Flatness Problems Research Articles

Design and fabrication of EBG and CWP antennas using inkjet printing technology

AbstractThis article presents a solution to bypass the cost and flatness problems for low‐cost electronic devices which is the inkjet printing. This process allows the use of flexible substrate materials, such as paper or plastics, suitable for a real‐to‐real process. More precisely, the procedure to design an electromagnetic band gap antenna using frequency selective surfaces and coplanar wire‐patch antenna for 2.5‐GHz applications is detailed. This kind of antenna has been designed before, but the used substrate is expensive and thin. These antennas were fabricated using inkjet printing technology on a flexible, low‐cost paper substrate using a simple, fast, and cheap process compared to the photolithography technology. The design characteristics of the antennas were verified and the experimental measurements were successfully compared to the simulated ones. © 2013 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:1520–1526, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27613

Steady Flow cosmological model

The possibility that the cosmological constant is decaying as the observable universe grows is explored, and we define a cosmological parameter, depending of the vacuum energy and the universe radius, which should be presently ca. 122 orders of magnitude smaller than at the Planck epoch. From it, a new version of the Friedmann equation for a flat universe is obtained, which allows the estimation of the Hubble parameter at any epoch and the reconstruction of the expansion history. The main result is a quasi-linear expansion dynamics in concurrence with a number of previous works. This behavior is compatible with the main features of observational cosmology and avoids the horizon, flatness, cosmological constant, coincidence and age problems without the need of neither inflation nor initial fine-tuning.

An Exact Scalar Field Inflationary Cosmological Model Which Solves Cosmological Constant Problem, Dark Matter Problem and Other Problems of Inflationary Cosmology

An exact scalar field cosmological model is constructed from the exact solution of the field equations. The solutions are exact and no approximation like slow roll is used. The model gives inflation, solves horizon and flatness problems. The model also gives a satisfactory estimate of present vacuum energy density as well as vacuum energy density at Planck epoch and solves cosmological constant problem of 120 orders of magnitude discrepancy of vacuum energy density. Further, this model predicts existence of dark matter/energy and gives an extremely accurate estimate of present energy density of dark matter and energy. Along with explanations of graceful exit, radiation era, matter domination, this model also indicates the reason for present accelerated state of the universe. In this work a method is shown following which one can construct an infinite number of exact scalar field inflationary cosmological models.

Cosmology on compact and stable supergravity background

We propose a cosmological model of D3-brane universe on compact and stable supergravity background of wrapped D7-branes in type IIB string theory previously argued to be dual to pure N=1 SU(N) gauge theory in four dimensions. A model universe of order Planck size near the UV boundary dynamically flows toward the IR with constant total energy density and accelerating expansion followed by smooth transition to decelerating expansion and collides with the wrapped D7-branes at the IR boundary. The model addresses the horizon and flatness problems with most of the expansion produced during the decelerating expansion phase. The inflationary scenario is used to generate sources of inhomogeneities in the cosmic microwave background radiation and seeds for large scale structure formation from quantum fluctuations which exit the Hubble radius early during the accelerating expansion phase and the model addresses the inhomogeneity problem with red tilt in the power spectrum. We propose that the kinetic energy of the model universe is converted to matter and radiation by the collision followed by formation of baryons that stabilizes the model universe against gravitational force from the background at a finite distance from the IR boundary with the wrapped D7-branes serving as sources of color. Friedmann evolution then takes over with a positive cosmological constant term coming from the remaining potential energy density which is interpreted as dark energy. The magnitude of dark energy density is smaller than the total energy density during the flow by a ratio of the scale factor when the model universe appears in the UV to the scale factor at the moment of collision and stays constant while the matter-radiation density falls during Friedmann expansion.

Analyzing cosmic bubble collisions

We develop a set of controlled, analytic approximations to study the effects of bubble collisions on cosmology. We expand the initial perturbation to the inflaton field caused by the collision in a general power series, and determine its time evolution during inflation in terms of the coefficients in the expansion. In models where the observer's bubble undergoes sufficient slow-roll inflation to solve the flatness problem, in the thin wall limit only one coefficient in the expansion is relevant to observational cosmology, allowing nearly model-independent predictions. We discuss two approaches to determining the initial perturbation to the inflaton and the implications for the sign of the effect (a hot or cold spot on the Cosmic Microwave Background temperature map). Lastly, we analyze the effects of collisions with thick-wall bubbles, i.e. away from the thin-wall limit.

The pseudo-conformal universe: scale invariance from spontaneous breaking of conformal symmetry

We present a novel theory of the very early universe which addresses the traditional horizon and flatness problems of big bang cosmology and predicts a scale invariant spectrum of perturbations. Unlike inflation, this scenario requires no exponential accelerated expansion of space-time. Instead, the early universe is described by a conformal field theory minimally coupled to gravity. The conformal fields develop a time-dependent expectation value which breaks the flat space so(4,2) conformal symmetry down to so(4,1), the symmetries of de Sitter, giving perturbations a scale invariant spectrum. The solution is an attractor, at least in the case of a single time-dependent field. Meanwhile, the metric background remains approximately flat but slowly contracts, which makes the universe increasingly flat, homogeneous and isotropic, akin to the smoothing mechanism of ekpyrotic cosmology. Our scenario is very general, requiring only a conformal field theory capable of developing the appropriate time-dependent expectation values, and encompasses existing incarnations of this idea, specifically the U(1) model of Rubakov and the Galileon Genesis scenario. Its essential features depend only on the symmetry breaking pattern and not on the details of the underlying lagrangian. It makes generic observational predictions that make it potentially distinguishable from standard inflation, in particular significant non-gaussianities and the absence of primordial gravitational waves.

Lorentz-violating dynamics in the pre-Planckian Universe

We have recently proposed a Lorentz-violating energy-momentum relation entailing an exact momentum cutoff and studied various physical applications of that dispersion law. By a simple phenomenological approach we here study Lorentz violation effects on early Universe and pre-Planckian cosmological radiation. In particular, we predict an effective infinite speed of light soon after the Big Bang instant, leading to a straightforward solution of the horizon and flatness problems without recourse to inflation, cosmological scalar fields or other ad hoc energy sources.

Is there a flatness problem in classical cosmology?

I briefly review the flatness problem within the context of classical cosmology and examine some of the debate in the literature with regard to its definition and even the question whether it exists. I then present some new calculations for cosmological models which will collapse in the future; together with previous work by others for models which will expand forever, this allows one to examine the flatness problem quantitatively for all cosmological models. This leads to the conclusion that the flatness problem does not exist, not only for the cosmological models corresponding to the currently popular values of lambda_0 and Omega_0 but indeed for all Friedmann-Lema\^itre models.

Low-scale supersymmetry from inflation

We investigate an inflation model with the inflaton being identified with a Higgs boson responsible for the breaking of U(1)B−L symmetry. We show that supersymmetry must remain a good symmetry at scales one order of magnitude below the inflation scale, in order for the inflation model to solve the horizon and flatness problems, as well as to account for the observed density perturbation. The upper bound on the soft supersymmetry breaking mass lies between 1 TeV and 103 TeV. Interestingly, our finding opens up a possibility that universes with the low-scale supersymmetry are realized by the inflationary selection. Our inflation model has rich implications; non-thermal leptogenesis naturally works, and the gravitino and moduli problems as well as the moduli destabilization problem can be solved or ameliorated; the standard-model higgs boson receives a sizable radiative correction if the supersymmertry breaking takes a value on the high side ∼ 103 TeV.

Cosmology with torsion: An alternative to cosmic inflation

We propose a simple scenario which explains why our Universe appears spatially flat, homogeneous and isotropic. We use the Einstein–Cartan–Kibble–Sciama (ECKS) theory of gravity which naturally extends general relativity to include the spin of matter. The torsion of spacetime generates gravitational repulsion in the early Universe filled with quarks and leptons, preventing the cosmological singularity: the Universe expands from a state of minimum but finite radius. We show that the dynamics of the closed Universe immediately after this state naturally solves the flatness and horizon problems in cosmology because of an extremely small and negative torsion density parameter, ΩS≈−10−69. Thus the ECKS gravity provides a compelling alternative to speculative mechanisms of standard cosmic inflation. This scenario also suggests that the contraction of our Universe preceding the bounce at the minimum radius may correspond to the dynamics of matter inside a collapsing black hole existing in another universe, which could explain the origin of the Big Bang.

Bubble, bubble, flow and Hubble: large scale galaxy flow from cosmological bubble collisions

We study large scale structure in the cosmology of Coleman-de Lucciabubble collisions. Within a set of controlled approximations wecalculate the effects on galaxy motion seen from inside a bubble whichhas undergone such a collision. We find that generically bubblecollisions lead to a coherent bulk flow of galaxies on some part ofour sky, the details of which depend on the initial conditions of thecollision and redshift to the galaxy in question. With otherparameters held fixed the effects weaken as the amount of inflationinside our bubble grows, but can produce measurable flows past thenumber of efolds required to solve the flatness and horizon problems.

Prediction of Formation of Wavy Surfaces in Rolled Plates by Post-Buckling Analysis

Excessive wavy surfaces formed by a cold- or hot-rolling process in a thin plate degrades the value of the plate significantly, which is called the flatness problem in the industry. It is a result of post-buckling due to the residual stress caused by the rolling process. Because the buckling occurs in a very long, continuous plate, a unique difficulty of the problem as a buckling problem is that the buckling length is not given but has to be found. In many previous works, the length that gives the lowest critical load of the plate for the given load profile was taken as the buckling length. In this work, it is shown that this approach is flawed, and a new approach is developed to solve the flatness problem by extending a classic post-buckling analysis method based on the energy principle. The approach determines the buckling length and amplitude without using any unfounded assumptions or hypothesis. Using simple displacement functions, approximate solutions are obtained in closed forms for the plate subjected to a linearly distributed residual stress. The new solution approach can be used to determine the condition for the maximum rolling production that does not cause the flatness problem.

Tachyacoustic cosmology: An alternative to inflation

We consider an alternative to inflation for the generation of superhorizon perturbations in the universe in which the speed of sound is faster than the speed of light. We label such cosmologies, first proposed by Armendariz-Picon, {\it tachyacoustic}, and explicitly construct examples of non-canonical Lagrangians which have superluminal sound speed, but which are causally self-consistent. Such models possess two horizons, a Hubble horizon and an acoustic horizon, which have independent dynamics. Even in a decelerating (non-inflationary) background, a nearly scale-invariant spectrum of perturbations can be generated by quantum perturbations redshifted outside of a shrinking acoustic horizon. The acoustic horizon can be large or even infinite at early times, solving the cosmological horizon problem without inflation. These models do not, however, dynamically solve the cosmological flatness problem, which must be imposed as a boundary condition. Gravitational wave modes, which are produced by quantum fluctuations exiting the Hubble horizon, are not produced.

THE EFFECTIVE THEORY OF INFLATION IN THE STANDARD MODEL OF THE UNIVERSE AND THE CMB+LSS DATA ANALYSIS

Inflation is today a part of the Standard Model of the Universe supported by the cosmic microwave background (CMB) and large scale structure (LSS) datasets. Inflation solves the horizon and flatness problems and naturally generates density fluctuations that seed LSS and CMB anisotropies, and tensor perturbations (primordial gravitational waves). Inflation theory is based on a scalar field φ (the inflaton) whose potential is fairly flat, leading to a slow-roll evolution. This review focuses on the following new aspects of inflation. We present the effective theory of inflation à la Ginsburg and Landau, in which the inflaton potential is a polynomial in the field φ and has the universal form [Formula: see text], where [Formula: see text], M ≪ M Pl is the scale of inflation and N ~ 60 is the number of e-folds since the cosmologically relevant modes exit the horizon till inflation ends. The slow-roll expansion becomes a systematic 1/N expansion and the inflaton couplings become naturally small as powers of the ratio (M/M Pl )2. The spectral index and the ratio of tensor/scalar fluctuations are [Formula: see text], [Formula: see text], while the running index turns out to be [Formula: see text] and therefore can be neglected. The energy scale of inflation M ~ 0.7 × 1016 GeV is completely determined by the amplitude of the scalar adiabatic fluctuations. A complete analytic study plus the Monte Carlo Markov chain (MCMC) analysis of the available CMB+LSS data (including WMAP5) with fourth degree trinomial potentials showed: (a) the spontaneous breaking of the φ → - φ symmetry of the inflaton potential; (b) a lower bound for r in new inflation: r > 0.023 (95% CL) and r > 0.046 (68 CL); (c) the preferred inflation potential is a double-well, even function of the field with a moderate quartic coupling yielding as the most probable values ns ≃ 0.964, r ≃ 0.051. This value for r is within reach of forthcoming CMB observations. The present data in the effective theory of inflation clearly prefer new inflation. Study of higher degree inflaton potentials shows that terms of degree higher than 4 do not affect the fit in a significant way. In addition, a horizon exit happens for [Formula: see text], making higher order terms in the potential w negligible. We summarize the physical effects of generic initial conditions (different from Bunch–Davies) on the scalar and tensor perturbations during slow roll and introduce the transfer function D(k), which encodes the observable initial condition effects on the power spectra. These effects are more prominent in the low CMB multipoles: a change in the initial conditions during slow roll can account for the observed CMB quadrupole suppression. Slow-roll inflation is generically preceded by a short, fast-roll stage. Bunch–Davies initial conditions are the natural initial conditions for the fast-roll perturbations. During fast roll, the potential in the wave equations of curvature and tensor perturbations is purely attractive and leads to a suppression of the curvature and tensor CMB quadrupoles. An MCMC analysis of the WMAP+SDSS data including fast roll shows that the quadrupole mode exits the horizon about 0.2 e-fold before fast roll ends and its amplitude gets suppressed. In addition, fast roll fixes the initial inflation redshift to be z init = 0.9 × 1056 and the total number of e-folds of inflation to be N tot ≃ 64. Fast roll fits the TT, the TE and the EE modes well, reproducing the quadrupole suppression. A thorough study of the quantum loop corrections reveals that they are very small and are controlled by powers of (H/M Pl )2 ~ 10-9, a conclusion that validates the reliability of the effective theory of inflation. The present review shows how powerful the Ginsburg–Landau effective theory of inflation is in predicting observables that are being or will soon be contrasted with observations.

Impact of Lorentz violation on the dynamics of inflation

This work deals with the dynamics of inflation in the context of a scalar-vector-tensor theory of gravity exhibiting spontaneous Lorentz violation at early times. We describe a first-order formalism which we use to obtain new exact Lorentz violating inflationary solutions for a broad family of models, some in the absence of a potential for the inflaton field. Our results show that different conditions are required to solve the horizon and flatness problems. In particular, we find a necessary condition for inflation to provide a solution to both problems and we show that in inflationary models with no inflaton potential a period of superinflation might be necessary to solve the flatness problem.

The Cosmological Slingshot Scenario in details

We generalize the Cosmological Slingshot Scenario for a Slingshot brane moving in a Klebanov-Strassler throat. We show that the horizon and isotropy problems of standard cosmology are avoided, while the flatness problem is acceptably alleviated. Regarding the primordial perturbations, we identify their vacuum state and elucidate the evolution from the quantum to the classical regimes. Also, we calculate their exact power spectrum showing its compatibility with current data. We discuss the bouncing solution from a four dimensional point of view. In this framework the radial and angular motion of the Slingshot brane are described by two scalar fields. We show that the bouncing solution for the scale factor in String frame is mapped into a monotonically increasing (in conformal time) solution in the Einstein frame. We finally discuss about the regularity of the geometry in Einstein frame.

The Cosmological constant and the coincidence problem in a new cosmological interpretation of the universal constant “c”

In a recent paper (Vigoureux et al. Int. J. Theor. Phys. 47:928, 2007) it has been suggested that the velocity of light and the expansion of the universe are two aspects of one single concept connecting space and time in the expanding universe. It has then be shown that solving Friedmann's equations with that interpretation (and keeping c = constant) can explain number of unnatural features of the standard cosmology (for example: the flatness problem, the problem of the observed uniformity in term of temperature and density of the cosmological background radiation, the small-scale inhomogeneity problem...) and leads to reconsider the Hubble diagram of distance moduli and redshifts as obtained from recent observations of type Ia supernovae without having to need an accelerating universe. In the present work we examine the problem of the cosmological constant. We show that our model can exactly generate $\Lambda$ (equation of state $P_\varphi = - \rho_\varphi c^2$ with $\Lambda \propto R^{-2}$) contrarily to the standard model which cannot generate it exactly. We also show how it can solve the so-called cosmic coincidence problem.

Watching worlds collide: effects on the CMB from cosmological bubble collisions

We extend our previous work on the cosmology of Coleman-de Luccia bubble collisions. Within a set of approximations we calculate the effects on the cosmic microwave background (CMB) as seen from inside a bubble which has undergone such a collision. We find that the effects are always qualitatively similar—an anisotropy that depends only on the angle to the collision direction—but can produce a cold or hot spot of varying size, as well as power asymmetries along the axis determined by the collision. With other parameters held fixed the effects weaken as the amount of inflation which took place inside our bubble grows, but generically survive order 10 efolds past what is required to solve the horizon and flatness problems. In some regions of parameter space the effects can survive arbitrarily long inflation.

Bimetric varying speed of light theories and primordial fluctuations

We exhibit a varying speed of light (VSL) theory that implements the recently proposed decaying speed of sound mechanism for generating density fluctuations. We avail ourselves of bimetric VSL theories, where the speed of gravity differs from that of light. We first show that a Dirac-Born-Infeld (DBI) type of $K$-essence has the necessary speed of sound profile to produce (near) scale-invariant fluctuations. We then examine the map between bimetric and $K$-essence models: typically the bi-scalar connecting the two metrics is a $K$-essence field in one of them. Remarkably, the DBI model is found to perturbatively represent the minimal bimetric model, where the bi-scalar is Klein-Gordon in the matter frame. But the full non-perturbative bimetric structure is even simpler: the bi-scalar dynamics should be simply driven by a cosmological constant in the matter frame, balanced by an opposite cosmological constant in the gravity frame. Thus the problem of structure formation receives an elegant and universal solution within bimetric VSL theories, which are known to also solve the flatness and entropy problems and evade a plethora of causality concerns.

Fantappié-Arcidiacono Spacetime and Its Consequences in Quantum Cosmology

Einstein’s gravitational theory gave rise to a new conception of the Universe and Cosmology has been enclosed in the realm of Science and not only of Philosophy as before the Einstein work. Despite this, the presence of the Big Bang singularity, flatness and horizon problems led to the statement that Standard Cosmological Model, based on General Relativity and Standard Model of particle physics, is inadequate to describe the Universe in extreme regimes. Due to this facts, alternative gravitational theories and alternative approaches to cosmology have been proposed during the years. One of the most fruitful approach has been that of Projective Relativity and, in this paper, we analyze the developments of this theory. Projective Relativity, initially proposed by Fantappie and subsequently developed by Arcidiacono, has been recently revisited by prof. Ignazio Licata and other authors. The cosmological consequences of such extension appear relevant. In the following, we analyze the effects of the group approach on the metrics and on the dynamics and we will consider its properties in connection with varying speed of light.