Exact solutions of Einstein’s equations for a scalar field with a potential V(Φ) =V0 cos2(1−n) (Φ/f(n)) (0<n<1) are presented describing the gravitational field of thick, plane symmetric domain walls. The scalar field has a time-independent kinklike distribution, whereas the metric depends on a time coordinate. The metric is conformally flat and the hypersurfaces parallel to the wall (z=const) are three-dimensional de-Sitter spaces. A particle horizon exists on which the metric becomes Minkowski space. It is shown that the gravitational field experienced by a test particle is repulsive.

We analyze the magnitude and angular pattern of distortions of the microwave background by collapsing spherical domain walls. We find a characteristic pattern of redshift distortions of red or blue spikes surrounded by blue disks. The width and height of a spike is related to the diameter and magnitude of the disk. A measurement of the relations between these quantities thus can serve as an unambiguous indicator for a collapsing spherical domain wall. From the redshift distortion in the blue disks we find an upper bound on the surface energy density of the walls cr<8 MeV 3 .PACS numbers: 98.80.Cq, 98.70.Vc A phase transition in the early Universe that allows a scalar field to settle down in different vacuum expectation values in different regions of the Universe would produce domain walls 1 between these regions. The renewed interest in domain walls is due to a scenario of galaxy formation proposed by Hill, Schramm, and Fry 2 in which these topological defects form after recombination and provide the seeds for the clustering of baryons. An important criterion for the viability of such a model of structure formation is whether the induced distortion of the microwave background is compatible with the observed isotropy.In this paper we calculate the redshift distortion induced by collapsing spherical domain walls. 3 We find that they lead to a distinctive pattern in the angular temperature fluctuations of the microwave background. This paper was stimulated by a discussion with Watkins, who has studied the microwave distortions that result when photons pass through collapsing domain walls and found that a pattern of spots on the microwave sky arises. 4 A domain wall that comes within the cosmic horizon will collapse due to its surface tension. The collapse will proceed almost with the velocity of light until the radius of the bubble becomes comparable to the wall thickness and the wall decays into scalar bosons. 5 These bosons move outwards in a shell with a thickness comparable to that of the original wall. It is also possible that the bubble forms a black hole. Outside the collapsing bubble the gravitational field is equivalent to that of a point mass. Inside, however, because of the vanishing energy density, there is no gravitational field. A photon passing through the gravitational field of the bubble receives a shift in its energy (i.e., a redshift or blueshift) mainly due to three effects: 6 (i) a shift in energy equal to the difference in the gravitational potential at the points where the photon enters and leaves the bubble, (ii) a change in the potential caused by the cosmic expansion, and (iii) a time delay that photons traversing the gravitational potential suffer with respect to photons unaffected by the potential. In an expanding universe this last contribution always corresponds to a blueshift in the energy of the photon.The net change in the energy of the photon depends on the gravitational field along the path of the photon. There are three qualitatively different trajectories (see Fig. 1).(I) The pho...

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