To narrow down the optimum time for life, Loeb then considered the sizes of stars. For a star like the sun, the first (and so far only) evidence for life on one of its planets dates back about 800 million years after Earth's formation. By that yardstick, stars that are about three times larger than the sun or bigger would explode before life had a chance to take root.
RELATED: Can Bacteria on Earth Help Us Find Alien Life?
Smaller stars will live much longer than the sun, giving any suitably positioned orbiting planets more time for life to evolve. Loeb estimates that stars with 10 percent of the sun's mass will burn for 10 trillion years. By comparison, the sun, which is about 4.6 billion years old, will burn out in another 7 billion years or so.
Many other factors besides a star's size could impact whether its planets are suitable for life.
For example, small red dwarf stars, which are the most common stars in the galaxy, emit strong flares and ultraviolet radiation when they are young which could leave any rocky orbiting planets without their life-critical atmospheres.
"If we insist that life near the sun is typical and not premature ... then we must conclude that the physical environments of low-mass stars are hazardous to life," Loeb writes in a paper to be published in the Journal of Cosmology and Astroparticle Physics.
RELATED: Black Holes Set the Clock for Life on Earth
"Future searches for molecular bio-signatures, such as oxygen combined with methane, in the atmospheres of planets around low mass stars could inform us whether life will exist at late cosmic times," he added.
The scientists point out that the emergence of life also may be tied or influenced by several other factors, including the existence of a moon to stabilize the climate on an Earth-like planet, the existence of asteroid belts, the orbital structure of the host planetary system, the effects of a binary star companion, the location of the planetary system within the host galaxy, and specific properties of the host galaxy, such as its type and chemical composition and how it is impacted quasars, gamma ray bursts and hot gases in its galaxy clusters.
"These additional factors are highly uncertain and complicated to model and were ignored for simplicity in our analysis," Loeb added.
The study is published in the online archive ArXiv.org.