Cosmological production of H_2 before the formation of the first galaxies

Previous calculations of the pregalactic chemistry have found that a small amount of H_2, x[H_2]=n[H_2]/n[H] = 2.6e-6, is produced catalytically through the H^-, H_2^+, and HeH^+ mechanisms. We revisit this standard calculation taking into account the effects of the nonthermal radiation background produced by cosmic hydrogen recombination, which is particularly effective at destroying H^- via photodetachment. We also take into consideration the non-equilibrium level populations of H_2^+, which occur since transitions among the rotational-vibrational levels are slow compared to photodissociation. The new calculation predicts a final H_2 abundance of x[H_2] = 6e-7 for the standard cosmology. This production is due almost entirely to the H^- mechanism, with ~1 per cent coming from HeH^+ and ~0.004 per cent from H_2^+. We evaluate the heating of the diffuse pregalactic gas from the chemical reactions that produce H_2 and from rotational transitions in H_2, and find them to be negligible.Comment: 13 pages, 5 figures, MNRAS submitte

Random versus holographic fluctuations of the background metric. II. Note on the dark energies arising due to microstructure of space-time

Over the last few years a certain class of dark-energy models decaying inversely proportional to the square of the horizon distance emerged on the basis either of Heisenberg uncertainty relations or of the uncertainty relation between the four-volume and the cosmological constant. The very nature of these dark energies is understood to be the same, namely it is the energy of background space/metric fluctuations. Putting together these uncertainty relations one finds that the model of random fluctuations of the background metric is favored over the holographic one.Comment: 3 page

The hypothesis of path integral duality II: corrections to quantum field theoretic results

In the path integral expression for a Feynman propagator of a spinless particle of mass $m$, the path integral amplitude for a path of proper length ${\cal R}(x,x'| g_{\mu\nu})$ connecting events $x$ and $x'$ in a spacetime described by the metric tensor $g_{\mu\nu}$ is $\exp-[m {\cal R}(x,x'| g_{\mu\nu})]$. In a recent paper, assuming the path integral amplitude to be invariant under the duality transformation ${\cal R} \to (L_P^2/{\cal R})$, Padmanabhan has evaluated the modified Feynman propagator in an arbitrary curved spacetime. He finds that the essential feature of this `principle of path integral duality' is that the Euclidean proper distance $(\Delta x)^2$ between two infinitesimally separated spacetime events is replaced by $[(\Delta x)^2 + 4L_P^2 ]$. In other words, under the duality principle the spacetime behaves as though it has a `zero-point length' $L_P$, a feature that is expected to arise in a quantum theory of gravity. In the Schwinger's proper time description of the Feynman propagator, the weightage factor for a path with a proper time $s$ is $\exp-(m^2s)$. Invoking Padmanabhan's `principle of path integral duality' corresponds to modifying the weightage factor $\exp-(m^2s)$ to $\exp-[m^2s + (L_P^2/s)]$. In this paper, we use this modified weightage factor in Schwinger's proper time formalism to evaluate the quantum gravitational corrections to some of the standard quantum field theoretic results in flat and curved spacetimes. We find that the extra factor $\exp-(L_P^2/s)$ acts as a regulator at the Planck scale thereby `removing' the divergences that otherwise appear in the theory. Finally, we discuss the wider implications of our analysis.Comment: 26 pages, Revte

Use of fluorescent immunohistochemistry to investigate NF-κB involvement in brain pathologies

2013 Fall.Includes bibliographical references.Nuclear Factor Kappa Beta (NF-κB) is a transcription factor ubiquitously expressed in mammalian cells and involved in a broad spectrum of physiological responses. In the central nervous system (CNS), NF-κB is responsible for the regulation of several brain-specific processes, ranging from synaptic plasticity to neuroinflammation (Mattson and Camandola, 2001). The effects of NF-κB activation are highly variable and the transcription factor appears to play a dichotomous role in brain pathologies. Parkinson's Disease (PD) is the second most prevalent neurodegenerative disease in the world and is characterized by the progressive, irreversible loss of dopaminergic neurons in the substantia nigra pars compacta (SNpc). Neuroinflammation, a CNS-specific immune response facilitated by glial cells, is now know to be an important contributing factor to PD pathology. Many neuroinflammatory responses have been linked to glial NF-κB activation, although the mechanisms have not yet been established. Drug-induced seizures are a serious adverse drug reaction (ADR) associated with both CNS- and non-CNS-targeting drugs. The current methods of drug safety evaluation rely solely on behavioral analysis and therefore often fail to identify potentially seizurogenic activity. Studies have suggested that neuronal NF-κB activation may be an early stress response and serve a neuroprotective function. The molecular mechanisms involved in seizurogenesis are also largely unknown. To study the role of NF-κB in these models of CNS injury, I employed fluorescent immunohistochemical (IHC) staining, a molecular technique that utilizes antibody-antigen binding to identify and visualize specific proteins in tissue. IHC has a wide range of applications and is often used for both laboratory research and clinical diagnostics. The following studies examined the role of NF-κB in CNS injury by using fluorescent IHC staining to characterize a transgenic mouse containing a NF-κB-driven enhanced green fluorescent protein (cis-NF-κBeGFP) construct in order to detect cell-specific changes in NF-κB activity. Using this method in the MPTP neurotoxin-induced model of Parkinson's Disease, I found that NF-κB-mediated glial activation accompanied loss of dopaminergic neurons and that treatment with novel pharmacological inhibitors of NF-κB attenuated this response. In the kainic acid (KA) model of drug-induced seizures, this method showed that neuronal activation of NF-κB occurs at sub-seizurogenic doses and may be an early, neuroprotective stress response. Fluorescent IHC staining in models of neuropathologies is useful for mechanistic research, but may also be an effective tool in drug-development. Use of fluorescent IHC with the NF-κB transgenic mouse allows for characterization of NF-κB signaling, as it relates to other proteins in vivo. Further optimization of this method could be extremely advantageous to NF-κB research

Radiation from collapsing shells, semiclassical backreaction and black hole formation

We provide a detailed analysis of quantum field theory around a collapsing shell and discuss several conceptual issues related to the emission of radiation flux and formation of black holes. Explicit calculations are performed using a model for a collapsing shell which turns out to be analytically solvable. We use the insights gained in this model to draw reliable conclusions regarding more realistic models. We first show that any shell of mass $M$ which collapses to a radius close to $r=2M$ will emit approximately thermal radiation for a period of time. In particular, a shell which collapses from some initial radius to a final radius $2M(1-\epsilon^2)^{-1}$ (where $\epsilon \ll 1$) without forming a black hole, will emit thermal radiation during the period $M\lesssim t \lesssim M\ln (1/\epsilon^2)$. Later on ($t\gg M \ln(1/\epsilon^2)$), the flux from such a shell will decay to zero exponentially. We next study the effect of backreaction computed using the vacuum expectation value of the stress tensor on the collapse. We find that, in any realistic collapse scenario, the backreaction effects do \emph{not} prevent the formation of the event horizon. The time at which the event horizon is formed is, of course, delayed due to the radiated flux -- which decreases the mass of the shell -- but this effect is not sufficient to prevent horizon formation. We also clarify several conceptual issues and provide pedagogical details of the calculations in the Appendices to the paper.Comment: 26 pages, 6 figures, revtex4; v2 -- minor reformatting, some typos fixed, one reference added, to appear in PR

Hawking radiation in different coordinate settings: Complex paths approach

We apply the technique of complex paths to obtain Hawking radiation in different coordinate representations of the Schwarzschild space-time. The coordinate representations we consider do not possess a singularity at the horizon unlike the standard Schwarzschild coordinate. However, the event horizon manifests itself as a singularity in the expression for the semiclassical action. This singularity is regularized by using the method of complex paths and we find that Hawking radiation is recovered in these coordinates indicating the covariance of Hawking radiation as far as these coordinates are concerned.Comment: 18 pages, 2 figures, Uses IOP style file; final version; accepted in Class. Quant. Gra

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

On the enigmatic Λ\Lambda - a true constant of spacetime

Had Einstein followed the Bianchi differential identity for the derivation of his equation of motion for gravitation, $\Lambda$ would have emerged as a true new constant of spacetime on the same footing as the velocity of light? It is then conceivable that he could have perhaps made the most profound prediction that the Universe may suffer accelerated expansion some time in the future! Further we argue that its identification with the quantum vacuum energy is not valid as it should have to be accounted for like the gravitational field energy by enlarging the basic framework of spacetime and not through a stress tensor. The acceleration of the expansion of the Universe may indeed be measuring its value for the first time observationally.Comment: 4 pages, a comprehensive revision with much refinement and new insights, more references adde

Response of finite-time particle detectors in non-inertial frames and curved spacetime

The response of the Unruh-DeWitt type monopole detectors which were coupled to the quantum field only for a finite proper time interval is studied for inertial and accelerated trajectories, in the Minkowski vacuum in (3+1) dimensions. Such a detector will respond even while on an inertial trajctory due to the transient effects. Further the response will also depend on the manner in which the detector is switched on and off. We consider the response in the case of smooth as well as abrupt switching of the detector. The former case is achieved with the aid of smooth window functions whose width, $T$, determines the effective time scale for which the detector is coupled to the field. We obtain a general formula for the response of the detector when a window function is specified, and work out the response in detail for the case of gaussian and exponential window functions. A detailed discussion of both $T \rightarrow 0$ and $T \rightarrow \infty$ limits are given and several subtlities in the limiting procedure are clarified. The analysis is extended for detector responses in Schwarzschild and de-Sitter spacetimes in (1+1) dimensions.Comment: 29 pages, normal TeX, figures appended as postscript file, IUCAA Preprint # 23/9

Initial state of matter fields and trans-Planckian physics: Can CMB observations disentangle the two?

The standard, scale-invariant, inflationary perturbation spectrum will be modified if the effects of trans-Planckian physics are incorporated into the dynamics of the matter field in a phenomenological manner, say, by the modification of the dispersion relation. The spectrum also changes if we retain the standard dynamics but modify the initial quantum state of the matter field. We show that, given {\it any} spectrum of perturbations, it is possible to choose a class of initial quantum states which can exactly reproduce this spectrum with the standard dynamics. We provide an explicit construction of the quantum state which will produce the given spectrum. We find that the various modified spectra that have been recently obtained from `trans-Planckian considerations' can be constructed from suitable squeezed states above the Bunch-Davies vacuum in the standard theory. Hence, the CMB observations can, at most, be useful in determining the initial state of the matter field in the standard theory, but it can {\it not} help us to discriminate between the various Planck scale models of matter fields. We study the problem in the Schrodinger picture, clarify various conceptual issues and determine the criterion for negligible back reaction due to modified initial conditions.Comment: revtex4; 17 page