Conformal vacuum and the fluctuation-dissipation theorem in a de Sitter universe and black hole spacetimes

Abstract

In the studies of quantum field theory in curved spacetime, the ambiguous concept of vacuum state and the particle content is a long-standing debatable aspect. So far it is well known to us that in the background of the curved spacetime, some privileged class of observers detect particle production in the suitably chosen vacuum states of the quantum matter fields. In this work we aim to study the characteristics behaviour of these produced particles in the background of the de-Sitter (dS) Friedmann-Lamaître-Robertson-Walker (FLRW) Universe (both for (1 + 1) and (3 + 1) dimensions) and (1 + 1)-dimensional Schwarzschild black hole (BH) spacetime, from the point of view of the respective privileged class of observers. Here the analysis is confined to the observers who perceive particle excitations in the conformal vacuum. We consider some test particles in the thermal bath of the produced particles and calculate the correlation function of the fluctuation of the random force as exerted by the produced quanta on the test particles. We obtain that the correlation function abides by the fluctuation-dissipation theorem, which in turn signifies that the test particles execute Brownian-like motion in the thermal bath of the produced quanta. 1

Black hole and cosmological particle production in Schwarzschild de Sitter

“…There is a significant body of research about choosing vacuum states in deSitter and inflationary cosmologies, see e.g. [8,[36][37][38][39][40][41][42][43][44][45][46], and for a pedagogical treatment and further references see [32]. The quantum mechanical production of particles in inflation has been computed in multiple contexts and compared in detail to observations.…”

“…The transmission coefficient T * ν has entered through the future boundary behavior of k ν . Combining (43), (45), and (46) gives…”

Detector response along null geodesics in black hole spacetimes and in a Friedmann-Lemaitre-Robertson-Walker universe

“…This can be obtained by finding the relation among t s and t p . Integrating (6) for the present value of f (r) one obtains…”

“…All these resemblance between these two facts is well compatible with the equivalence principle. Several recent investigations has been done related to the nature of the observed particles in this thermal bath [4][5][6][7]. A very recent investigation reveled that these particles can exhibit Brownian like motion in this thermal bath and satisfy the well known equilibrium fluctuation-dissipation theorem [4,6].…”

How robust is the indistinguishability between quantum fluctuation seen from noninertial frame and real thermal bath

“…Therefore we argue that the indistinguishability between the real thermal bath and the Rindler frame may not be totally true.PACS numbers: * blue chandramouli@alumni.iitg.ac.in,chandramouli.chowdhury@icts.res.in † blue susmita.das@alumni.iitg.ac.in, susmitad210@gmail.com ‡ blue suroj176121013@iitg.ac.in § blue bibhas.majhi@iitg.ac.in 1 Similar findings have also been obtained for conformal vacuum, seen by the comoving observers, in the case of de-Sitter (dS) Friedmann-Lamatre-Robertson-Walker (FLRW) Universe. An extension to (1 + 1) Schwarzschild black hole revels that the particles in Kruskal and Unruh vacuum states, seen by the Schwarzschild static observer, exhibits same fluctuationdissipation theorem (see [11] for details).…”