperunified field theory by deriving the dynamics of fundamental fields as basic laws of nature and conservation laws relative to basic symmetries and showing Higgs-like bosons and three families of lepton–quark states. We provide a detailed analysis on inflationary early universe with evolving graviscalar field and a discussion on scaling gauge field as dark matter candidate and ${{𝒬}}_c$-spin scalar field as source of dark energy.

We study cosmological perturbations and observational aspects for mutated hilltop model of inflation. Employing mostly analytical treatment, we evaluate observable parameters during inflation as well as post-inflationary perturbations. This further leads to exploring observational aspects related to cosmic microwave background (CMB) radiation. This semi-analytical treatment reduces complications related to numerical computation to some extent for studying the different phenomena related to CMB angular power spectrum for mutated hilltop inflation.

In this paper, we consider dark spinor and Higgs fields coupled to gravity and calculate their contributions to the energy density and pressure in Friedmann–Robertson–Walker spacetime. We seek solutions of the fields to yield a de Sitter universe and investigate stability properties of the solutions using linear approximation. We discuss the possibility that the inflationary period of our universe can be described by a combination of the dark spinor and Higgs fields.

A primordial gravitational wave background is a hallmark of inflationary cosmology. The recent announcement made by the BICEP2 collaboration of a possible measurement of B-mode polarization of the CMB on degree scales has produced an abundance of ideas and speculations on how such a signal constrains the inflationary paradigm, or possible alternative mechanisms of gravitational wave production. Here the possibility of a contribution to the gravitational wave background from the relaxation of a scalar field after a global phase transition is reviewed. The general contribution to the overall power is shown, and it is then demonstrated that if the BICEP2 result were to hold, this mechanism could at best produce a very small fraction of the measured tensor power.

By studying the chameleon model during inflation, we investigate whether it can be a successful inflationary model, wherein we employ the common typical potential usually used in the literature. Thus, in the context of the slow-roll approximations, we obtain the e-folding number for the model to verify the ability of resolving the problems of standard big bang cosmology. Meanwhile, we apply the constraints on the form of the chosen potential and also on the equation of state parameter coupled to the scalar field. However, the results of the present analysis show that there is not much chance of having the chameleonic inflation. Hence, we suggest that if through some mechanism the chameleon model can be reduced to the standard inflationary model, then it may cover the whole era of the universe from the inflation up to the late time.

In this paper, we have studied inflationary paradigm through an inflationary equation-of-state. With a single parameter equation-of-state as a function of the scalar field responsible for accelerated expansion, we find an observationally viable model satisfying all the constraints as laid down by the recent observations. The resulting model can efficiently cover a wide range of tensor-to-scalar ratio ranging from $r\sim {𝒪}(10^{-1})$ to ${𝒪}(10^{-6})$, other inflationary observables being consistent with the latest data. Nowadays, ultimate eliminator between inflationary models is the tensor-to-scalar ratio, the model presented here is capable of keeping up with the future probes of tensor-to-scalar ratio at the same time having good agreement with other inflationary observables.

We investigate the early-time accelerated universe after the Big Bang. We pay attention to the dissipative properties of the inflationary universe in the presence of a soft type singularity, making use of the parameters of the generalized equation of state of the fluid. Flat Friedmann–Robertson–Walker metric is being used. We consider cosmological models leading to the so-called type IV singular inflation. Our obtained theoretical results are compared with observational data from the Planck satellite. The theoretical predictions for the spectral index turn out to be in agreement with the data, while for the scalar-to-tensor ratio, there are minor deviations.

The inflationary expansion of our early-time universe is considered in terms of the van der Waals equation, as equation of state for the cosmic fluid, where a bulk viscosity contribution is assumed to be present. The corresponding gravitational equations for the energy density in a homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker universe are solved, and an analytic expression for the scale factor is obtained. Attention is paid, specifically, to the role of the viscosity term in the accelerated expansion; the values of the slow-roll parameters, the spectral index, and the tensor-to-scalar ratio for the van der Waals model are calculated and compared with the most recent astronomical data from the Planck satellite. By imposing reasonable restrictions on the parameters of the van der Waals equation, in the presence of viscosity, it is shown to be possible for this model to comply quite precisely with the observational data. One can therefore conclude that the inclusion of viscosity in the theory of the inflationary epoch may definitely improve the cosmological models.

In this paper, we investigate the effects of Type IV singularity through $f(T)$ gravity description of inflationary Universe, where $T$ denotes the torsion scalar. With the Friedmann equations of the theory, we reconstruct a $f(T)$ model according to a given Hubble rate susceptible to describe the inflationary era near the Type IV singularity. One obtains an interesting well-known $f(T)$ model but with additional constant parameter $c_0$ staying as the Type IV singularity contribution. Moreover, we calculate the Hubble flow parameters in order to determine the dynamical evolution of the cosmological system. The results show that some of the Hubble flow parameters are small near the Type IV singularity and become singular at Type IV singularity, indicating that a dynamical instability of the cosmological system occurs at that point. This means that the dynamical cosmological evolution up to that point ceases to be the final attractor since the system is abruptly interrupted. Furthermore, by considering the $f(T)$ trace anomaly equation, the previous result on the Type IV singularity is consolidated by the conditional instability coming from the de Sitter inflationary description of the reconstructed $f(T)$ model. The model leads to instability strongly governed by the Type IV singularity parameter $c_0$ is viewed as the graceful exit from inflation. Our theoretical $f(T)$ description based on slow-roll parameters not only confirms some observational data on spectral index and the scalar-to-tensor ratio from Planck data and BICEP$2$/Keck-Array data, but also shows the property of $f(T)$ gravity in describing the early and late-time evolution of our Universe.

This paper is fundamentally devoted to the cosmological reconstruction and dynamic studying in homogeneous BIANCHI-I space-time under the $f(T)$ background. Its content is supported by the fact that in the General Relativity description of the standard cosmological paradigm, the evolution from an anisotropic universe into an Friedmann–Lemaitre–Robertson–Walker (FLRW) one can be achieved by a period of inflationary expansion. Nowadays, modified gravity theories like $f(T)$ are widely accepted to provide a real description of some universe evolution phases like inflation era, matter-dominated era, etc. So, we aim to examine here what $f(T)$ gravity model can accommodate with an anisotropic universe, an expanding universe and even the transition between both evolutions. To reach this goal, we use a reconstruction method based on dynamic equations in Bianchi-I space-time by assuming a particular form for the metric anisotropy and by specifying some time functions describing average scale factor. Most of the obtained models are consistent with certain known results in the literature but other add new results in this work. In the second part of this work, the dynamical behaviors of the Bianchi-I space-time are addressed through the reconstruction of an autonomous dynamical system. For an aleatory choice of anisotropic fluid, the numerical analysis of the system shows that the metric anisotropy decreases with expansion. Then, an attractor point is reached and becomes unstable by the end of inflation. Such interesting properties found in this work on Bianchi-I space-time are often interpreted as graceful exit from inflation which doesn’t occur in ordinary FLRW space-time.

In this work, the cosmological inflationary parameters in the correspondence of teleparallel gravity for the scalar–tensor theory are investigated. After the review of $f(T)$ and $f(T,B)$ gravity cosmology, we use the slow-roll approximations to study the behavior of the inflationary parameters namely the spectral index $n_s$ and tensor-to-scalar ratio $r$, and a comparison with observational data for different paradigmatic $f(T)$ gravity models such as exponential, Linder and power-law models is considered. We also consider the boundary term $B$ associated with these three models. The obtained behavior of the parameters under consideration shows that it is possible to constrain $f(T)$ and $f(T,B)$ models based on observational data.

We argue that the emergent spacetime picture admits a background-independent formulation of cosmic inflation. The inflation in this picture corresponds to the dynamical emergence of spacetime while the conventional inflation is simply an (exponential) expansion of a preexisting spacetime owing to the vacuum energy carried by an inflaton field. We show that the cosmic inflation arises as a time-dependent solution of the matrix quantum mechanics describing the dynamical process of Planck energy condensate in vacuum without introducing any inflaton field as well as an ad hoc inflation potential. Thus the emergent spacetime picture realizes a background-independent description of the inflationary universe which has a sufficiently elegant and explanatory power to defend the integrity of physics against the multiverse hypothesis.