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T. Padmanabhan

Publications and source records attributed to T. Padmanabhan.

At least 163 records · Page 9Linked to original sources
arXiv2003

Role of Horizons in Semiclassical Gravity: Entropy and the Area Spectrum

In any space-time, it is possible to have a family of observers who have access to only part of the space-time manifold, because of the existence of a horizon. We demand that \emph{physical theories in a given coordinate system must be formulated entirely in terms of variables that an observer using that coordinate system can access}. In the coordinate frame in which these observers are at rest, the horizon manifests itself as a (coordinate) singularity in the metric tensor. Regularization of this singularity removes the inaccessible region, and leads to the following consequences: (a) The non-trivial topological structure for the effective manifold allows one to obtain the standard results of quantum field theory in curved space-time. (b) In case of gravity, this principle requires that the effect of the unobserved degrees of freedom should reduce to a boundary contribution $A_{\rm boundary}$ to the gravitational action. When the boundary is a horizon, $A_{\rm boundary}$ reduces to a single, well-defined term proportional to the area of the horizon. Using the form of this boundary term, it is possible to obtain the full gravitational action in the semiclassical limit. (c) This boundary term must have a quantized spectrum with uniform spacing, $ΔA_{boundary}=2π\hbar$, in the semiclassical limit. This, in turn, yields the following results for semiclassical gravity: (i) The area of any one-way membrane is quantized. (ii) The information hidden by a one-way membrane amounts to an entropy, which is always one-fourth of the area of the membrane in the leading order. (iii) In static space-times, the action for gravity can be given a purely thermodynamic interpretation and the Einstein equations have a formal similarity to laws of thermodynamics.

gr-qc↗
arXiv2003

Gravitational clustering in Static and Expanding Backgrounds

A brief summary of several topics in the study of gravitational many body problem is given. The discussion covers both static backgrounds (applicable to astrophysical systems) as well as clustering in an expanding background (relevant for cosmology)

astro-ph↗
arXiv2003

String theory T-duality and the zero point length of spacetime

It has been often conjectured that the correct theory of quantum gravity will act as a UV regulator in the low energy limit of quantum field theory. Earlier work has shown that if the path integral defining the quantum field theory propagator is modified, so that the amplitude is invariant under the duality transformation l--> 1/l where l is the length of the path, then the propagator is UV-finite and exhibits a ``zero-point length'' of the spacetime. Since string theory uses extended structures and has a T-duality, these results should also emerge directly from string theory. We show, by explicit path integral computation, that this is indeed the case. The lowest order string theory correction to the propagator is the same as that obtained by the hypothesis of path integral duality.

hep-th↗
arXiv2003

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/ρ=-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.

astro-ph↗
arXiv2003

Response of distance measures to the equation of state

We show that the distance measures (such as the luminosity and angular diameter distances) are linear functionals of the equation-of-state function w(z) of the dark energy to a fair degree of accuracy in the regimes of interest. That is, the distance measures can be expressed as a sum of (i) a constant and (ii) an integral of a weighting function multiplied by the equation of state parameter w(z). The existence of such an accurate linear response approximation has several important implications: (a) Fitting a constant w model to the data drawn from an evolving model has a simple interpretation as a weighted average of w(z). (b) Any polynomial (or other expansion coefficients can also be expressed as weighted sums of the true w(z). (c) A replacement for the commonly used heuristic equation for the effective w(z), as determined by the CMB, can be derived and the result is found to be quite close to the heuristic expression commonly used. (d) The reconstruction of w(z) by Huterer et al. (2002) can be expressed as a matrix inversion. In each case the limitations of the linear response approximation are explored and found to be surprisingly small.

astro-ph↗
arXiv2003

Semiclassical quantization of gravity I: Entropy of horizons and the area spectrum

The principle of equivalence provides a description of gravity in terms of the metric tensor and determines how gravity affects the light cone structure of the space-time. This, in turn, leads to the existence of observers (in any space-time) who do not have access to regions of space-time bounded by horizons. To take into account this generic possibility, it is necessary to demand that \emph{physical theories in a given coordinate system must be formulated entirely in terms of variables that an observer using that coordinate system can access}. This principle is powerful enough to obtain the following results: (a) The action principle of gravity must be of such a structure that, in the semiclassical limit, the action of the unobserved degrees of freedom reduces to a boundary contribution $A_{\rm boundary}$ obtained by integrating a four divergence. (b) When the boundary is a horizon, $A_{\rm boundary}$ essentially reduces to a single, well-defined, term. (c) This boundary term must have a quantized spectrum with uniform spacing, $ΔA_{boundary}=2π\hbar$, in the semiclassical limit. Using this principle in conjunction with the usual action principle in gravity, we show that: (i) The area of any one-way membrane is quantized. (ii) The information hidden by a one-way membrane leads to an entropy which is always one-fourth of the area of the membrane, in the leading order. (iii) In static space-times, the action for gravity can be given a purely thermodynamic interpretation and the Einstein equations have a formal similarity to laws of thermodynamics.

hep-th↗
arXiv2003

Cosmology with tachyon field as dark energy

We present a detailed study of cosmological effects of homogeneous tachyon matter coexisting with non-relativistic matter and radiation, concentrating on the inverse square potential and the exponential potential for the tachyonic scalar field. A distinguishing feature of these models (compared to other cosmological models) is that the matter density parameter and the density parameter for tachyons remain comparable even in the matter dominated phase. For the exponential potential, the solutions have an accelerating phase, followed by a phase with a(t) ~ t^{2/3} as t goes to infinity. This eliminates the future event horizon present in LCDM models and is an attractive feature from the string theory perspective. A comparison with supernova Ia data shows that for both the potentials there exists a range of models in which the universe undergoes an accelerated expansion at low redshifts and are also consistent with requirements of structure formation. They do require fine tuning of parameters but not any more than in the case of LCDM or quintessence models.

astro-ph↗
arXiv2003

Cosmological Constant - the Weight of the Vacuum

Recent cosmological observations suggest the existence of a positive cosmological constant $Λ$ with the magnitude $Λ(G\hbar/c^3) \approx 10^{-123}$. This review discusses several aspects of the cosmological constant both from the cosmological (sections 1-6) and field theoretical (sections 7-11) perspectives. The first section introduces the key issues related to cosmological constant and provides a brief historical overview. This is followed by a summary of the kinematics and dynamics of the standard Friedmann model of the universe paying special attention to features involving the cosmological constant. Section 3 reviews the observational evidence for cosmological constant, especially the supernova results, constraints from the age of the universe and a few others. Theoretical models (quintessence, tachyonic scalar field, ...) with evolving cosmological `constant' are described from different perspectives in the next section. Constraints on dark energy from structure formation and from CMBR anisotropies are discussed in the next two sections. The latter part of the review (sections 7-11) concentrates on more conceptual and fundamental aspects of the cosmological constant. Section 7 provides some alternative interpretations of the cosmological constant which could have a bearing on the possible solution to the problem. Several relaxation mechanisms have been suggested in the literature to reduce the cosmological constant to the currently observed value and some of these attempts are described in section 8. Next section gives a brief description of the geometrical structure of the de Sitter spacetime and the thermodynamics of the de Sitter universe is taken up in section 10. The last section deals with the role of string theory in the cosmological constant problem.

hep-th↗
arXiv2003

A Viable Cosmology with a Scalar Field Coupled to the Trace of the Stress-Tensor

We study the cosmological evolution of a scalar field that couples to the trace $T=T^{a}_a$ of energy momentum tensor of all the fields (including itself). In the case of a shallow exponential potential, the presence of coupling to the trace $T$ in the field equation makes the energy density of the scalar field decrease faster thereby hastening the commencement of radiation domination. This effect gradually diminishes at later epochs allowing the scalar field to dominate the energy density again. We interpret this phase as the current epoch of cosmic acceleration with $Ω_ϕ=0.7$. A variant of this model can lead to accelerated expansion at the present epoch followed by a $a(t)\propto t^{2/3}$ behaviour as $t\to \infty$, making the model free from future event horizon. The main features of the model are independent of initial conditions. However, fine tuning of parameters is necessary for viable evolution.

hep-th↗
arXiv2003

Gravity from Spacetime Thermodynamics

The Einstein-Hilbert action (and thus the dynamics of gravity) can be obtained by combining the principle of equivalence, special relativity and quantum theory in the Rindler frame and postulating that the horizon area must be proportional to the entropy. This approach uses the local Rindler frame as a natural extension of the local inertial frame, and leads to the interpretation that the gravitational action represents the free energy of the spacetime geometry. As an aside, one obtains an insight into the peculiar structure of Einstein-Hilbert action and a natural explanation to the questions:(i) Why does the covariant action for gravity contain second derivatives of the metric tensor? (ii) Why is the gravitational coupling constant is positive ? Some geometrical features of gravitational action are clarified.

gr-qc↗
arXiv2002

Can the clustered dark matter and the smooth dark energy arise from the same scalar field ?

Cosmological observations suggest the existence of two different kinds of energy densities dominating at small ($ \lesssim 500$ Mpc) and large ($\gtrsim 1000 $ Mpc) scales. The dark matter component, which dominates at small scales, contributes $Ω_m \approx 0.35$ and has an equation of state $p=0$ while the dark energy component, which dominates at large scales, contributes $Ω_V \approx 0.65$ and has an equation of state $p\simeq -ρ$. It is usual to postulate wimps for the first component and some form of scalar field or cosmological constant for the second component. We explore the possibility of a scalar field with a Lagrangian $L =- V(ϕ) \sqrt{1 - \del^i ϕ\del_i ϕ}$ acting as {\it both} clustered dark matter and smoother dark energy and having a scale dependent equation of state. This model predicts a relation between the ratio $ r = ρ_V/ρ_{\rm DM}$ of the energy densities of the two dark components and expansion rate $n$ of the universe (with $a(t) \propto t^n$) in the form $n = (2/3) (1+r) $. For $r \approx 2$, we get $n \approx 2$ which is consistent with observations.

hep-th↗
arXiv2002

Classical and Quantum Thermodynamics of horizons in spherically symmetric spacetimes

A general formalism for understanding the thermodynamics of horizons in spherically symmetric spacetimes is developed. The formalism reproduces known results in the case of black hole spacetimes. But its power lies in being able to handle more general situations like: (i) spacetimes which are not asymptotically flat (like the de Sitter spacetime) and (ii) spacetimes with multiple horizons having different temperatures (like the Schwarzschild-de Sitter spacetime) and provide a consistent interpretation for temperature, entropy and energy. I show that it is possible to write Einstein's equations for a spherically symmetric spacetime in the form $TdS-dE=PdV$ near {\it any} horizon of radius $a$ with $S=(1/4)(4πa^2), |E| = (a/2)$ and the temperature $T$ determined from the surface gravity at the horizon. The pressure $P$ is provided by the source of the Einstein's equations and $dV$ is the change in the volume when the horizon is displaced infinitesimally. The same results can be obtained by evaluating the quantum mechanical partition function {\it without using Einstein's equations or WKB approximation for the action}. Both the classical and quantum analysis provide a simple and consistent interpretation of entropy and energy for de Sitter spacetime as well as for $(1+2)$ dimensional gravity. For the Rindler spacetime the entropy per unit transverse area turns out to be $(1/4)$ while the energy is zero. The approach also shows that the de Sitter horizon -- like the Schwarzschild horizon -- is effectively one dimensional as far as the flow of information is concerned, while the Schwarzschild-de Sitter, Reissner-Nordstrom horizons are not. The implications for spacetimes with multiple horizons are discussed.

gr-qc↗
arXiv2002

Why do we observe a small but non zero cosmological constant ?

The current observations seem to suggest that the universe has a positive cosmological constant of the order of $H_0^2$ while the most natural value for the cosmological constant will be $L_P^{-2}$ where $L_P = (G\hbar/c^3)^{1/2}$ is the Planck length. This reduction of the cosmological constant from $L_P^{-2} $ to $L_P^{-2}(L_PH_0)^2$ may be interpreted as due to the ability of quantum micro structure of spacetime to readjust itself and absorb bulk vacuum energy densities. Being a quantum mechanical process, such a cancellation cannot be exact and the residual quantum fluctuations appear as the ``small'' cosmological constant. I describe the features of a toy model for the spacetime micro structure which could allow for the bulk vacuum energy densities to be canceled leaving behind a small residual value of the the correct magnitude. Some other models (like the ones based on canonical ensemble for the four volume or quantum fluctuations of the horizon size) lead to an insignificantly small value of $H_0^2(L_PH_0)^n$ with $n=0.5-1$ showing that obtaining the correct order of magnitude for the residual fluctuations in the cosmological constant is a nontrivial task, becaue of the existence of the small dimensionless number $H_0L_P$ .

gr-qc↗
arXiv2002

Evolution of the Correlation Function for a Class of Processes involving Non Local Self - Replication

A large class of evolutionary processes can be modeled by a rule which involves self-replication of some physical quantity with a non local rescaling. I show that a class of such models are exactly solvable -- in the discrete as well as continuum limit -- and can represent several physical situations as varied from the formation of galaxies in some cosmological models to growth of bacterial cultures. This class of models, in general, has no steady state solution and evolve unstably as $t \to \infty$ for generic initial conditions. They can however exhibit (unstable) power law correlation function in the continuum limit, for an intermediate range of times and length scales.

astro-ph↗
arXiv2002

Statistical Mechanics of gravitating systems in static and cosmological backgrounds

This pedagogical review addresses several issues related to statistical description of gravitating systems in both static and expanding backgrounds, focusing on the latter. After briefly reviewing the results for the static background, I describe the key issues and recent progress in the context of gravitational clustering of collision-less particles in an expanding universe. The questions addressed include: (a) How does the power injected into the system at a given wave number spread to smaller and larger scales? (b) How does the power spectrum of density fluctuations behave asymptotically at late times? (c) What are the universal characteristics of gravitational clustering that are independent of the initial conditions and manifest at the late time evolution of the system? The review is intended for non cosmologists and will be of interest to people working in fluid mechanics, non linear dynamics and condensed matter physics.

astro-ph↗
arXiv2002

Is gravity an intrinsically quantum phenomenon? Dynamics of Gravity from the Entropy of Spacetime and the Principle of Equivalence

The two surprising features of gravity are (a) the principle of equivalence and (b) the connection between gravity and thermodynamics. Using principle of equivalence and special relativity in the {\it local inertial frame}, one could obtain the insight that gravity must possess a geometrical description. I show that, using the same principle of equivalence, special relativity and quantum theory in the {\it local Rindler frame} one can obtain the Einstein-Hilbert action functional for gravity and thus the dynamics of the spacetime. This approach, which essentially involves postulating that the horizon area must be proportional to the entropy, uses the local Rindler frame as a natural extension of the local inertial frame and leads to the interpretation that the gravitational action represents the free energy of the spacetime geometry. As an aside, one also obtains a natural explanation as to: (i) why the covariant action for gravity contains second derivatives of the metric tensor and (ii) why the gravitational coupling constant is positive. The analysis suggests that gravity is intrinsically holographic and even intrinsically quantum mechanical.

hep-th↗
arXiv2002

The Holography of Gravity encoded in a relation between Entropy, Horizon area and Action for gravity

I provide a general proof of the conjecture that one can attribute an entropy to the area of {\it any} horizon. This is done by constructing a canonical ensemble of a subclass of spacetimes with a fixed value for the temperature $T=β^{-1}$ and evaluating the {\it exact} 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 black-hole spacetimes and provides a simple and consistent interpretation of entropy and energy for De Sitter spacetime. For the Rindler spacetime the entropy per unit transverse area turns out to be $(1/4)$ while the energy is zero. Further, I show that the relationship between entropy and area allows one to construct the action for the gravitational field on the bulk and thus the full theory. In this sense, gravity is intrinsically holographic.

gr-qc↗