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Register a new userIs a pole type singularity an alternative to inflation?
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In this paper, we apply a method of reducing the dynamics of FRW cosmological models with the barotropic form of the equation of state to the dynamical system of the Newtonian type to detect the finite scale factor singularities and the finite-time singularities. In this approach all information concerning the dynamics of the system is contained in a diagram of the potential function $V(a)$ of the scale factor. Singularities of the finite scale factor manifest by poles of the potential function. In our approach the different types of singularities are represented by critical exponents in the power-law approximation of the potential. The classification can be given in terms of these exponents. We have found that the pole singularity can mimick an inflation epoch. We demonstrate that the cosmological singularities can be investigated in terms of the critical exponents of the potential function of the cosmological dynamical systems. We assume the general form of the model contains matter and some kind of dark energy which is parameterized by the potential. We distinguish singularities (by ansatz about the Lagrangian) of the pole type with the inflation and demonstrate that such a singularity can appear in the past.
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It was recently shown that gravitons with a very small mass should have formed a Bose-Einstein condensate in the very early Universe, whose density and quantum potential can account for the dark matter and dark energy in the Universe respectively. Here we show that the condensation can also naturally explain the observed large scale homogeneity and isotropy of the Universe. Furthermore gravitons continue to fall into their ground state within the condensate at every epoch, accounting for the observed flatness of space at cosmological distances scales. Finally, we argue that the density perturbations due to quantum fluctuations within the condensate give rise to a scale invariant spectrum. This therefore provides a viable alternative to inflation, which is not associated with the well-known problems associated with the latter.
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.
We examine the class of initial conditions which give rise to inflation. Our analysis is carried out for several popular models including: Higgs inflation, Starobinsky inflation, chaotic inflation, axion monodromy inflation and non-canonical inflation. In each case we determine the set of initial conditions which give rise to sufficient inflation, with at least $60$ e-foldings. A phase-space analysis has been performed for each of these models and the effect of the initial inflationary energy scale on inflation has been studied numerically. This paper discusses two scenarios of Higgs inflation: (i) the Higgs is coupled to the scalar curvature, (ii) the Higgs Lagrangian contains a non-canonical kinetic term. In both cases we find Higgs inflation to be very robust since it can arise for a large class of initial conditions. One of the central results of our analysis is that, for plateau-like potentials associated with the Higgs and Starobinsky models, inflation can be realised even for initial scalar field values which lie close to the minimum of the potential. This dispels a misconception relating to plateau potentials prevailing in the literature. We also find that inflation in all models is more robust for larger values of the initial energy scale.
Considering the evolution of a perfect fluid with self-similarity of the second kind, we have found that an initial naked singularity can be trapped by an event horizon due to collapsing matter. The fluid moves along time-like geodesics with a self-similar parameter $alpha = -3$. Since the metric obtained is not asymptotically flat, we match the spacetime of the fluid with a Schwarzschild spacetime. All the energy conditions are fulfilled until the naked singularity.
We study inflation in Weyl gravity. The original Weyl quadratic gravity, based on Weyl conformal geometry, is a theory invariant under Weyl symmetry of (gauged) local scale transformations. In this theory Planck scale ($M$) emerges as the scale where this symmetry is broken spontaneously by a geometric Stueckelberg mechanism, to Einstein-Proca action for the Weyl photon (of mass near $M$). With this action as a low energy broken phase of Weyl gravity, century-old criticisms of the latter (due to non-metricity) are avoided. In this context, inflation with field values above $M$ is natural, since this is just a phase transition scale from Weyl gravity (geometry) to Einstein gravity (Riemannian geometry), where the massive Weyl photon decouples. We show that inflation in Weyl gravity coupled to a scalar field has results close to those in Starobinsky model (recovered for vanishing non-minimal coupling), with a mildly smaller tensor-to-scalar ratio ($r$). Weyl gravity predicts a specific, narrow range $0.00257 leq rleq 0.00303$, for a spectral index $n_s$ within experimental bounds at $68%$CL and e-folds number $N=60$. This range of values will soon be reached by CMB experiments and provides a test of Weyl gravity. Unlike in the Starobinsky model, the prediction for $(r, n_s)$ is not affected by unknown higher dimensional curvature operators (suppressed by some large mass scale) since these are forbidden by the Weyl gauge symmetry.
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