Quantum cosmology for inflationary scenary
J. Socorro* and O. Obregón†
Instituto de Física de la Universidad de Guanajuato, Apartado Postal E-143, C.P. 37150, León, Guanajuato, México. *socorro@ifug3.ugto.mx, †octavio@ifug3.ugto.mx
Recibido el 24 de agosto de 2001. ]]> Aceptado el 31 de enero de 2002.
Abstract
We study quantum and super quantum cosmology for a Friedman-Robertson Walker (FRW) flat universe in the presence of an inflation exponential potential with the corresponding kinetic term for the scalar field. We exhibit exact solutions for the corresponding Wheeler-DeWitt (WDW) equation and its square root. In both cases, solutions, as is known for the Bianchi models, of the form eiΦ exist, where Φ is the Hamilton-Jacobi function. For a particular factor ordering of the standard Wheeler-DeWitt equation we show a "wave packet" in which for large χ (with the radius of expansion of the universe a ~ e-x), φ the scalar field and χ "compete" modulating the behaviour of the "wave packet".
Keywords: Inflation; quantum exact solutions; supersymmetric quantum cosmology; factor ordering; Einstein-Hamilton-Jacobi equation.
Resumen
Se estudian soluciones cosmológicas cuánticas y supercuánticas exactas para un universo plano tipo Friedman-Robertson-Walker (FRW) en presencia de un potencial exponencial de inflación con un término cinético para el campo escalar. Se presentan soluciones exactas a la ecuación de Wheeler-DeWitt (WDW) y su correspondiente raíz cuadrada. En ambos casos, las soluciones, como es conocido de los modelos Bianchi, son de la forma eiΦ, donde Φ es la función de Hamilton-Jacobi. Para un valor particular del parámetro de ordenamiento de factores en la ecuación de Wheeler-DeWitt, se muestra un "paquete de ondas" en el cual para grandes valores de χ (con el radio de expansión del universo definido a ~ e-x), el campo escalar φ "compite" con χ en la modulación del comportamiento del "paquete de ondas".
Descriptores: Inflación; soluciones exactas cuánticas; cosmología cuántica supersimétrica; ordenamiento de factores; ecuación de Einstein-Hamilton-Jacobi.
PACS: 04.20.Jb; 04.40.Nr; 12.60.Jv; 98.80.Hw
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Acknowledgments
This work was partially supported by CONACYT grant E28454. We thank N. Lopez for critical reading of the manuscript.
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