Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-2/37e/c/i/solution

With and , the Friedmann effective potential for pressureless matter is
Although has one maximum, it is negative, so lies above it and never vanishes. An initially small expanding universe therefore expands forever. At large ,
so the expansion approaches the exponential de Sitter scale factor in flat slicing. There is no turning point.

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