{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T12:46:22Z","timestamp":1768740382484,"version":"3.49.0"},"reference-count":64,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2011,2,17]],"date-time":"2011-02-17T00:00:00Z","timestamp":1297900800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The cosmological constant \u039b can be achieved as the result of entangled and statistically correlated minisuperspace cosmological states, built up by using a minimal choice of observable quantities, i.e., \u03a9m and \u03a9k, which assign the cosmic dynamics. In particular, we consider a cosmological model where two regions, corresponding to two correlated eras, are involved; the present universe description would be, in this way, given by a density matrix \u02c6\u03c1, corresponding to an entangled final state. Starting from this assumption, it is possible to infer some considerations on the cosmic thermodynamics by evaluating the Von Neumann entropy. The correlation between different regions by the entanglement phenomenon results in the existence of \u039b (in particular \u03a9\u039b) which could be interpreted in the framework of the recent astrophysical observations. As a byproduct, this approach could provide a natural way to solve the so called coincidence problem.<\/jats:p>","DOI":"10.3390\/e13020528","type":"journal-article","created":{"date-parts":[[2011,2,17]],"date-time":"2011-02-17T11:15:15Z","timestamp":1297941315000},"page":"528-541","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Entangled States in Quantum Cosmology and the Interpretation of \u039b"],"prefix":"10.3390","volume":"13","author":[{"given":"Salvatore","family":"Capozziello","sequence":"first","affiliation":[{"name":"Dipartimento di Scienze Fisiche, Universit\u00e0 di Napoli Federico II, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126 Napoli, Italy"}]},{"given":"Orlando","family":"Luongo","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica, Universit\u00e0 di Roma La Sapienza, I-00185 Roma, Italy"},{"name":"ICRANet and ICRA (International Center of Relativistic Astrophysics Networks), Piazzale della Repubblica 10, I-65122 Pescara, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2011,2,17]]},"reference":[{"key":"ref_1","unstructured":"Hartle, J.B. (2005, January 1\u20133). The Quantum Structure of Space and Time. Proceedings of the 23rd Solvay Conference on Physics, Brussels, Belgium."},{"key":"ref_2","first-page":"257","article-title":"The problem of time and gauge invariance in the quantization of cosmological models","volume":"10","author":"Shestakova","year":"2004","journal-title":"Grav. Cosmol."},{"key":"ref_3","unstructured":"Hartle, J.B. (1986). 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The Dynamics of General Relativity, John Wiley & Sons."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1627","DOI":"10.1088\/0264-9381\/24\/6\/016","article-title":"The cosmological constant as an eigenvalue of f(R)-gravity Hamiltonian constraint","volume":"24","author":"Capozziello","year":"2007","journal-title":"Class. Quant. Grav."},{"key":"ref_46","unstructured":"It is easy to understand, considering the homogeneity and isotropy of the observed universe, that to describe cosmic dynamics, only two quantities are needed, for example H and \u03a9m; the others, as for example the remaining cosmographic parameters, can be expressed in terms of them."},{"key":"ref_47","unstructured":"With equivalence between A and B."},{"key":"ref_48","unstructured":"Note that \u03bb1 ln \u03bb1 = \u03bb2 ln \u03bb2 = 0 because \u03bb1,2 = 0 and entropy in this case is defined 0 ln 0 = 0."},{"key":"ref_49","unstructured":"We do not expect that this condition is crucial and physically important; a mixture of external products among states, with the same weight, allows us only to simplify the \n\t\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t\t              \n\t\t\t\t\t\t\t\t                \u03c1\n\t\t\t\t\t\t\t\t                ^\n\t\t\t\t\t\t\t\t              \n\t\t\t\t\t\t\t\t             \n\t\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t\t           expression."},{"key":"ref_50","unstructured":"For the sake of simplicity, this result is written in the easy case of \n\t\t\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t\t\t\t\t\t  \n\t\t\t\t\t\t\t\t\t                p\n\t\t\t\t\t\t\t\t\t                -\n\t\t\t\t\t\t\t\t\t              \n\t\t\t\t\t\t\t\t\t\t\t\t  =\n\t\t\t\t\t\t\t\t\t              \n\t\t\t\t\t\t\t\t\t                 1\n\t\t\t\t\t\t\t\t\t                 2\n\t\t\t\t\t\t\t\t\t               \n\t\t\t\t\t\t\t\t\t             \n\t\t\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t\t\t           and, here, restoring, also, the definitions of \u03a9m2 and \u03a9k2, without the simplest positions."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Birrel, N.D., and Davies, P.C.W. 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