2002 (IPP)
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Item Cosmology with tachyon field as dark energy(2011-07-06) Bagla, J. S.; Jassal, H. K.; Padmanabhan, T.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 expo- nential 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 → ∞. This elimi- nates the future event horizon present in ΛCDM 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 ΛCDM or quintessence models.Item Cosmological constant - The weight of the vacuum(2011-07-06) Padmanabhan, T.Recent cosmological observations suggest the existence of a positive cosmological constant Λ with the magnitude Λ(G~/c3) ≈ 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. After a brief introduction to the key issues related to cosmological constant and a historical overview, a summary of the kinematics and dynamics of the standard Friedmann model of the universe is provided. The observational evidence for cosmological constant, especially from the supernova results, and the constraints from the age of the universe, structure for- mation, Cosmic Microwave Background Radiation (CMBR) anisotropies and a few others are described in detail, followed by a discussion of the theoretical models (quintessence, tachyonic scalar field, ...) from different perspectives. The latter part of the review (sections 7–11) concentrates on more conceptual and fundamental aspects of the cosmological constant like some alternative interpretations of the cosmological constant, relaxation mechanisms to reduce the cosmological constant to the currently observed value, the geometrical structure of the de Sitter space- time, thermodynamics of the de Sitter universe and the role of string theory in the cosmological constant problem.Item Classical and quantum thermodynamics of horizons in spherically symmetric spacetimes(2011-07-06) Padmanabhan, T.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 and can 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 any horizon of radius a with S = (1/4)(4πa2), |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 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.Item Can the clustered dark matter and the smooth dark energy arise from the same scalar field?(2011-07-06) Padmanabhan, T.; Choudhury, T. RoyCosmological observations suggest the existence of two different kinds of energy densities domi- nating at small (< ∼ 500 Mpc) and large (> ∼ 1000 Mpc) scales. The dark matter component, which dominates at small scales, contributes Ωm ≈ 0.35 and has an equation of state p = 0, while the dark energy component, which dominates at large scales, contributes ΩV ≈ 0.65 and has an equation of state p ≃ −ρ. It is usual to postulate weakly interacting massive particles (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) p1 − ∂iφ∂iφ acting as 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 = ρV /ρDM of the energy densities of the two dark components and expansion rate n of the universe [with a(t) ∝ t n] in the form n = (2/3)(1 +r). For r ≈ 2, we get n ≈ 2 which is consistent with observations.Item Accelerated expansion of the universe driven by tachyonic matter(2011-07-06) Padmanabhan, T.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 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 L = (1/2)∂aφ∂aφ−V (φ) used in quintessence/dark energy models; (ii) A tachyonic field with Lagrangian L = −V (φ)[1−∂aφ∂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 nterpretation of the current phase of the universe with tachyonic condensate acting as effective cosmological constant.