arXiv subjects

T. Padmanabhan

Publications and source records attributed to T. Padmanabhan.

At least 181 records · Page 10Linked to original sources

arXiv2002

Accelerated expansion of the universe driven by tachyonic matter

It is an accepted practice in cosmology to invoke a scalar field with potential $V(ϕ)$ when observed evolution of the universe cannot be reconciled with theoretical prejudices. Since one function-degree-of-freedom in the expansion factor $a(t)$ can be traded off for the function $V(ϕ)$, it is {\it always} possible to find a scalar field potential which will reproduce a given evolution. I provide a recipe for determining $V(ϕ)$ from $a(t)$ in two cases:(i) Normal scalar field with Lagrangian ${\cal L} = (1/2)\partial_aϕ\partial^aϕ- V(ϕ)$ used in quintessence/dark energy models. (ii) A tachyonic field with Lagrangian ${\cal L} = -V(ϕ) [ 1- \partial_aϕ\partial^aϕ]^{1/2} $, motivated by recent string theoretic results. In the latter case, it is possible to have accelerated expansion of the universe during the late phase in certain cases. This suggests a string theory based interpretation of the current phase of the universe with tachyonic condensate acting as effective cosmological constant.

hep-th↗

arXiv2002

A simple analytical model for the abundance of damped Ly-αabsorbers

A simple analytical model for estimating the fraction (Ω_{gas}) of matter in gaseous form within the collapsed dark matter (DM) haloes is presented. The model is developed using (i) the Press-Schechter formalism to estimate the fraction of baryons in DM haloes, and (ii) the observational estimates of the star formation rate at different redshifts. The prediction for Ω_{gas} from the model is in broad agreement with the observed abundance of the damped Ly-αsystems. Furthermore, it can be used for estimating the circular velocities of the collapsed haloes at different redshifts, which could be compared with future observations.

astro-ph↗

arXiv2002

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.

gr-qc↗

arXiv2002

Entropy and energy of a class of spacetimes with horizon: a general derivation

Euclidean continuation of several Lorentzian spacetimes with horizons requires treating the Euclidean time coordinate to be periodic with some period $β$. Such spacetimes (Schwarzschild, deSitter,Rindler .....) allow a temperature $T=β^{-1}$ to be associated with the horizon. I construct a canonical ensemble of a subclass of such spacetimes with a fixed value for $β$ and evaluate the partition function $Z(β)$. For spherically symmetric spacetimes with a horizon at r=a, the partition function has the generic form $Z\propto \exp[S-βE]$, where $S= (1/4) 4πa^2$ and $|E|=(a/2)$. Both S and E are determined entirely by the properties of the metric near the horizon. This analysis reproduces the conventional result for the blackhole spacetimes and provides a simple and consistent interpretation of entropy and energy for deSitter spacetime. For the Rindler spacetime the entropy per unit transverse area turns out to be (1/4) while the energy is zero. The implications are discussed.

gr-qc↗

arXiv2002

Thermodynamics and/of Horizons: A Comparison of Schwarzschild,RINDLER and desitter Spacetimes

The notions of temperature, entropy and `evaporation', usually associated with spacetimes with horizons, are analyzed using general approach and the following results, applicable to different spacetimes, are obtained at one go. (i) The concept of temperature associated with the horizon is derived in a unified manner and is shown to arise from purely kinematic considerations. (ii) QFT near any horizon is mapped to a conformal field theory without introducing concepts from string theory. (iii) For spherically symmetric spacetimes (in D=1+3) with a horizon at r=l, the partition function has the generic form $Z\propto \exp[S-βE]$, where $S= (1/4) 4πl^2$ and $|E|=(l/2)$. This analysis reproduces the conventional result for the blackhole spacetimes and provides a simple and consistent interpretation of entropy and energy for deSitter spacetime. (iv) For the Rindler spacetime the entropy per unit transverse area turns out to be (1/4) while the energy is zero. (v) In the case of a Schwarzschild black hole there exist quantum states (like Unruh vacuum) which are not invariant under time reversal and can describe blackhole evaporation. There also exist quantum states (like Hartle-Hawking vacuum) in which temperature is well-defined but there is no flow of radiation to infinity. In the case of deSitter universe or Rindler patch in flat spacetime, one usually uses quantum states analogous to Hartle-Hawking vacuum and obtains a temperature without the corresponding notion of evaporation. It is, however, possible to construct the analogues of Unruh vacuum state in the other cases as well. Associating an entropy or a radiating vacuum state with a general horizon raises conceptual issues which are briefly discussed.

gr-qc↗

arXiv2001

Cosmic inventory of energy densities: issues and concerns

The dynamics of our universe is characterised by the density parameters for cosmological constant ($Ω_V$), nonbaryonic darkmatter($Ω_{\rm wimp}$), radiation ($Ω_R$) and baryons ($Ω_B$). To these parameters -- which describe the smooth background universe -- one needs to add at least another dimensionless number ($\sim 10^{-5}$) characterising the strength of primordial fluctuations in the gravitational potential, in order to ensure formation of structures by gravitational instability. I discuss several issues related to the description of the universe in terms of these numbers and argue that we do not yet have a fundamental understanding of these issues.

gr-qc↗

arXiv2001

On the 1/3 factor in the CMB Sachs-Wolfe effect

We point out that a pseudo-Newtonian interpretations of the $(1/3)$ factor in the Sachs-Wolfe effect, which relates the fluctuations in temperature and potential, $(δT/ T) = (1/ 3) δΦ$, is not supported by the General Relativistic analysis. Dividing the full gravitational effect into separate parts depends on the choice of time slicing (gauge) and there exist infinitely many different choices. More importantly, interpreting the parts as being due to the gravitational redshift and the time dilation is not justified in the rigorous relativistic perturbation theory. We suggest to regard the $(1/3)$ factor as the General Relativistic result which applies in a restricted situation of adiabatic perturbation in the $K = 0 = Λ$ model with the last scattering occuring in the matter dominated era. For an isocurvature initial condition the corresponding result, $(δT/ T) = 2 δΦ$, has a different numerical coefficient.

astro-ph↗

arXiv2001

Combining general relativity and quantum theory: points of conflict and contact

The issues related to bringing together the principles of general relativity and quantum theory are discussed. After briefly summarising the points of conflict between the two formalisms I focus on four specific themes in which some contact has been established in the past between GR and quantum field theory: (i) The role of planck length in the microstructure of spacetime (ii) The role of quantum effects in cosmology and origin of the universe (iii) The thermodynamics of spacetimes with horizons and especially the concept of entropy related to spacetime geometry (iv) The problem of the cosmological constant.

gr-qc↗

arXiv2001

Semi analytic approach to understanding the distribution of neutral hydrogen in the universe: Comparison of simulations with observations

Following Bi & Davidsen (1997), we perform one dimensional semi analytic simulations along the lines of sight to model the intergalactic medium (IGM). Since this procedure is computationally efficient in probing the parameter space -- and reasonably accurate -- we use it to recover the values of various parameters related to the IGM (for a fixed background cosmology) by comparing the model predictions with different observations. For the currently favoured LCDM model (Ω_m=0.4, Ω_Λ=0.6 and h=0.65), we obtain, using statistics obtained from the transmitted flux, constraints on (i) the combination f=(Ω_B h^2)^2/J_{-12}, where Ω_B is the baryonic density parameter and J_{-12} is the total photoionisation rate in units of 10^{-12} s^{-1}, (ii) temperature T_0 corresponding to the mean density and (iii) the slope γof the effective equation of state of the IGM at a mean redshift z \simeq 2.5. We find that 0.8 <(T_0/10^4 K)< 2.5 and 1.3<γ<2.3. while the constraint obtained on f is 0.020^2 1.2, the lower bound on Ω_B h^2 is in violation of the BBN value.

astro-ph↗

arXiv2001

Method of complex paths and general covariance of Hawking radiation

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 semi-classical 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. This also shows that there is no correspondence between the particles detected by the model detector and the particle spectrum obtained by the quantum field theoretic analysis -- a result known in other contexts as well.

gr-qc↗

arXiv2001

Vanishing of cosmological constant in nonfactorizable geometry

We generalize the results of Randall and Sundrum to a wider class of four-dimensional space-times including the four-dimensional Schwarzschild background and de Sitter universe. We solve the equation for graviton propagation in a general four dimensional background and find an explicit solution for a zero mass bound state of the graviton. We find that this zero mass bound state is normalizable only if the cosmological constant is strictly zero, thereby providing a dynamical reason for the vanishing of cosmological constant within the context of this model. We also show that the results of Randall and Sundrum can be generalized without any modification to the Schwarzschild background.

hep-th↗

arXiv2001

Probes of the vacuum structure of quantum fields in classical backgrounds

We compare the different approaches presently available in literature to probe the vacuum structure of quantum fields in classical electromagnetic and gravitational backgrounds. We compare the results from the Bogolubov transformations and the effective Lagrangian approach with the response of monopole detectors (of the Unruh-DeWitt type) in non-inertial frames in flat spacetime and in inertial frames in different types of classical electromagnetic backgrounds. We also carry out such a comparison in inertial and rotating frames when boundaries are present in flat spacetime. We find that the results from these different approaches do not, in general, agree with each other. We attempt to identify the origin of these differences and then go on to discuss its implications for classical gravitational backgrounds.

gr-qc↗

arXiv2001

The effects of anti-correlation on gravitational clustering

We use non-linear scaling relations (NSRs) to investigate the effects arising from the existence of negative correlations on the evolution of gravitational clustering in an expanding universe. It turns out that such anti-correlated regions have important dynamical effects on {\it all} scales. In particular, the mere existence of negative values for the linear two-point correlation function $\xib_L$ over some range of scales starting from $l = L_o$, implies that the non-linear correlation function is bounded from above at {\it all} scales $x < L_o$. This also results in the relation $\xib \propto x^{-3}$, at these scales, at late times, independent of the original form of the correlation function. Current observations do not rule out the existence of negative $\xib$ for $ 200 h^{-1}$ Mpc $\la \xib \la 1000 h^{-1}$ Mpc; the present work may thus have relevance for the real Universe. The only assumption made in the analysis is the {\it existence} of the NSR; the results are independent of the form of the NSR as well as of the stable clustering hypothesis.

astro-ph↗

arXiv2001

Hypothesis of path integral duality: Applications to QED

We use the modified propagator for quantum field based on a ``principle of path integral duality" proposed earlier in a paper by Padmanabhan to investigate several results in QED. This procedure modifies the Feynman propagator by the introduction of a fundamental length scale. We use this modified propagator for the Dirac particles to evaluate the first order radiative corrections in QED. We find that the extra factor of the modified propagator acts like a regulator at the Planck scales thereby removing the divergences that otherwise appear in the conventional radiative correction calculations of QED. We find that:(i) all the three renormalisation factors $Z_1$, $Z_2$, and $Z_3$ pick up finite corrections and (ii) the modified propagator breaks the gauge invariance at a very small level of ${\mathcal{O}}(10^{-45})$. The implications of this result to generation of the primordial seed magnetic fields are discussed.

gr-qc↗

arXiv2000

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, γare of the same order, which means that we cannot constrain both the parameters simultaneously. However, it is possible to constrain γand 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 γobtained 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 θ, 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 γ. Our calculations suggest that one can rule out γ> 1.6 for z \simeq 2.31 using the column density distribution. However, one cannot rule higher values of γat higher redshifts.

astro-ph↗

arXiv2000

Constraints on Omega_B, Omega_m and h from MAXIMA and BOOMERANG

We analyse the BOOMERANG and MAXIMA results in the context of models with $Ω_{\rm Total} = 1$ and $n_s = 1$. We attempt to constrain three other parameters---$h$, $Ω_B$, and $Ω_m$---from these observations. We show that: (a) the value of $Ω_B h^2$ is too high to be compatible with primordial nucleosynthesis observations at 95% confidence level (b) universe with age greater than $ 12 \rm Gyr$ is ruled out at 95% confidence level and (c) the value of $Ω_m h$ is too high to be compatible with the shape of the power spectrum of gravitational clustering. In effect, our analysis shows that models with $Ω_{\rm Total} = 1$ and $n_s = 1$ are ruled out by BOOMERANG and MAXIMA observations.

astro-ph↗

arXiv2000

The Issue of Choosing Nothing: What Determines the Low Energy Vacuum State of Nature?

Starting from an (unknown) quantum gravitational model, one can invoke a sequence of approximations to progressively arrive at quantum field theory (QFT) in curved spacetime, QFT in flat spacetime, nonrelativistic quantum mechanics and newtonian mechanics. The more exact theory can put restrictions on the range of possibilities allowed for the approximate theory which are not derivable from the latter - an example being the symmetry restrictions on the wave function for a pair of electrons. We argue that the choice of vacuum state at low energies could be such a `relic' arising from combining the principles of quantum theory and general relativity, and demonstrate this result in a simple toy model. Our analysis suggests that the wave function of the universe, when it describes the large volume limit of the universe, dynamically selects a vacuum state for matter fields - which in turn defines the concept of particle in the low energy limit. The result also has the potential for providing a concrete quantum mechanical version of Mach's principle.

gr-qc↗

arXiv2000

Nonlinear density evolution from an improved spherical collapse model

We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we introduce a physically motivated closure condition which specifies the dependence of the additional terms on the density contrast, $δ$. The modified equation can be used to model the behaviour of an overdense region over a sufficiently large range of $δ$. The key new idea is a Taylor series expansion in ($1/δ$) to model the non-linear epoch. We show that the modified equations quite generically lead to the formation of stable structures in which the gravitational collapse is halted at around the virial radius. The analysis also allows us to connect up the behaviour of individual overdense regions with the non-linear scaling relations satisfied by the two point correlation function.

astro-ph↗