{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T14:49:36Z","timestamp":1773672576929,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2012,8,23]],"date-time":"2012-08-23T00:00:00Z","timestamp":1345680000000},"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>We develop the general reconstruction scheme in two scalar model. The quintom-like theory which may describe (different) non-singular Little Rip or de Sitter cosmology is reconstructed. The number of scalar phantom dark energy models (with Little Rip cosmology or asymptotically de Sitter evolution) is presented. Stability issue of such dark energy cosmologies as well as the flow to fixed points are studied. The stability of Little Rip universe which leads to dissolution of bound objects sometime in future indicates that no classical transition to de Sitter space occurs. The possibility of unification of inflation with Little Rip dark energy in two scalar theory is briefly mentioned.<\/jats:p>","DOI":"10.3390\/e14081578","type":"journal-article","created":{"date-parts":[[2012,8,23]],"date-time":"2012-08-23T11:05:47Z","timestamp":1345719947000},"page":"1578-1605","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Stability of Accelerating Cosmology in Two Scalar-Tensor Theory: Little Rip versus de Sitter"],"prefix":"10.3390","volume":"14","author":[{"given":"Yusaku","family":"Ito","sequence":"first","affiliation":[{"name":"Department of Physics, Nagoya University, Nagoya 464-8602, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shin\u2019ichi","family":"Nojiri","sequence":"additional","affiliation":[{"name":"Department of Physics, Nagoya University, Nagoya 464-8602, Japan"},{"name":"Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergei D.","family":"Odintsov","sequence":"additional","affiliation":[{"name":"Instituci\u00f2 Catalana de Recerca i Estudis Avan\u00e7ats (ICREA) and Institut de Ciencies de l\u2019Espai (IEEC-CSIC), Campus UAB, Facultat de Ciencies, Torre C5-Par-2a pl, E-08193 Bellaterra (Barcelona), Spain"},{"name":"Tomsk State Pedagogical University, 634041, Tomsk, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,8,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"955","DOI":"10.1038\/35010035","article-title":"A flat universe from high resolution maps of the cosmic microwave background radiation","volume":"404","author":"Ade","year":"2000","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Hanany, S., Ade, P., Balbi, A., Bock, J., Borrill, J., Boscaleri, A., de Bernardis, P., Ferreira, P.G., Hristov, V.V., and Jaffe, A.H. (2000). MAXIMA-1: A measurement of the cosmic microwave background anisotropy on angular scales of 10 arcminutes to 5 degrees. Astrophys. J., 545.","DOI":"10.1086\/317322"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1086\/307221","article-title":"Measurements of omega and lambda from 42 high redshift supernovae","volume":"517","author":"Perlmutter","year":"1999","journal-title":"Astrophys. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1038\/34124","article-title":"Discovery of a supernova explosion at half the age of the Universe and its cosmological implications","volume":"391","author":"Perlmutter","year":"1998","journal-title":"Nature"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1086\/300499","article-title":"Observational evidence from supernovae for an accelerating universe and a cosmological constant","volume":"116","author":"Riess","year":"1998","journal-title":"Astron. J."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Silvestri, A., and Trodden, M. (2009). Approaches to understanding cosmic acceleration. Rep. Prog. Phys., 72.","DOI":"10.1088\/0034-4885\/72\/9\/096901"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1088\/0253-6102\/56\/3\/24","article-title":"Dark energy","volume":"56","author":"Li","year":"2011","journal-title":"Commun. Theor. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1146\/annurev-nucl-010709-151330","article-title":"The physics of cosmic acceleration","volume":"59","author":"Caldwell","year":"2009","journal-title":"Ann. Rev. Nucl. Part. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1753","DOI":"10.1142\/S021827180600942X","article-title":"Dynamics of dark energy","volume":"D15","author":"Copeland","year":"2006","journal-title":"Int. J. Mod. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2012.01.001","article-title":"Modified gravity and cosmology","volume":"513","author":"Clifton","year":"2012","journal-title":"Phys. Rep."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0067-0049\/192\/1\/1","article-title":"Supernova constraints and systematic uncertainties from the first 3 years of the supernova legacy survey","volume":"192","author":"Conley","year":"2011","journal-title":"Astrophys. J. Suppl."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Sullivan, M., Guy, J., Conley, A., Regnault, N., Astier, P., Balland, C., Basa, S., Carlberg, R.G., Fouchez, D., and Hardin, D. (2011). SNLS3: Constraints on dark energy combining the supernova legacy survey three year data with other probes. Astrophys. J., 737.","DOI":"10.1088\/0004-637X\/737\/2\/102"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Komatsu, E., Smith, K.M., Dunkley, J., Bennett, C.L., Gold, B., Hinshaw, G., Jarosik, N., Larson, D., Nolta, M.R., and Page, L. (2011). Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Cosmological interpretation. Astrophys. J. Suppl., 192.","DOI":"10.1088\/0067-0049\/192\/2\/18"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Dunkley, J., Hlozek, R., Sievers, J., Acquaviva, V., Ade, P.A.R., Aguirre, P., Amiri, M., and Appel, J.W. (2011). The atacama cosmology telescope: Cosmological parameters from the 2008 power spectra. Astrophys. J., 739.","DOI":"10.1088\/0004-637X\/739\/1\/52"},{"key":"ref_15","first-page":"60","article-title":"Cosmological constraints from the clustering of the sloan digital sky survey DR7 luminous red galaxies","volume":"404","author":"Reid","year":"2010","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Giannantonio, T., Scranton, R., Crittenden, R.G., Nichol, R.C., Boughn, S.P., Myers, A.D., and Richards, G.T. (2008). Combined analysis of the integrated Sachs-Wolfe effect and cosmological implications. Phys. Rev., D77.","DOI":"10.1103\/PhysRevD.77.123520"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Ho, S., Hirata, C., Padmanabhan, N., Seljak, U., and Bahcall, N. (2008). Correlation of CMB with large-scale structure: I. ISW tomography and cosmological implications. Phys. Rev., D78.","DOI":"10.1103\/PhysRevD.78.043519"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Caldwell, R.R., Kamionkowski, M., and Weinberg, N.N. (2003). Phantom energy and cosmic doomsday. Phys. Rev. Lett., 91.","DOI":"10.1103\/PhysRevLett.91.071301"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Nojiri, S., Odintsov, S.D., and Tsujikawa, S. (2005). Properties of singularities in (phantom) dark energy universe. Phys. Rev., D71.","DOI":"10.1103\/PhysRevD.71.063004"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"L79","DOI":"10.1088\/0264-9381\/21\/11\/L03","article-title":"Sudden future singularities","volume":"21","author":"Barrow","year":"2004","journal-title":"Class. Quantum Grav."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5619","DOI":"10.1088\/0264-9381\/21\/23\/020","article-title":"More general sudden singularities","volume":"21","author":"Barrow","year":"2004","journal-title":"Class. Quantum Grav."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.physrep.2011.04.001","article-title":"Unified cosmic history in modified gravity: From F(R) theory to Lorentz non-invariant models","volume":"505","author":"Nojiri","year":"2011","journal-title":"Phys. Rep."},{"key":"ref_23","first-page":"063003","article-title":"The little rip","volume":"D84","author":"Frampton","year":"2011","journal-title":"Phys. Rev."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.physletb.2012.01.048","article-title":"Models for little rip dark energy","volume":"B708","author":"Frampton","year":"2012","journal-title":"Phys. Lett."},{"key":"ref_25","first-page":"207","article-title":"Cyclic, ekpyrotic and little rip universe in modified gravity","volume":"1458","author":"Nojiri","year":"2011","journal-title":"AIP Conf. Proc."},{"key":"ref_26","first-page":"103508:1","article-title":"Viscous little rip cosmology","volume":"D84","author":"Brevik","year":"2011","journal-title":"Phys. Rev."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Frampton, P.H., and Ludwick, K.J. (2011). Seeking evolution of dark energy. Eur. Phys. J., C71.","DOI":"10.1140\/epjc\/s10052-011-1735-x"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Granda, L.N., and Loaiza, E. (2012). Big Rip and Little Rip solutions in scalar model with kinetic and Gauss Bonnet couplings. Int. J. Mod. Phys., D2.","DOI":"10.1142\/S0218271812500022"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Capozziello, S., de Laurentis, M., Nojiri, S., and Odintsov, S.D. (2009). Classifying and avoiding singularities in the alternative gravity dark energy models. Phys. Rev., D79.","DOI":"10.1103\/PhysRevD.79.124007"},{"key":"ref_30","first-page":"083001:1","article-title":"Pseudo-rip: Cosmological models intermediate between the cosmological constant and the little rip","volume":"D85","author":"Frampton","year":"2012","journal-title":"Phys. Rev."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.physletb.2004.12.071","article-title":"Dark energy constraints from the cosmic age and supernova","volume":"B607","author":"Feng","year":"2005","journal-title":"Phys. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Elizalde, E., Nojiri, S., and Odintsov, S.D. (2004). Late-time cosmology in (phantom) scalar-tensor theory: Dark energy and the cosmic speed-up. Phys. Rev., D70.","DOI":"10.1103\/PhysRevD.70.043539"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2010.04.001","article-title":"Quintom cosmology: Theoretical implications and observations","volume":"493","author":"Cai","year":"2010","journal-title":"Phys. Rep."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1285","DOI":"10.1007\/s10714-006-0301-6","article-title":"Unifying phantom inflation with late-time acceleration: Scalar phantom-non-phantom transition model and generalized holographic dark energy","volume":"38","author":"Nojiri","year":"2006","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Chimento, L.P., Forte, M.I., Lazkoz, R., and Richarte, M.G. (2009). Internal space structure generalization of the quintom cosmological scenario. Phys. Rev., D 79.","DOI":"10.1103\/PhysRevD.79.043502"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Nesseris, S., and Perivolaropoulos, L. (2007). Crossing the phantom divide: Theoretical implications and observational status. J. Cosmol. Astropart. Phys., 0701.","DOI":"10.1088\/1475-7516\/2007\/01\/018"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1016\/j.physletb.2005.11.012","article-title":"Unified phantom cosmology: Inflation, dark energy and dark matter under the same standard","volume":"B632","author":"Capozziello","year":"2006","journal-title":"Phys. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Vikman, A. (2005). Can dark energy evolve to the phantom?. Phys. Rev., D71.","DOI":"10.1103\/PhysRevD.71.023515"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1229","DOI":"10.1142\/S0218271808012784","article-title":"Constraints on the sound speed of dynamical dark energy","volume":"D17","author":"Xia","year":"2008","journal-title":"Int. J. Mod. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0370-2693(02)02589-3","article-title":"A phantom menace?","volume":"B545","author":"Caldwell","year":"2002","journal-title":"Phys. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1088\/0004-637X\/716\/1\/712","article-title":"Spectra and light curves of six type Ia supernovae at 0.511 < z < 1.12 and the union2 compilation","volume":"716","author":"Amanullah","year":"2010","journal-title":"Astrophys. J."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/8\/1578\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:51:57Z","timestamp":1760219517000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/8\/1578"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,23]]},"references-count":41,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2012,8]]}},"alternative-id":["e14081578"],"URL":"https:\/\/doi.org\/10.3390\/e14081578","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8,23]]}}}