arXiv subjects

T. Padmanabhan

Publications and source records attributed to T. Padmanabhan.

At least 217 records · Page 12Linked to original sources

arXiv1997

Quantum gravitational corrections to propagator in arbitrary spacetimes

The action for a relativistic free particle of mass m receives a contribution $-m R(x,y)$ from a path of length R(x,y) connecting the events $x^i$ and $y^i$. Using this action in a path integral, one can obtain the Feynman propagator for a spinless particle of mass m in any background spacetime. If one of the effects of quantizing gravity is to introduce a minimum length scale $L_P$ in the spacetime, then one would expect the segments of paths with lengths less than $L_P$ to be suppressed in the path integral. Assuming that the path integral amplitude is invariant under the `duality' transformation ${\cal R}\to L_P^2/R$, one can calculate the modified Feynman propagator in an arbitrary background spacetime. It turns out that the key feature of this modification is the following: The proper distance $(Δx)^2$ between two events, which are infinitesimally separated, is replaced by $Δx^2 + L_P^2$; that is the spacetime behaves as though it has a `zero-point length' of $L_P$. This equivalence suggests a deep relationship between introducing a `zero-point-length' to the spacetime and postulating invariance of path integral amplitudes under duality transformations. In the Schwinger's proper time description of the propagator, the weightage for a path with proper time s becomes $m(s+L_P^2/s)$ rather than as ms. As to be expected, the ultraviolet behavior of the theory is improved significantly and divergences will disappear if this modification is taken into account. Implications of this result are discussed.

gr-qc↗

arXiv1997

Non-trivial classical backgrounds with vanishing quantum corrections

Vacuum polarization and particle production effects in classical electromagnetic and gravitational backgrounds can be studied by the effective lagrangian method. Background field configurations for which the effective lagrangian is zero are special in the sense that the lowest order quantum corrections vanishes for such configurations. We propose here the conjecture that there will be neither particle production nor vacuum polarization in classical field configurations for which all the scalar invariants are zero. We verify this conjecture, by explicitly evaluating the effective lagrangian, for non-trivial electromagnetic and gravitational backgrounds with vanishing scalar invariants. The implications of this result are discussed.

hep-th↗

arXiv1996

Critical Index and Fixed Point in the Transfer of Power in Nonlinear Gravitational Clustering

We investigate the transfer of power between different scales and coupling of modes during non-linear evolution of gravitational clustering in an expanding universe. We start with a power spectrum of density fluctuations that is exponentially damped outside a narrow range of scales and use numerical simulations to study evolution of this power spectrum. Non-Linear effects generate power at other scales with most power flowing from larger to smaller scales. The ``cascade'' of power leads to equipartition of energy at smaller scales, implying a power spectrum with index $n\approx -1$. We find that such a spectrum is produced in the range $1 < δ< 200$ for density contrast $δ$. This result continues to hold even when small scale power is added to the initial power spectrum. Semi-analytic models for gravitational clustering suggest a tendency for the effective index to move towards a critical index $n_c\approx -1$ in this range. For n n_c, it grows at a slower rate - thereby changing the index closer to n_c. At scales larger than the narrow range of scales with initial power, a k^4 tail is produced. We demonstrate that non-linear small scales do not effect the growth of perturbations at larger scales.

astro-ph↗

arXiv1996

Duality and zero-point length of spacetime

The action for a relativistic free particle of mass $m$ receives a contribution $-mds$ from a path segment of infinitesimal length $ds$. Using this action in a path integral, one can obtain the Feynman propagator for a spinless particle of mass $m$. If one of the effects of quantizing gravity is to introduce a minimum length scale $L_P$ in the spacetime, then one would expect the segments of paths with lengths less than $L_P$ to be suppressed in the path integral. Assuming that the path integral amplitude is invariant under the `duality' transformation $ds\to L_P^2/ds$, one can calculate the modified Feynman propagator. I show that this propagator is the same as the one obtained by assuming that: quantum effects of gravity leads to modification of the spacetime interval $(x-y)^2$ to $(x-y)^2+L_P^2$. This equivalence suggests a deep relationship between introducing a `zero-point-length' to the spacetime and postulating invariance of path integral amplitudes under duality transformations.

hep-th↗

arXiv1996

Nonlinear Gravitational Clustering in Expanding Universe

The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is possible to understand the nonlinear clustering in terms of three well defined regimes: (1) linear regime; (2) quasilinear regime which is dominated by scale-invariant radial infall and (3) nonlinear regime dominated by nonradial motions and mergers. Modelling each of these regimes separately I show how the nonlinear two point correlation function can be related to the linear correlation function in hierarchical models. This analysis leads to results which are in good agreement with numerical simulations thereby providing an explanation for numerical results. Using this model and some simple extensions, it is possible to understand the transfer of power from large to small scales and the behaviour of higher order correlation functions. The ideas presented here will also serve as a powerful analytical tool to investigate nonlinear clustering in different models.

astro-ph↗

arXiv1996

Pattern in Nonlinear Gravatational Clustering: A Numerical Investigation

The nonlinear clustering of dark matter particles in an expanding universe is usually studied by N-body simulations. One can gain some insight into this complex problem if simple relations between physical quantities in the linear and nonlinear regimes can be extracted from the results of N-body simulations. Hamilton et al. (1991) and Nityananda and Padmanabhan (1994) have made an attempt in this direction by relating the mean relative pair velocities to the mean correlation function in a useful manner. We investigate this relation and other closely related issues in detail for the case of six different power spectra: power laws with spectral indexes $n=-2,-1$, cold dark matter (CDM), and hot dark matter models with density parameter $Ω=1$; CDM including a cosmological constant ($Λ$) with $Ω_{CDM}=0.4$, $Ω_Λ=0.6$; and $n=-1$ model with $Ω=0.1$. We find that: (i) Power law spectra lead to self-similar evolution in an $Ω=1$ universe. (ii) Stable clustering does not hold in an $Ω=1$ universe to the extent our simulations can ascertain. (iii) Stable clustering is a better approximation in the case of $Ω<1$ universe in which structure formation freezes out at some low redshift. (iv) The relation between dimensionless pair velocity and the mean correlation function, $\barξ$, is only approximately independent of the shape of the power spectrum. At the nonlinear end, the asymptotic value of the dimensionless pair velocity decreases with increasing small scale power, because the stable clustering assumption is not universally true. (v) The relation between the evolved $\barξ$ and the linear regime $\barξ$ is also not universal but shows a weak spectrum dependence. We present simple theoretical arguments for these conclusions.

astro-ph↗

arXiv1996

`Thermal' ambience and fluctuations in classical field theory

A plane monochromatic wave will not appear monochromatic to a noninertial observer. We show that this feature leads to a `thermal' ambience in an accelerated frame {\it even in classical field theory}. When a real, monochromatic, mode of a scalar field is Fourier analyzed with respect to the proper time of a uniformly accelerating observer, the resulting power spectrum consists of three terms: (i)~a factor $(1/2)$ that is typical of the ground state energy of a quantum oscillator, (ii)~a Planckian distribution $N(Ω)$ and---most importantly---(iii)~a term $\sqrt{N(N+1)}$, which is the root mean square fluctuations about the Planckian distribution. It is the appearance of the root mean square fluctuations that motivates us to attribute a `thermal' nature to the power spectrum. This result shows that some of the `purely' quantum mechanical results might have a classical analogue. The `thermal' ambience that we report here also proves to be a feature of observers stationed at a constant radius in the Schwarzschild and de-Sitter spacetimes.

gr-qc↗

arXiv1996

Does a non-zero tunnelling probability imply particle production in time independent classical electromagnetic backgrounds?

In this paper, we probe the validity of the tunnelling interpretation that is usually called forth in literature to explain the phenomenon of particle production by time independent classical electromagnetic backgrounds. We show that the imaginary part of the effective lagrangian is zero for a complex scalar field quantized in a time independent, but otherwise arbitrary, magnetic field. This result implies that no pair creation takes place in such a background. But we find that when the quantum field is decomposed into its normal modes in the presence of a spatially confined and time independent magnetic field, there exists a non-zero tunnelling probability for the effective Schr{\" o}dinger equation. According to the tunnelling interpretation, this result would imply that spatially confined magnetic fields can produce particles, thereby contradicting the result obtained from the effective lagrangian. This lack of consistency between these two approaches calls into question the validity of attributing a non-zero tunnelling probability for the effective Schr{\" o}dinger equation to the production of particles by the time independent electromagnetic backgrounds. The implications of our analysis are discussed.

hep-th↗

arXiv1995

Crisis in Cosmology : Observational Constraints on Omega and H_0

Thanks to new technology of observations and fresh inputs from particle physics, cosmology has advanced on both observational and theoretical fronts. It is therefore opportune that we take stock of the cosmological situation today and examine the observational and theoretical constraints as they are now. The bottom line in this review is that despite the availability of the cosmological constant as an extra parameter for flat Friedmann models, the allowed parameter space for such models is very small. The observations that we consider here include the ages of globular clusters, measurement of Hubble's constant, abundance of rich clusters of galaxies, fraction of mass contributed by baryons in rich clusters and abundance of high redshift objects.

astro-ph↗

arXiv1995

Gravitational Dynamics in an Expanding Universe

The dynamical evolution of collisionless particles in an expanding background is described. After discussing qualitatively the key features, the gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is indeed possible to understand the nonlinear clustering in terms of three well defined regimes: (1) linear regime (2) quasilinear regime which is dominated by scale-invariant radial infall and (3) nonlinear regime dominated by nonradial motions and mergers. Modelling each of these regimes separately I show how the nonlinear two point correlation function can be related to the linear correlation function in hierarchical models. This analysis leads to results which are in good agreement with numerical simulations thereby providing an explanation for numerical results. The ideas presented here will also serve as a powerful analytical tool to investigate nonlinear clustering in different models. Several implications of the result are discussed.

astro-ph↗

arXiv1995

A New Statistical Indicator to Study Nonlinear Gravitational Clustering and Structure Formation

In an expanding universe, velocity field and gravitational force field are proportional to each other in the linear regime. Neither of these quantities evolve in time and these can be scaled suitably so that the constant of proportionality is unity and velocity and force field are equal. The Zeldovich approximation extends this feature beyond the linear regime, until formation of pancakes. Nonlinear clustering which takes place {\it after} the breakdown of Zeldovich approximation, breaks this relation and the mismatch between these two vectors increases as the evolution proceeds. We suggest that the difference of these two vectors could form the basis for a powerful, new, statistical indicator of nonlinear clustering. We define an indicator called velocity contrast, study its behaviour using N-Body simulations and show that it can be used effectively to delineate the regions where nonlinear clustering has taken place. We discuss several features of this statistical indicator and provide simple analytic models to understand its behaviour. Particles with velocity contrast higher than a threshold have a correlation function which is biased with respect to the original sample. This bias factor is scale dependent and tends to unity at large scales.

astro-ph↗

arXiv1995

Modelling the Nonlinear Gravitational Clustering in the Expanding Universe

The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is indeed possible to understand the nonlinear clustering in terms of three well defined regimes: (1) linear regime (2) quasilinear regime which is dominated by scale-invariant radial infall and (3) nonlinear regime dominated by nonradial motions and mergers. Modelling each of these regimes separately I show how the nonlinear two point correlation function can be related to the linear correlation function in heirarchical models. This analysis leads to results which are in good agreement with numerical simulations thereby providing an explanation for numerical results. The ideas presented here will also serve as a powerful anlytical tool to investigate nonlinear clustering in different models. Several implications of the result are discussed.

astro-ph↗

arXiv1995

Structure formation: Models, Dynamics and Status

The constraints on the models for the structure formation arising from various cosmological observations at different length scales are reviewed. The status of different models for structure formation is examined critically in the light of these observations.

astro-ph↗

arXiv1995

Evolution Of Gravitational Potential In The Quasilinear And Nonlinear Regimes

We study the evolution of the power spectrum of gravitational potential during the nonlinear clustering in an $Ω=1$ matter dominated phase. N-body simulations suggest that the potential does not evolve in time even in the quasilinear phase for an $n=-1$ power spectrum. For $n=-2$, the potential evolves in the quasilinear phase but not in the extreme nonlinear phase. Becauase of these facts, the evolution of the gravitational potential in spectra like CDM is less than what would have been expected naively. We discuss a class of CDM like models in which such an interesting conspiracy between the amplitude and local index occurs.

astro-ph↗

arXiv1994

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.

gr-qc↗

arXiv1994

Constraints on the Models for Structure Formation from the Abundance of Damped Lyman Alpha Systems

Models for structure formation attempt to predict the power spectrum of density perturbations in the present universe from the initial power spectrum and the nature of dark matter. Observational constraints on the power spectrum at different scales in the present epoch can, therefore, be used to eliminate (or choose between) different theoretical models. Such a comparison is fairly easy at large scales (at which linear theory is valid), and one can use observations like the MBR anisotropy, large scale steaming motions etc to constrain the models. But to discriminate between the models effectivley, it is necessay to constrain the power spectrum at small scales. The most reliable constraints on the power spectra at small scales come from the predicted abundance of bound systems which can be estimated reasonably accurately using Press-Schecter (or similar) methods$^1$. In the past, this method has been used in conjunction with the quasar abundance$^{2-4}$ and cluster abundance$^{5-7}$. We show here that the abundance of damped lyman alpha systems (DLAS, hereafter), provides a far stronger constraint on the models for structure formation. Models with a mixture of hot and cold dark matter $^{8-11}$ (which are consistent with large scale observations) are strongly ruled out by the DLAS constraints while models with cosmological constant $^{12}$ are marginally inconsistent. It is also possible to combine the constraints from the abundance of clusters, DLAS and QSO's to obtain model-independent bounds on the power spectrum at the nonlinear scales. These bounds are to be respected by any viable model for structure formation.

astro-ph↗

arXiv1993

Baryonic Content of Galactic Halos and Constraints on Models for Structure Formation

The recent detection of microlensing of stars of LMC by compact objects in the halo of our galaxy suggests that our galaxy is surrounded by a non-luminous halo made of compact objects with mass of about $(0.03-0.5) \msun$. The rate of detection could be consistent with the assumption that these halo objects are distributed with a softened isothermal profile with a core radius of $(2-8)$Kpc and asymptotic circular velocity of $220\kms$. Taken in isolation, this observation is consistent with a universe having only baryonic dark matter (BDM, hereafter) contributing $Ω_b=Ω_{total}\simeq0.06$ which will, however, violently contradict several other large scale observations, notably the COBE-DMR results. Alternatively one can assume that galaxies like ours are surrounded by both BDM and non-baryonic dark matter (NBDM, hereafter). A model with a single component for NBDM with, say, $Ω_b\simeq0.06,Ω_{cdm}\simeq0.94$, is also ruled out if we demand that: (i) at least thirty percent of the dark matter density within $100$ kpc is baryonic and (ii) galactic structures should have collapsed by redshift of $z=1$. Further if half or more of the dark matter within $100 kpc$ is baryonic then the maximum value of $Ω_{dm}$, contributed by NBDM clustered at galactic scales, can only be about $Ω_{max}\simeq0.29$. Models with C+HDM cannot satisfy this constraint but $Λ$+ CDM models are still

astro-ph↗

arXiv1993

Nonlinear Evolution of Density Perturbations

: From the epoch of recombination $(z\approx 10^3)$ till today, the typical density contrasts have grown by a factor of about $10^6$ in a Friedmann universe with $Ω=1$. However, during the same epoch the typical gravitational potential has grown only by a factor of order unity. We present theoretical arguments explaining the origin of this approximate constancy of gravitational potential. This fact can be exploited to provide a new, powerful, approximation scheme to study the formation of nonlinear structures in the universe. The essential idea of this method is to evolve the initial distribution of particles using a gravitational potential frozen in time (Frozen Potential Approximation). This approximation provides valuable insight into understanding various features of nonlinear evolution; for example, it provides a simple explanation as to why pancakes remain thin during the evolution even in the absence of any artificial, adhesion-like, damping terms. We compare the trajectories of particles in various approximations. We also discuss a few applications of the frozen potential approximation.

gr-qc↗