Semi analytic approach to understanding the distribution of neutral hydrogen in the universe

Analytic derivations of the correlation function and the column density distribution for neutral hydrogen in the IGM are presented, assuming that the non-linear baryonic mass density distribution in the IGM is lognormal. This ansatz was used earlier by Bi & Davidsen (1997) to perform 1D simulations of lines-of-sight and analyse the properties of absorption systems. Our approach is completely analytic, which allows us to explore a wide region of the parameter space for our model. The analytic results have been compared with observations, whenever possible. Two kinds of correlation functions are defined: along the line-of-sight (LOS) and across the transverse direction. We find that the effects on the LOS correlation due to change in cosmology and the slope of the equation of state of the IGM, \gamma are of the same order, which means that we cannot constrain both the parameters simultaneously. However, it is possible to constrain \gamma and its evolution using the observed LOS correlation function at different epochs, provided one knows the background cosmology. We suggest that the constraints on the evolution of \gamma obtained using the LOS correlation can be used as an independent tool to probe the reionisation history of the universe. From the transverse correlation function, we find that the excess probability, over random, of finding two neutral hydrogen overdense regions separated by an angle \theta, is always less than 1 per cent for redshifts greater than 2. Our models also reproduce the observed column density distribution for neutral hydrogen and the shape of the distribution depends on \gamma. Our calculations suggest that one can rule out \gamma > 1.6 for z \simeq 2.31 using the column density distribution. However, one cannot rule higher values of \gamma at higher redshifts.Comment: 16 pages, 8 figures. Accepted for publication in MNRAS. Revised following referee's comment

Reply to [arXiv:1105.5653]: "Comment on 'Quasinormal modes in Schwarzschild-de Sitter spacetime: A simple derivation of the level spacing of the frequencies'"

We explain why the analysis in our paper [Phys. Rev. D 69, 064033 (2004), arXiv:gr-qc/0311064 ] is relevant and correct.Comment: 2 page

Theoretical and observational constraints on the H i intensity power spectrum

Mapping of the neutral hydrogen (H i) 21-cm intensity fluctuations across redshifts promises a novel and powerful probe of cosmology. The neutral hydrogen gas mass density $\Omega _{\rm H\,\small {i}}$ and bias parameter $b_{\rm H\,\small {i}}$ are key astrophysical inputs to the H i intensity fluctuation power spectrum. We compile the latest theoretical and observational constraints on $\Omega _{\rm H\,\small {i}}$ and $b_{\rm H\,\small {i}}$ at various redshifts in the post-reionization universe. Constraints are incorporated from galaxy surveys, H i intensity mapping experiments, damped Lyman α system observations, theoretical prescriptions for assigning H i to dark matter haloes and the results of numerical simulations. Using a minimum variance interpolation scheme, we obtain the predicted uncertainties on the H i intensity fluctuation power spectrum across redshifts 0-3.5 for three different confidence scenarios. We provide a convenient tabular form for the interpolated values of $\Omega _{\rm H\,\small {i}}$, $b_{\rm H\,\small {i}}$ and the H i power spectrum amplitude and their uncertainties. We discuss the consequences for the measurement of the power spectrum by current and future intensity mapping experiment

A theoretician's analysis of the supernova data and the limitations in determining the nature of dark energy

Current cosmological observations show a strong signature of the existence of a dark energy component with negative pressure. The most obvious candidate for this dark energy is the cosmological constant (with the equation of state w_X=p/\rho=-1), which, however, raises several theoretical difficulties. This has led to models for dark energy component which evolves with time. We discuss certain questions related to the determination of the nature of dark energy component from observations of high redshift supernova. The main results of our analysis are: (i) Even if the precise value of w_X is known from observations, it is not possible to determine the nature of the unknown dark energy source using only kinematical and geometrical measurements. We have given explicit examples to show that different types of sources can give rise to a given w_X. (ii) Although the full data set of supernova observations (which are currently available) strongly rule out models without dark energy, the high (z>0.25) and low (z<0.25) redshift data sets, individually, admit decelerating models with zero dark energy. Any possible evolution in the absolute magnitude of the supernovae, if detected, might allow the decelerating models to be consistent with the data. (iii) We have introduced two parameters, which can be obtained entirely from theory, to study the sensitivity of the luminosity distance on w_X. Using these two parameters, we have argued that although one can determine the present value of w_X accurately from the data, one cannot constrain the evolution of w_X.Comment: Revised versio

Dark Energy and Gravity

I review the problem of dark energy focusing on the cosmological constant as the candidate and discuss its implications for the nature of gravity. Part 1 briefly overviews the currently popular `concordance cosmology' and summarises the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as the candidate and emphasises why no other approach really solves the conceptual problems usually attributed to the cosmological constant. Part 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract the key ingredients which must be present in any viable solution. I argue that (i)the cosmological constant problem cannot be satisfactorily solved until gravitational action is made invariant under the shift of the matter lagrangian by a constant and (ii) this cannot happen if the metric is the dynamical variable. Hence the cosmological constant problem essentially has to do with our (mis)understanding of the nature of gravity. Part 3 discusses an alternative perspective on gravity in which the action is explicitly invariant under the above transformation. Extremizing this action leads to an equation determining the background geometry which gives Einstein's theory at the lowest order with Lanczos-Lovelock type corrections. (Condensed abstract).Comment: Invited Review for a special Gen.Rel.Grav. issue on Dark Energy, edited by G.F.R.Ellis, R.Maartens and H.Nicolai; revtex; 22 pages; 2 figure

Concept of temperature in multi-horizon spacetimes: Analysis of Schwarzschild-De Sitter metric

In case of spacetimes with single horizon, there exist several well-established procedures for relating the surface gravity of the horizon to a thermodynamic temperature. Such procedures, however, cannot be extended in a straightforward manner when a spacetime has multiple horizons. In particular, it is not clear whether there exists a notion of global temperature characterizing the multi-horizon spacetimes. We examine the conditions under which a global temperature can exist for a spacetime with two horizons using the example of Schwarzschild-De Sitter (SDS) spacetime. We systematically extend different procedures (like the expectation value of stress tensor, response of particle detectors, periodicity in the Euclidean time etc.) for identifying a temperature in the case of spacetimes with single horizon to the SDS spacetime. This analysis is facilitated by using a global coordinate chart which covers the entire SDS manifold. We find that all the procedures lead to a consistent picture characterized by the following features: (a) In general, SDS spacetime behaves like a non-equilibrium system characterized by two temperatures. (b) It is not possible to associate a global temperature with SDS spacetime except when the ratio of the two surface gravities is rational (c) Even when the ratio of the two surface gravities is rational, the thermal nature depends on the coordinate chart used. There exists a global coordinate chart in which there is global equilibrium temperature while there exist other charts in which SDS behaves as though it has two different temperatures. The coordinate dependence of the thermal nature is reminiscent of the flat spacetime in Minkowski and Rindler coordinate charts. The implications are discussed.Comment: 12 page