Microscopic origin of Einstein's field equations and the raison d'être for a positive cosmological constant

Abstract

In the paradigm of effective field theory, one hierarchically obtains the effective action ${\mathcal{A}}_{\mathrm{eff}}[q,\cdots ]$ for some low(er) energy degrees of freedom $q$, by integrating out the high(er) energy degrees of freedom $\xi$, in a path integral, based on an action $\mathcal{A}[q,\xi ,\cdots ]$. We show how one can integrate out a vector field $v^a$ in an action $\mathcal{A}[\Gamma ,v,\cdots ]$ and obtain an effective action ${\mathcal{A}}_{\mathrm{eff}}[\Gamma ,\cdots ]$ which, on variation with respect to the connection $\Gamma$, leads to the Einstein's field equations and a metric compatible with the connection. The derivation \textit{predicts} a non-zero, positive, \cc, which arises as an integration constant. The Euclidean action $\mathcal{A}[\Gamma ,v,\cdots ]$, has an interpretation as the heat density of null surfaces, when translated into the Lorentzian spacetime. The vector field $v^a$ can be interpreted as the Euclidean analogue of the microscopic degrees of freedom hosted by any null surface. Several implications of this approach are discussed.

Published Version; 12 pages; Prof. T. Padmanabhan has passed away on 17th September, 2021, while this paper was under review in a journal

References in corpus (4)

• Dark Energy and Gravity
• Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces
• Boundary terms of the Einstein-Hilbert action
• Eddington gravity with matter: An emergent perspective

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