arXiv subjects

T. Padmanabhan

Publications and source records attributed to T. Padmanabhan.

At least 127 records · Page 7Linked to original sources

arXiv2006

Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons

There is an intriguing analogy between the gravitational dynamics of the horizons and thermodynamics. In case of general relativity, as well as for a wider class of Lanczos-Lovelock theories of gravity, it is possible to interpret the field equations near any spherically symmetric horizon as a thermodynamic identity TdS = dE + PdV. We study this approach further and generalize the results to two more generic cases within the context of general relativity: (i) stationary axis-symmetric horizons and (ii) time dependent evolving horizons. In both the cases, the near horizon structure of Einstein equations can be expressed as a thermodynamic identity under the virtual displacement of the horizon. This result demonstrates the fact that the thermodynamic interpretation of gravitational dynamics is not restricted to spherically symmetric or static horizons but is quite generic in nature and indicates a deeper connection between gravity and thermodynamics.

gr-qc↗

arXiv2006

Why Does Gravity Ignore the Vacuum Energy?

The equations of motion for matter fields are invariant under the shift of the matter lagrangian by a constant. Such a shift changes the energy momentum tensor of matter by T^a_b --> T^a_b +ρδ^a_b. In the conventional approach, gravity breaks this symmetry and the gravitational field equations are not invariant under such a shift of the energy momentum tensor. I argue that until this symmetry is restored, one cannot obtain a satisfactory solution to the cosmological constant problem. I describe an alternative perspective to gravity in which the gravitational field equations are [G_{ab} -κT_{ab}] n^an^b =0 for all null vectors n^a. This is obviously invariant under the change T^a_b --> T^a_b +ρδ^a_b and restores the symmetry under shifting the matter lagrangian by a constant. These equations are equivalent to G_{ab} = κT_{ab} + Cg_{ab} where C is now an integration constant so that the role of the cosmological constant is very different in this approach. The cosmological constant now arises as an integration constant, somewhat like the mass M in the Schwarzschild metric, the value of which can be chosen depending on the physical context. These equations can be obtained from a variational principle which uses the null surfaces of spacetime as local Rindler horizons and can be given a thermodynamic interpretation. This approach turns out to be quite general and can encompass even the higher order corrections to Einstein's gravity and suggests a principle to determine the form of these corrections in a systematic manner.

gr-qc↗

arXiv2006

Holography of Gravitational Action Functionals

Einstein-Hilbert (EH) action can be separated into a bulk and a surface term, with a specific ("holographic") relationship between the two, so that either can be used to extract information about the other. The surface term can also be interpreted as the entropy of the horizon in a wide class of spacetimes. Since EH action is likely to just the first term in the derivative expansion of an effective theory, it is interesting to ask whether these features continue to hold for more general gravitational actions. We provide a comprehensive analysis of lagrangians of the form L=Q_a^{bcd}R^a_{bcd}, in which Q_a^{bcd} is a tensor with the symmetries of the curvature tensor, made from metric and curvature tensor and satisfies the condition \nabla_cQ^{abcd}=0, and show that they share these features. The Lanczos-Lovelock lagrangians are a subset of these in which Q^{abcd} is a homogeneous function of the curvature tensor. They are all holographic, in a specific sense of the term, and -- in all these cases -- the surface term can be interpreted as the horizon entropy. The thermodynamics route to gravity, in which the field equations are interpreted as TdS=dE+pdV, seems to have greater degree of validity than the field equations of Einstein gravity itself. The results suggest that the holographic feature of EH action could also serve as a new symmetry principle in constraining the semiclassical corrections to Einstein gravity. The implications are discussed.

hep-th↗

arXiv2006

Thermodynamic route to Field equations in Lanczos-Lovelock Gravity

Spacetimes with horizons show a resemblance to thermodynamic systems and one can associate the notions of temperature and entropy with them. In the case of Einstein-Hilbert gravity, it is possible to interpret Einstein's equations as the thermodynamic identity TdS = dE + PdV for a spherically symmetric spacetime and thus provide a thermodynamic route to understand the dynamics of gravity. We study this approach further and show that the field equations for Lanczos-Lovelock action in a spherically symmetric spacetime can also be expressed as TdS = dE + PdV with S and E being given by expressions previously derived in the literature by other approaches. The Lanczos-Lovelock Lagrangians are of the form L=Q_a^{bcd}R^a_{bcd} with \nabla_b Q^{abcd}=0. In such models, the expansion of Q^{abcd} in terms of the derivatives of the metric tensor determines the structure of the theory and higher order terms can be interpreted quantum corrections to Einstein gravity. Our result indicates a deep connection between the thermodynamics of horizons and the allowed quantum corrections to standard Einstein gravity, and shows that the relation TdS = dE + PdV has a greater domain of validity that Einstein's field equations.

hep-th↗

arXiv2006

Dark Energy: Mystery of the Millennium

Nearly seventy per cent of the energy density in the universe is unclustered and exerts negative pressure. This conclusion -- now supported by numerous observations -- poses the greatest challenge for theoretical physics today. I discuss this issue with special emphasis on the cosmological constant as the possible choice for the dark energy. Several curious features of a universe with a cosmological constant are described and some possible approaches to understand the nature of the cosmological constant are reviewed. In particular, I show how some of the recent ideas, related to a thermodynamic route to gravity, allow us to: (i) create a paradigm in which the bulk value of cosmological constant is irrelevant and (ii) obtain the correct, observed, value for the cosmological constant from vacuum fluctuations in a region confined by the deSitter horizon.

astro-ph↗

arXiv2006

Thermodynamics of horizons from a dual quantum system

It was shown recently that, in the case of Schwarschild black hole, one can obtain the correct thermodynamic relations by studying a model quantum system and using a particular duality transformation. We study this approach further for the case a general spherically symmetric horizon. We show that the idea works for a general case only if we define the entropy S as a congruence ("observer") dependent quantity and the energy E as the integral over the source of the gravitational acceleration for the congruence. In fact, in this case, one recovers the relation S=E/2T between entropy, energy and temperature previously proposed by one of us in gr-qc/0308070. This approach also enables us to calculate the quantum corrections of the Bekenstein-Hawking entropy formula for all spherically symmetric horizons.

gr-qc↗

arXiv2006

A new perspective on Gravity and the dynamics of Spacetime

The Einstein-Hilbert action has a bulk term and a surface term (which arises from integrating a four divergence). I show that one can obtain Einstein's equations from the surface term alone. This leads to: (i) a novel, completely self contained, perspective on gravity and (ii) a concrete mathematical framework in which the description of spacetime dynamics by Einstein's equations is similar to the description of a continuum solid in the thermodynamic limit.

gr-qc↗

arXiv2006

Gravity: A New Holographic Perspective

A general paradigm for describing classical (and semiclassical) gravity is presented. This approach brings to the centre-stage a holographic relationship between the bulk and surface terms in a general class of action functionals and provides a deeper insight into several aspects of classical gravity which have no explanation in the conventional approach. After highlighting a series of unresolved issues in the conventional approach to gravity, I show that (i) principle of equivalence, (ii) general covariance and (iii)a reasonable condition on the variation of the action functional, suggest a generic Lagrangian for semiclassical gravity of the form $L=Q_a^{bcd}R^a_{bcd}$ with $\nabla_b Q_a^{bcd}=0$. The expansion of $Q_a^{bcd}$ in terms of the derivatives of the metric tensor determines the structure of the theory uniquely. The zeroth order term gives the Einstein-Hilbert action and the first order correction is given by the Gauss-Bonnet action. Any such Lagrangian can be decomposed into a surface and bulk terms which are related holographically. The equations of motion can be obtained purely from a surface term in the gravity sector. Hence the field equations are invariant under the transformation $T_{ab} \to T_{ab} + λg_{ab}$ and gravity does not respond to the changes in the bulk vacuum energy density. The cosmological constant arises as an integration constant in this approach. The implications are discussed.

gr-qc↗

arXiv2006

Casimir Effect confronts Cosmological Constant

It has been speculated that the zero-point energy of the vacuum, regularized due to the existence of a suitable ultraviolet cut-off scale, could be the source of the non-vanishing cosmological constant that is driving the present acceleration of the universe. We show that the presence of such a cut-off can significantly alter the results for the Casimir force between parallel conducting plates and even lead to repulsive Casimir force when the plate separation is smaller than the cut-off scale length. Using the current experimental data we rule out the possibility that the observed cosmological constant arises from the zero-point energy which is made finite by a suitable cut-off. Any such cut-off which is consistent with the observed Casimir effect will lead to an energy density which is about 10^{12} times larger than the observed one, if gravity couples to these modes. The implications are discussed.

astro-ph↗

arXiv2006

Properties of High Redshift Quasars-II: What does the quasar luminosity function tell us about super-massive black-hole evolution?

In the local universe, the masses of Super-Massive Black-Holes (SMBH) appear to correlate with the physical properties of their hosts, including the mass of the dark-matter halo. Using these clues as a starting point many studies have produced models that can explain phenomena like the quasar luminosity function. The shortcoming of this approach is that working models are not unique, and as a result it is not always clear what input physics is being constrained. Here we take a different approach. We identify critical parameters that describe the evolution of SMBHs at high redshift, and constrain their parameter space based on observations of high redshift quasars from the Sloan Digital Sky Survey. We find that the luminosity function taken in isolation is somewhat limited in its ability to constrain SMBH evolution due to some strong degeneracies. This explains the presence in the literature of a range of equally successful models based on different physical hypotheses. Including the constraint of the local SMBH to halo mass ratio breaks some of the degeneracies, and our results suggest halo masses at z~4.8 of 10^{12.5+/-0.3}M_solar (with 90% confidence), with a SMBH to halo mass ratio that decreases with time (>99%). We also find a quasar luminosity to halo mass ratio that increases with halo mass (>99%). These features need to be incorporated in all successful models of SMBH evolution. On the other hand current observations do not permit any conclusions regarding the evolution of quasar lifetime, or the SMBH occupation fraction in dark matter halos.

astro-ph↗

arXiv2006

Advanced Topics in Cosmology: A Pedagogical Introduction

These lecture notes provide a concise, rapid and pedagogical introduction to several advanced topics in contemporary cosmology. The discussion of thermal history of the universe, linear perturbation theory, theory of CMBR temperature anisotropies and the inflationary generation of perturbation are presented in a manner accessible to someone who has done a first course in cosmology. The discussion of dark energy is more research oriented and reflects the personal bias of the author. Contents: (I) The cosmological paradigm and Friedmann model (II) Thermal history of the universe (III) Structure formation and linear perturbation theories (IV) Perturbations in dark matter and radiation (V) Transfer function for matter perturbations (VI) Temperature anisotropies of CMBR (VII) Generation of initial perturbations from inflation (VIII) The dark energy.

astro-ph↗

arXiv2005

Power transfer in nonlinear gravitational clustering and asymptotic universality

We study the non linear gravitational clustering of collisionless particles in an expanding background using an integro-differential equation for the gravitational potential. In particular, we address the question of how the nonlinear mode-mode coupling transfers power from one scale to another in the Fourier space if the initial power spectrum is sharply peaked at a given scale. We show that the dynamical equation allows self similar evolution for the gravitational potential $ϕ_{\bf k}(t)$ in Fourier space of the form $ϕ_{\bf k}(t) = F(t)D({\bf k}) $ where the function $F(t)$ satisfies a second order non-linear differential equation. We provide a complete analysis of the relevant solutions of this equation thereby determining the asymptotic time evolution of the gravitational potential and density contrast. The analysis shows that both $F(t) $ and $D({\bf k})$ have well defined asymptotic forms indicating that the power transfer leads to a universal power spectrum at late times. The analytic results are compared with numerical simulations showing good agreement.

astro-ph↗

arXiv2005

Challenges in Non-Linear Gravitational Clustering

This article addresses some issues related to statistical description of gravitating systems in an expanding backgrounds. In particular, I describe (a) how the non linear mode-mode coupling transfers power from one scale to another in the Fourier space if the initial power spectrum is sharply peaked at a given scale and (b) what are the asymptotic characteristics of gravitational clustering that are independent of the initial conditions. The analysis uses a new approach based on an integro-differential equation for the evolution of the gravitational potential in the Fourier space. I show how this equation allows one to understand several aspects of nonlinear gravitational clustering and provides insight in to the transfer of power from one scale to another through nonlinear mode coupling. Numerical simulations as well as analytic work shows that power transfer leads to a universal power spectrum at late times, somewhat reminiscent of the existence of Kolmogorov spectrum in fluid turbulence.

astro-ph↗

arXiv2005

A possible approach to understand nonlinear gravitational clustering in expanding background

A new approach to study the nonlinear phase of gravitational clustering in an expanding universe is explored. This approach is based on an integro-differential equation, for the evolution of the gravitational potential in the Fourier space, which is obtained by using a physically motivated closure condition. I show how this equation allows one to understand several aspects of nonlinear gravitational clustering and provides insight in to the transfer of power from one scale to another through nonlinear mode coupling.

astro-ph↗

arXiv2005

Darker Side of the Universe

Observations suggest that nearly seventy per cent of the energy density in the universe is unclustered and exerts negative pressure. Theoretical understanding of this component (`dark energy'), which is driving an accelerated expansion of the universe, is {\it the} problem in cosmology today. I discuss this issue with special emphasis on the cosmological constant as the possible choice for the dark energy. Several curious features of a universe with a cosmological constant are described and some possible approaches to understand the nature of the cosmological constant are discussed.

astro-ph↗

arXiv2005

Zero-point length from string fluctuations

One of the leading candidates for quantum gravity, viz. string theory, has the following features incorporated in it. (i) The full spacetime is higher dimensional, with (possibly) compact extra-dimensions; (ii) There is a natural minimal length below which the concept of continuum spacetime needs to be modified by some deeper concept. On the other hand, the existence of a minimal length (or zero-point length) in four-dimensional spacetime, with obvious implications as UV regulator, has been often conjectured as a natural aftermath of any correct quantum theory of gravity. We show that one can incorporate the apparently unrelated pieces of information - zero-point length, extra-dimensions, string T-duality - in a consistent framework. This is done in terms of a modified Kaluza-Klein theory that interpolates between (high-energy) string theory and (low-energy) quantum field theory. In this model, the zero-point length in four dimensions is a ``virtual memory'' of the length scale of compact extra-dimensions. Such a scale turns out to be determined by T-duality inherited from the underlying fundamental string theory. From a low energy perspective short distance infinities are cut off by a minimal length which is proportional to the square root of the string slope, i.e. \sqrt{α^\prime}. Thus, we bridge the gap between the string theory domain and the low energy arena of point-particle quantum field theory.

hep-th↗

arXiv2005

Observational constraints on low redshift evolution of dark energy: How consistent are different observations?

The dark energy component of the universe is often interpreted either in terms of a cosmological constant or as a scalar field. A generic feature of the scalar field models is that the equation of state parameter w= P/rho for the dark energy need not satisfy w=-1 and, in general, it can be a function of time. Using the Markov chain Monte Carlo method we perform a critical analysis of the cosmological parameter space, allowing for a varying w. We use constraints on w(z) from the observations of high redshift supernovae (SN), the WMAP observations of CMB anisotropies and abundance of rich clusters of galaxies. For models with a constant w, the LCDM model is allowed with a probability of about 6% by the SN observations while it is allowed with a probability of 98.9% by WMAP observations. The LCDM model is allowed even within the context of models with variable w: WMAP observations allow it with a probability of 99.1% whereas SN data allows it with 23% probability. The SN data, on its own, favors phantom like equation of state (w<-1) and high values for Omega_NR. It does not distinguish between constant w (with w<-1) models and those with varying w(z) in a statistically significant manner. The SN data allows a very wide range for variation of dark energy density, e.g., a variation by factor ten in the dark energy density between z=0 and z=1 is allowed at 95% confidence level. WMAP observations provide a better constraint and the corresponding allowed variation is less than a factor of three. Allowing for variation in w has an impact on the values for other cosmological parameters in that the allowed range often becomes larger. (Abridged)

astro-ph↗

arXiv2005

Gravitational Collapse in an Expanding Universe: Scaling Relations for Two-Dimensional Collapse Revisited

We investigate non-linear scaling relations for two-dimensional gravitational collapse in an expanding background using a 2D TreePM code and study the strongly non-linear regime ($\barξ\leq 200$) for power law models. Evolution of these models is found to be scale-invariant in all our simulations. We find that the stable clustering limit is not reached, but there is a model independent non-linear scaling relation in the asymptotic regime. This confirms results from an earlier study which only probed the mildly non-linear regime ($\barξ\leq 40$). The correlation function in the extremely non-linear regime is a less steep function of scale than reported in earlier studies. We show that this is due to coherent transverse motions in massive haloes. We also study density profiles and find that the scatter in the inner and outer slopes is large and that there is no single universal profile that fits all cases. We find that the difference in typical density profiles for different models is smaller than expected from similarity solutions for halo profiles and transverse motions induced by substructure are a likely reason for this difference being small.

astro-ph↗