He has promoted a conspiracy theory that coronavirus vaccines were developed to control people via microchips. He has endorsed the false notion that antidepressants are linked to school shootings. And he has pushed the decades-old theory that the C.I.A. killed his uncle, former President John F. Kennedy.

Robert F. Kennedy Jr., an environmental lawyer, is a leading vaccine skeptic and purveyor of conspiracy theories who has leaned heavily on misinformation as he mounts his long-shot 2024 campaign for the Democratic nomination.

But as voters express discontentment at a likely rematch between President Biden and former President Donald J. Trump, Mr. Kennedy has garnered as much as 20 percent of the vote in recent Democratic primary polling.

Mr. Biden and the Democratic National Committee have not publicly acknowledged Mr. Kennedy’s candidacy and have declined to comment on his campaign. Nevertheless, the public scrutiny that accompanies a White House bid has highlighted other questionable beliefs and statements Mr. Kennedy has elevated over the years.

Here are five of the many baseless claims Mr. Kennedy has peddled on the campaign trail and beyond.

He has falsely linked vaccines to various medical conditions.

Mr. Kennedy has promoted many false, specious or unproven claims that center on public health and the pharmaceutical industry — most notably, the scientifically discredited belief that childhood vaccines cause autism.

That notion has been rejected by more than a dozen peer-reviewed scientific studies across multiple countries. The National Academy of Medicine reviewed eight vaccines for children and adults and found that with rare exceptions, the vaccines are very safe, according to the Centers for Disease Control and Prevention.

Seen by many as the face of the vaccine resistance movement, Mr. Kennedy has asserted that he is “not anti-vaccine” and seeks to make vaccines more safe. But he has advertised misleading information about vaccine ingredients and circulated retracted studies linking vaccines to various medical conditions.

At a rally in Washington last year, he compared the vaccination records some called “vaccine passports” to life in Germany during the Holocaust, a statement he later apologized for. And he falsely told Louisiana lawmakers in 2021 that the coronavirus vaccine was the “deadliest vaccine ever made.”

Children’s Health Defense, an organization Mr. Kennedy originally founded as the World Mercury Project, has frequently campaigned against vaccines. Facebook and Instagram removed the group’s accounts last year for espousing vaccine misinformation, and Mr. Kennedy has often lamented the perils of “censorship” in campaign speeches since.

He has made baseless claims about a connection between gender dysphoria and chemical exposure.

In an interview last month with Jordan Peterson, a conservative Canadian psychologist and public speaker, Mr. Kennedy falsely linked chemicals present in water sources to transgender identity.

“A lot of the problems we see in kids, particularly boys, it’s probably underappreciated how much of that is coming from chemical exposures, including a lot of sexual dysphoria that we’re seeing,” he said. He referred to research on an herbicide, atrazine, in which scientists found that it “induces complete feminization and chemical castration” in certain frogs.

But no evidence exists to indicate that the chemical, typically used on farms to kill weeds, causes the same effects in humans, let alone gender dysphoria. And according to the Centers for Disease Control and Prevention, “Most people are not exposed to atrazine on a regular basis.”

He has falsely linked antidepressants to school shootings.

Drawing on longstanding dubious claims, Mr. Kennedy has repeatedly endorsed the idea that mass shootings have increased because of heightened use of antidepressants.

“Kids always had access to guns, and there was no time in American history or human history where kids were going to schools and shooting their classmates,” he told the comedian Bill Maher on a recent episode of the podcast, “Club Random With Bill Maher.” “It really started happening conterminous with the introduction of these drugs, with Prozac and the other drugs.”

While both antidepressant use and mass shooting occurrences have increased in the last several decades, the scientific community has found “no biological plausibility” to back a link between the two, according to Ragy Girgis, an associate professor of clinical psychiatry at Columbia University.

Antidepressants often have warnings that reference suicidal thoughts, Mr. Girgis said. But those warnings refer to the possibility that people who already experience suicidal ideation might share pre-existing beliefs aloud once they take the medicine as part of their treatment.

Mr. Kennedy, however, has pointed to such warnings as evidence of the false notion that the drugs might induce “homicidal tendencies.”

Several high-profile figures, including Representative Marjorie Taylor Greene of Georgia and the former Fox News host Tucker Carlson, have amplified similar claims following recent mass shootings.

Most school shooters were not prescribed with psychotropic medications before committing acts of violence, a 2019 study found. And even when they were, researchers wrote, “no direct or causal association was found.”

He has bolstered a conspiracy theory that the C.I.A. assassinated his uncle.

Mr. Kennedy has long promoted a conspiracy theory that the C.I.A. killed his uncle, President John F. Kennedy.

He claimed, without evidence, during a Fox News interview with Sean Hannity in May that Allen W. Dulles, the director of the C.I.A. at the time President Kennedy was killed, helped cover up evidence of the organization’s involvement.

Referencing a House committee inquiry in 1976, he said: “Most of the people in that investigation believed it was the C.I.A. that was behind it because the evidence was so overwhelming to them.”

But even that investigation, which found that President Kennedy was “probably” the victim of a conspiracy of some kind, flatly concluded that the C.I.A. was “not involved.”

And the Warren Commission, convened in 1963 to investigate the Kennedy assassination, found that the killer, Lee Harvey Oswald, acted alone and was not connected to any governmental agency.

And he has said that Republicans stole the 2004 presidential election.

Mr. Kennedy told The Washington Post in June that he still believed that John Kerry, the Democratic candidate, had won the 2004 presidential election.

Mr. Kennedy first promoted that idea in a 2006 article in Rolling Stone, asserting that Republicans had “mounted a massive, coordinated campaign to subvert the will of the people” and assure the re-election of President George W. Bush. He claimed that their efforts “prevented more than 350,000 voters in Ohio from casting ballots or having their votes counted.”

But it is one thing to complain of vote suppression; it is another thing to demonstrate that Mr. Kerry won more of the votes cast.

Mr. Bush defeated Mr. Kerry by a margin of 35 electoral college votes nationally; he carried Ohio and its 20 electoral votes by more than 118,000 ballots.

The Times reported in 2004 that a glitch in an electronic Ohio voting machine added 3,893 votes to Mr. Bush’s tally. That error was caught in preliminary vote counts, officials said. But the event, alongside other voting controversies nationwide, spurred widespread questions about election integrity that caught traction with people like Mr. Kennedy.

Mr. Kerry, however, conceded the race a day after the election.