Future of an expanding universe

Observations suggest that the expansion of the universe will continue forever. If so, then a popular theory is that the universe will cool as it expands, eventually becoming too cold to sustain life. For this reason, this future scenario is popularly called the Heat Death.

If dark energy—represented by the cosmological constant, a constant energy density filling space homogeneously, or scalar fields, such as quintessence or moduli, dynamic quantities whose energy density can vary in time and space—accelerates the expansion of the universe, then the space between clusters of galaxies will grow at an increasing rate. Redshift will stretch ancient, incoming photons (even gamma rays) to undetectably long wavelengths and low energies.Stars are expected to form normally for 10¹² to 10¹⁴ (1–100 trillion) years, but eventually the supply of gas needed for star formation will be exhausted. As existing stars run out of fuel and cease to shine, the universe will slowly and inexorably grow darker, one star at a time. According to theories that predict proton decay, the stellar remnants left behind will disappear, leaving behind only black holes, which themselves eventually disappear as they emit Hawking radiation. Ultimately, if the universe reaches a state in which the temperature approaches a uniform value, no further work will be possible, resulting in a final heat death of the universe.

Infinite expansion does not determine the spatial curvature of the universe. It can be open (with negative spatial curvature), flat, (positive spatial curvature), although if it is closed, sufficient dark energy must be present to counteract the gravitational forces. Open and flat universes will expand forever even in the absence of dark energy.

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Wikipedia