A class of cosmological models with spatially constant sign-changing curvature
Metadatos
Mostrar el registro completo del ítemAutor
Sánchez Caja, MiguelEditorial
EMS Press
Materia
Cosmological models Space topology change Constant curvature
Fecha
2023-03-17Referencia bibliográfica
Miguel Sánchez Caja, A class of cosmological models with spatially constant sign-changing curvature. Port. Math. 80 (2023), no. 3/4, pp. 291–313 [DOI 10.4171/PM/2099]
Patrocinador
A-FQM-494-UGR18 (Junta de Andalucía/ FEDER); PID2020-116126GB-I00 (MCIN/ AEI/10.13039/501100011033); IMAG/ María de Maeztu, CEX2020-001105-MCIN/ AEI/ 10.13039/ 501100011033Resumen
We construct globally hyperbolic spacetimes such that each slice {t=t0} of the universal time t is a model space of constant curvature k(t0) which may not only vary with t0∈R but also change its sign. The metric is smooth and slightly different to FLRW spacetimes, namely, g=−dt2+dr2+Sk(t)2(r)gSn−1, where gSn−1 is the metric of the standard sphere, Sk(t)(r)=sin(k(t)
r)/k(t)
when k(t)≥0 and Sk(t)(r)=sinh(−k(t)
r)/−k(t)
when k(t)≤0.
In the open case, the t-slices are (non-compact) Cauchy hypersurfaces of curvature k(t)≤0, thus homeomorphic to Rn; a typical example is k(t)=−t2 (i.e., Sk(t)(r)=sinh(tr)/t). In the closed case, k(t)>0 somewhere, a slight extension of the class shows how the topology of the t-slices changes. This makes at least one comoving observer to disappear in finite time t showing some similarities with an inflationary expansion. Anyway, the spacetime is foliated by Cauchy hypersurfaces homeomorphic to spheres, not all of them t-slices.