These are the core "legislative facts" that lawmakers and voters have relied on in limiting marriage to man-woman unions, it says.
"And even when contravened by other evidence, they are not subject to second-guessing by the judiciary without a showing that no rational person could believe them," the state said.
The plaintiffs' attorneys shot down Utah's procreation argument, made primarily at the district court level, and also contend its assertion that same-sex parents are inferior parents is false.
In a footnote, the state said based on other Supreme Court decisions it has no burden to prove that "its views on marriage are correct or sound."
Rather, "the research discussed here briefly sketches what Utah and its citizens could rationally believe about the benefits of limiting marriage to man-woman unions," it said.
A state that allows same-sex marriage "necessarily loses much of its ability to encourage gender complementarity as the preferred parenting arrangement," the application states.
"And it thereby substantially increases the likelihood that any given child will be raised without the everyday influence of his or her biological mother and father indeed, without the everyday influence of a father or mother at all."
The state said the Supreme Court's decision in United States v. Windsor holds that states are "constitutionally permitted to decide that this risk is offset, for example, by the risk that children being raised in families headed by same-sex couples will feel demeaned by their families' inability to use the term 'marriage.' "
"We think the court unlikely to hold after carefully considering the manifest benefits of gender complementarity that a sovereign state is constitutionally compelled to make that choice," Utah said.
In his decision, Judge Robert Shelby said both sides provided numerous studies about child-rearing in opposite-sex and same-sex households, creating a "factual dispute about the optimal environment for children" but that the state failed "to demonstrate any rational link between its prohibition of same-sex marriage and its goal of having more children raised in the family structure the state wishes to promote."