Cosmic Information, the Cosmological Constant and the Amplitude of primordial perturbations

A unique feature of gravity is its ability to control the information accessible to any specific observer. We quantify the notion of cosmic information ('CosmIn') for an eternal observer in the universe. Demanding the finiteness of CosmIn requires the universe to have a late-time accelerated expansion. Combining the introduction of CosmIn with generic features of the quantum structure of spacetime (e.g., the holographic principle), we present a holistic model for cosmology. We show that (i) the numerical value of the cosmological constant, as well as (ii) the amplitude of the primordial, scale invariant, perturbation spectrum can be determined in terms of a single free parameter, which specifies the energy scale at which the universe makes a transition from a pre-geometric phase to the classical phase. For a specific value of the parameter, we obtain the correct results for both (i) and (ii). This formalism also shows that the quantum gravitational information content of spacetime can be tested using precision cosmology.Comment: 9 pages; 1 figur

CosMIn: The Solution to the Cosmological Constant Problem

The current acceleration of the universe can be modeled in terms of a cosmological constant. We show that the extremely small value of \Lambda L_P^2 ~ 3.4 x 10^{-122}, the holy grail of theoretical physics, can be understood in terms of a new, dimensionless, conserved number CosMIn (N), which counts the number of modes crossing the Hubble radius during the three phases of evolution of the universe. Theoretical considerations suggest that N ~ 4\pi. This single postulate leads us to the correct, observed numerical value of the cosmological constant! This approach also provides a unified picture of cosmic evolution relating the early inflationary phase to the late-time accelerating phase.Comment: ver 2 (6 pages, 2 figures) received Honorable Mention in the Gravity Research Foundation Essay Contest, 2013; to appear in Int.Jour.Mod.Phys.

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.Comment: Revtex document; 4 page

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.Comment: 5 pages; no figure

Structural Aspects Of Gravitational Dynamics And The Emergent Perspective Of Gravity

I describe several conceptual aspects of a particular paradigm which treats the field equations of gravity as emergent. These aspects are related to the features of classical gravitational theories which defy explanation within the conventional perspective. The alternative interpretation throws light on these features and could provide better insights into possible description of quantum structure of spacetime. This review complements the discussion in arXiv:1207.0505, which describes space itself as emergent in the cosmological context.Comment: Updated version of talks given at: (a) Sixth International School on Field Theory and Gravitation - 2012, Petropolis, Brazil; (b) Colloquium at Institute of Astrophysics, Paris, 2012 and (c) Discussion meeting on String Theory, International Centre for Theoretical Sciences, Bangalore, 201