C${\cal C}$osmological G${\cal G}$eometric P${\cal P}$hase F${\cal F}$rom P${\cal P}$ure Q${\cal Q}$uantum S${\cal S}$tates: A Study without/ with having Bell's Inequality Violation

Abstract

In this paper, using the concept of Lewis Riesenfeld invariant quantum operator method for finding continuous eigenvalues of quantum mechanical wave functions we derive the analytical expressions for the cosmological geometric phase, which is commonly identified to be the Pancharatnam Berry phase from primordial cosmological perturbation scenario. We compute this cosmological geometric phase from two possible physical situations, (1) In the absence of Bell's inequality violation and (2) In the presence of Bell's inequality violation having the contributions in the sub Hubble region (−kτ≫1$-k\tau \gg 1$), super Hubble region (−kτ≪1$-k\tau \ll 1$) and at the horizon crossing point (−kτ=1$-k\tau = 1$) for massless field (m/scriptH≪1$m/{\cal H}\ll 1$), partially massless field (m/scriptH∼1$m/{\cal H}\sim 1$) and massive/heavy field (m/scriptH≫1$m/{\cal H}\gg 1$), in the background of quantum field theory of spatially flat quasi De Sitter geometry. The prime motivation for this work is to investigate the various unknown quantum mechanical features of primordial universe. To give the realistic interpretation of the derived theoretical results we express everything initially in terms of slowly varying conformal time dependent parameters, and then to connect with cosmological observation we further express the results in terms of cosmological observables, which are spectral index/tilt of scalar mode power spectrum (nζ$n_{\zeta }$) and tensor‐to‐scalar ratio (r). Finally, this identification helps us to provide the stringent numerical constraints on the Pancharatnam Berry phase, which confronts well with recent cosmological observation.

Avaliação das características e resistência à abrasão de tintas imobiliárias formulados com pigmento de Curcuma Longa L.

“…Como aditivo foi utilizado o "kakishibu" (fermentado de caquis verdes adstringentes rico em taninos) elaborado pela artesã gaúcha Marion Rupp, que passou por fermentação durante 24 meses (Figura 2a), apresentando pH de 3,4 e viscosidade de 0,92 cp a 25 °C no momento em que foi adicionado às misturas de tinta (Figura 2b). Como agente bactericida foi utilizada a cal de pintura pois, devido à sua alcalinidade, atua como agente bactericida e fungicida, além de impedir a formação de manchas evitando danos nos revestimentos e proporcionando economia de tinta (Coelho;Torgal;Jalali, 2009). A cal é comumente utilizada em construções de terra crua com outros insumos naturais para conferir a resistência à ação da água (Camões; Eires; Jalali, 2012), e na pintura de paredes internas de casas coloniais brasileiras (Alvarenga, 2006).…”

Entanglement negativity in de Sitter biverse from Stringy Axionic Bell pair: An analysis using Bunch-Davies vacuum

“…See refs. [14][15][16][68][69][70][71][72][73][74][75][76][77] for more details on the Bell's inequality and its violation in various contexts including cosmology.…”