Cosmological perturbations in inflationary-universe models

A brief introduction to the gauge invariant classical and quantum theory of cosmological perturbations is given. Applications include a consistent and unified description of the generation and evolution of fluctuations in inflationary Universe models, and a definition of nonequilibrium entropy for the gravitational field at the linearized level.

Search Radius Setting and Updation for Sphere Decoder for MIMO systems

I briefly review the main features of inflationary universe models. Inflation provides a mechanism which produces energy density fluctuations on cosmological scales. In the original models it was not possible to obtain the correct magnitude of these fluctuations without fine tuning the particle physics models. I discuss two mechanisms, “chaotic inflation”, and a “dynamical relaxation” process, by which inflation may be realized in models which give the right magnitude of fluctuations.

We contrast the possibility of inflation starting (a) from the universe's inception or (b) from an earlier noninflationary state. Neither case is ideal since (a) assumes that quantum mechanical reasoning is straightforwardly applicable to the early universe, while case (b) requires that a singularity still be present. Further, in agreement with Vachaspati and Trodden case (b) can only solve the horizon problem if the noninflationary phase has an equation of state $\ensuremath{\gamma}<4/3,$ thereby excluding radiation or massless scalar field dominated cases. Other alternative models, such as the smooth branch change in the pre-big-bang model, have related problems of requiring homogeneity over noncausally connected large scales.

Three dimensional discrete element simulation of cylindrical cavity expansion from zero initial radius in sand

view Abstract Citations (85) References (24) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Analyzing Cosmological Perturbations Using the Covariant Approach Hwang, Jai-Chan ; Vishniac, Ethan T. Abstract In this paper, we have presented a complete set of equations using the covariant approach to the linear analysis of cosmological perturbations in general relativity without fixing gauges and by using gauge-invariant variables. In addition, we have extended Hawking's analysis of the evolution of vorticity and Jackson's analysis of the density evolution equation to include the effects of an imperfect fluid in exact covariant form. We have explicitly corrected the error in Hawking's covariant analysis and compare the result with other approaches using different gauges. In addition, we have extended the recently derived Ellis and Bruni equations to the case of an imperfect fluid and show that their variables can be identified with the variables used by Bardeen in his gauge-invariant approach to cosmological perturbation analysis. Our calculation is done in the particle frame, so that the energy flux terms appear explicitly with a background that allows for a cosmological constant. Finally, we present an explicit solution for the evolution of large-scale cosmological density perturbations assuming a perfect fluid, but making no other restrictions on the background cosmological model. We conclude by emphasizing the advantages of the covariant approach in perturbation analysis and future applications of the covariant approach. Publication: The Astrophysical Journal Pub Date: April 1990 DOI: 10.1086/168583 Bibcode: 1990ApJ...353....1H Keywords: Computational Astrophysics; Cosmology; Covariance; Galactic Evolution; Perturbation Theory; Density Distribution; Harmonic Analysis; Relativity; Astrophysics; COSMOLOGY; GALAXIES: CLUSTERING; GALAXIES: FORMATION; HYDRODYNAMICS; RELATIVITY full text sources ADS |

The Everett-type interpretations of quantum mechanics and quantum cosmology proposed independently by Hartle, Geroch, and Wada are discussed. They essentially involve regarding a strong peak in the wave function as a definite prediction. Wave functions in quantum cosmology are usually peaked about correlations between coordinates and momenta, and methods for identifying such correlations are introduced. The first method involves Wigner's function, a quantum-mechanical analogue of the classical phase-space distribution. The properties of this distribution are discussed and it is shown how it can be of use in describing the emergence of classical behavior from quantum systems. The second method involves a suitably chosen canonical transformation. These methods are applied to harmonic-oscillator examples, which are of relevance to scalar field fluctuations in inflationary universe models. These methods are also applied to WKB wave functions in quantum mechanics and quantum cosmology. The manner in which the wave function becomes peaked about sets of classical solutions is elucidated. This is extended to include inhomogeneous perturbations about minisuperspace in quantum cosmology, and the derivation of the semiclassical Einstein equations, ${G}_{\ensuremath{\mu}\ensuremath{\nu}}$=8\ensuremath{\pi}G〈${T}_{\ensuremath{\mu}\ensuremath{\nu}}$〉, from the Wheeler-DeWitt equation is considered. A condition under which they are valid is derived. It is essentially the requirement that the distribution of ${T}_{\ensuremath{\mu}\ensuremath{\nu}}$, as a function of the matter modes, is strongly peaked about its average value. Some situations in which this condition is satisfied are discussed.

Evolution equation for the expectation value of a scalar field in spatially flat RW universes

We consider an inflationary universe model in the context of generalized cosmic Chaplygin gas by taking matter field as standard and tachyon scalar fields. We evaluate the corresponding scalar fields and scalar potentials during intermediate and logamediate inflationary regimes by modifying the first Friedmann equation. In each case, we evaluate the number of e-folds, scalar as well as tensor power spectra, scalar spectral index and important observational parameter, i.e., tensor-scalar ratio in terms of inflatons. The graphical behavior of this parameter shows that the model remains incompatible with WMAP7 and Planck observational data in each case.

We study the production of large-scale (\ensuremath{\sim}Mpc) magnetic fields in inflationary Universe models. The magnetic fields produced are uninterestingly small unless the conformal invariance of the electromagnetic field is broken. Once the conformal invariance is broken, a mechanism akin to ``superadiabatic amplification'' can operate and lead to sizable primeval magnetic fields. We consider three ways of breaking the conformal invariance: through gravitational couplings of the photon; through the coupling of the photon to a charged massless, nonconformally invariant scalar field; and through the anomalous coupling of the photon to axions. The primeval magnetic fields which result can have astrophysically interesting strengths, but are very model dependent.

The dynamics of expansion of the Universe and evolution of scalar perturbations are studied for the quintessential scalar fields $Q$ with the classical Lagrangian satisfying the additional condition $w=const$ or $c^2_a=0$. Both quintessential fields are studied for the same cosmological model. The systems of evolutionary equations for gauge-invariant perturbations of metrics, matter and quintessence have been analysed analyticaly for the early stage of the Universe life and numerically up to the present epoch. It is shown that amplitudes of the adiabatic matter density perturbations grow like in $\Lambda$CDM-model but time dependences of amplitudes of the quintessence perturbations are more varied: gauge-invariant variables $D_g^{(Q)}$ and $D_s^{(Q)}$ decay from initial constant value after entering the particle horizon while $D^{(Q)}$ and $V^{(Q)}$ grow at the early stage before entering the horizon and decay after that -- in the quintessence-dominated epoch, when gravitational potential starts to decay -- so, that at the current epoch they are approximately two orders lower than matter ones at the supercluster scale. Therefore, at the subhorizon scales the quintessential scalar fields are smoothed out while the matter clusters. It is also shown that both quintessential scalar fields suppress the growth of matter density perturbations and the amplitude of gravitational potential. In these QCDM-models -- unlike $\Lambda$CDM ones -- such suppression is scale dependent and more visible for the quintessence with $c^2_a=0$.

We study transitions of hadronic matter (HM) to 3-flavor quark matter (3QM),\nregarding the conversion processes as combustion and describing them\nhydrodynamically. Under the assumption that HM is metastable with their free\nenergies being larger than those of 3QM but smaller than those of 2-flavor\nquark matter (2QM), we consider in this paper the conversion induced by\ndiffusions of seed 3QM. This is a sequel to our previous paper, in which the\nshock-induced conversion was studied in the same frame work. We not only pay\nattention to the jump condition on both sides of the conversion front but the\nstructures inside the front are also considered by taking into account what\nhappens during the conversion processes on the time scale of weak interactions.\nWe employ for HM the Shen's EOS, which is based on the relativistic mean field\ntheory, and the bag model-based EOS for QM just as in the previous paper. We\ndemonstrated in that paper that in this combination of EOS's the combustion\nwill occur for a wide range of the bag constant and strong coupling constant in\nthe so-called endothermic regime, in which the Hugoniot curve for combustion\nruns below the initial state. We find that weak deflagration nearly always\noccurs and that weak detonation is possible only when the diffusion constant is\n(unrealistically) large and the critical strange fraction is small. The\nvelocities of the conversion front are ~ $10^3-10^7$ cm/s depending on the\ninitial temperature and density as well as the parameters in the QM EOS and\nbecome particularly small when the final state is in the mixed phase. Finally\nwe study linear stability of the laminar weak-deflagration front and find that\nit is unstable in the exothermic regime (Darrius-Landau instability) but stable\nin the endothermic regime, which is quite contrary to the ordinary combustions.\n

I briefly review the main features of inflationary universe models. Inflation provides a mechanism which produces energy density fluctuations on cosmological scales. In the original models it was not possible to obtain the correct magnitude of these fluctuations without fine tuning the particle physics models. I discuss a modified model, “chaotic inflation”, in which the fine tuning problem is less severe. I also mention other approaches to early universe cosmology.

In a previous paper, we extended the Tao and Mason equation of state (TM EOS) to refrigerant fluids using speed of sound data. Herein, we employ the TM EOS to predict volumetric properties of multi-component mixtures of liquefied natural gas (LNG). The second virial coefficient, B2(T), necessary for the mixture version of the TM EOS, in the absence of sufficient experimental data on B2(T), were calculated from the corresponding state correlation. Analysis of our predicted results shows that the TM EOS is capable of accurately predicting the densities of multi-component liquefied natural gas mixtures over wide range of temperatures and pressures. The overall average absolute deviation (AAD) of the calculated densities from the literature ones for 222 data points was found to be 2.37%. Furthermore, the densities of LNG mixtures obtained from the TM EOS have been compared with those calculated from Peng–Robinson (PR) and Ihm–Song–Mason (ISM) equations of state. Generally, our results show that the TM EOS is favorable over the two other equations of state. The overall average absolute deviation for the 222 data points calculated by ISM and PR equations of state were of the order of 2.90% and 4.85%, respectively.

We report the effects of entropic corrections to the Friedmann equations on the growth of perturbations in the early stages of the universe. We consider two types of corrections to the area law of entropy, known as Tsallis and Barrow entropy. Using these corrections to entropy, we derive the modified Friedmann equations and explore the growth of perturbations in a flat universe filled with dark matter (DM) and the cosmological constant. We employ the spherically symmetric collapse formalism and work in the linear regime for the perturbations. Interestingly enough, we find that the profile of density contrast is quite different from the standard cosmology in Tsallis and Barrow cosmology. We observe that the growth rate of matter perturbations crucially depends on the values of Tsallis and Barrow parameters. By increasing these entropy correction parameters, the total density contrast increases as well. This implies that perturbations grow faster in a universe with modified entropy-corrected Friedmann equations.