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Register a new userQuasi-Steady State Cosmology
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G. Burbidge
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A brief historical account of modern cosmology shows that the standard big bang (BB) model, believed by so many, does not have the strong observational foundations that are frequently claimed for it. The theory of the Quasi-Steady State Cosmology (QSSC) and explosive cosmogony is outlined. Comparisons are made between the two theories in explaining the observed properties of the universe, namely, the expansion, chemical composition, CMB, QSO redshifts and explosive events, galaxy formation, and the m-z and theta-z relations. Only two of the observed properties have ever been predicted from the theories (a) the expansion predicted from Einsteins theory by Friedmann and Lemaitre, and (b) the acceleration predicted by the classical steady state theory and the QSSC.
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In this paper we show that, within the framework of the QSSC, the small scale deviations on angular scales $lesssim 1^{0}$ expected in the MBR are due to inhomogeneities in the distribution of galaxies and clusters. It is shown how these can be estimated on the galaxy-cluster-supercluster scale at the epoch of redshift $sim 5$ when the universe was last passing through the minimum phase of the scale factor. Rich clusters on the scale of 5-10 Mpc generate the kind of peak in the fluctuation power spectrum observed by the Boomrang and Maxima projects. Weaker inhomogeneities on smaller scales with $l~sim 10^3$ are expected to arise from individual galaxies and small groups.
We calculate the expected angular power spectrum of the temperature fluctuations in the microwave background radiation (MBR) generated in the quasi-steady state cosmology (QSSC). The paper begins with a brief description of how the background is produced and thermalized in the QSSC. We then discuss within the framework of a simple model, the likely sources of fluctuations in the background due to astrophysical and cosmological causes. Power spectrum peaks at $l approx 6-10$, 180-220 and 600-900 are shown to be related in this cosmology respectively to curvature effects at the last minimum of the scale factor, clusters and groups of galaxies. The effect of clusters is shown to be related to their distribution in space as indicated by a toy model of structure formation in the QSSC. We derive and parameterize the angular power spectrum using six parameters related to the sources of temperature fluctuations at three characteristic scales. We are able to obtain a satisfactory fit to the observational band power estimates of MBR temperature fluctuation spectrum. Moreover, the values of `best fit parameters are consistent with the range of expected values.
This note discusses a theoretical issue regarding the application of the Modular Response Analysis method to quasi-steady state (rather than steady-state) data.
In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by non-elementary reaction rate functions (e.g. Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the non-elementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of non-elementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the non-elementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in non-elementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the pre-factor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when non-elementary reaction functions are obtained using the total QSSA. Our work provides a novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales.
A preceding paper demonstrated that explicit asymptotic methods generally work much better for extremely stiff reaction networks than has previously been shown in the literature. There we showed that for systems well removed from equilibrium explicit asymptotic methods can rival standard implicit codes in speed and accuracy for solving extremely stiff differential equations. In this paper we continue the investigation of systems well removed from equilibrium by examining quasi-steady-state (QSS) methods as an alternative to asymptotic methods. We show that for systems well removed from equilibrium, QSS methods also can compete with, or even exceed, standard implicit methods in speed, even for extremely stiff networks, and in many cases give somewhat better integration speed than for asymptotic methods. As for asymptotic methods, we will find that QSS methods give correct results, but with non-competitive integration speed as equilibrium is approached. Thus, we shall find that both asymptotic and QSS methods must be supplemented with partial equilibrium methods as equilibrium is approached to remain competitive with implicit methods.
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