-
1
-
-
84927881640
-
-
For reviews see, for example, A.D. Linde, Particle Physics and Inflationary Cosmology (Harwood Academic, Chur Switzerland, 1990); E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, New York, 1990).
-
-
-
-
2
-
-
84927881639
-
-
The inflationary expansion is driven by the potential energy of a scalar field cphi, while the field slowly ``rolls down'' its potential V ( φ ). When cphi reaches the minimum of the potential this vacuum energy thermalizes, and inflation is followed by the usual radiation-dominated expansion. The evolution of the field cphi is influenced by quantum fluctuations, and as a result thermalization does not occur simultaneously in different parts of the Universe. Fluctuations in the thermalization time give rise to small density fluctuations on observable scales, but result in large deviations from homogeneity and isotropy on much larger scales.
-
-
-
-
3
-
-
84927881638
-
-
The spacelike character of the boundaries of thermalized regions is a general feature of slow rollover inflation. More generally, in the slow-rollover regime the surfaces of constant field cphi are spacelike. To show this, we note that during the slow-rollover the field cphi varies at the rate φ dot >> H2, where H is the local expansion rate of the Universe [1]. Quantum fluctuations cause cphi to vary by app H on the horizon scale H-1; the resulting spatial gradients are of the order | partialiφ partialiφ | app H4. Hence, partialμφ partialμφ > 0 and the surfaces of constant cphi are spacelike [our metric has signature (+ , - , - , - )]. The situation here is different from that in the old inflationary scenario [12,13] where the bubble walls expand at speeds approaching the speed of light and their worldsheets are timelike surfaces. Note that although the boundaries of thermalized regions are spacelike surfaces, they are not Cauchy surfaces for the entire spacetime, and therefore the Universe can contain a large number of nonoverlapping thermalized regions.
-
-
-
-
6
-
-
84927881637
-
-
edited by, M. J. de Vega, N. Sanchez, Lecture Notes in Physics Vol. 246, Springer-Verlag, New York
-
(1986)
Field Theory, Quantum Gravity and Strings, Proceedings of the Seminar Series, Meudon and Paris, France, 1984-1985
-
-
Starobinsky, A.A.1
-
16
-
-
84927881636
-
-
also see Ref. [6] for an extension of these results.
-
-
-
-
17
-
-
84927881635
-
-
Note that we are not assuming that there is a nonzero probability for a point p to have a finite-volume past [i.e., a finite volume for I-(p) ]. Such an assumption would mean that an arbitrarily chosen point has a finite probability to be in the inflating region. It has been shown, however, that at least in some models the inflating region is a fractal of dimension smaller than 4, and therefore occupies a vanishing fraction of the total volume (see Ref. [4]).
-
-
-
-
18
-
-
84927881634
-
-
This may be seen by introducing a pseudo-orthonormal basis lcurl Na, La, X1a, X2arcurl where La is a null vector such that NaLa= 1 [in a convention where the metric has signature ( + , - , - , - ) ] and X1a and X2a are unit spacelike vectors orthogonal to Na and La. The deviation vector Za may be written as Za= n Na+ l La+ x1X1a+ x2X2a. Now, it is possible to choose the affine parametrization so that n = 0. Further, l = ZaNa and the derivative of l vanishes in the direction of Na [i.e., NbDb( ZaNa) = 0 ].
-
-
-
|
