Asymptotic symmetries in spatially flat FRW spacetimes

Abstract

We perform an off-shell treatment of asymptotically decelerating spatially flat FRW spacetimes at future null infinity. We obtain supertranslation and superrotation-like asymptotic diffeomorphisms which are consistent with the global symmetries of FRW and we compute how the asymptotic data is transformed under them. Further, we study in detail the effect of these diffeomorphisms on some simple backgrounds including unperturbed FRW and Sultana-Dyer black hole. In particular, we investigate how these transformations act on several cosmologically perturbed backgrounds.

Holography and black holes in asymptotically flat FLRW spacetimes

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In this paper, we extend the treatment of asymptotically decelerating spatially flat FLRW spacetimes initiated in [1]. We show that a certain class of those metrics is ruled by the asymptotic algebra bms s , which belongs to a one-parameter family of deformations of bms.

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“…Asymptotic symmetries in decelerating spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes at future null infinity I + have been explored recently in [1,2]. Both studies introduce a novel extension into a cosmological setting of the original work developed by Bondi, van der Burg, Metzner and Sachs in asymptotically flat spacetimes [3][4][5].…”

“…In particular, in [1] we obtained supertranslation and superrotation-like asymptotic diffeomorphisms consistent with the global symmetries of FLRW, computed how the asymptotic data is transformed under them and studied the effect of these diffeomorphisms on pure FLRW, Sultana-Dyer, and cosmologically perturbed backgrounds. The present work aims to deepen into these findings by understanding the asymptotic symmetry algebra and extending our ansatz to include Diff(S 2 ) transformations and cosmological black holes.…”

On deformations and extensions of Diff(S2)

“…Besides being mathematically interesting per se and scarcely studied, it pops up ubiquitously in physics literature. Although Diff(S 2 ) plays a major role in membrane theory [9][10][11] and fluid-gravity duality [28,29], our main motivation emerges from recent investigations in asymptotically flat [16,17,[19][20][21] and asymptotically spatially flat FLRW [22,49,50] spacetimes, where the asymptotic symmetry algebras contain as superrotation subalgebra that of vector fields on S 2 . In section 2, we restricted to smooth vector fields, which form the algebra vect(S 2 ).…”

“…) known as gbms s vect(C * ) s s s algebras10 [22] has recently played a role as an asymptotic symmetry algebra of decelerating asymptotically spatially flat Friedmann spacetimes at I +[22,49,50]. It turns out that this algebra forms part of a bigger family of deformations of gbms, analogously to the W (a, b; ā, b) deformations for bms[34,35] 11.…”