که برای k مقادیر ۰ , -۱ , +۱ قابل رخداد است.

بر اساس موارد بالا، متریک فریدمن رابرتسون واکر به اینصورت فرمول بندی میشود:
.
t زمان کیهانی^[۱۹۴]، r شعاع بدون بعد و و زوایای معمول مختصات کروی هستند. K نشان‌دهنده انحنای بخش قطبی است که می‌تواند ۰ ،۱+ یا ۱- باشد. a(t) فاکتور مقیاس است.
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