Justin Theroux on HBO 2014 ”The Leftovers “ (Paul Schiraldi/Paul Schiraldi Photography)

Whether or not anyone wants to spend the summer staring directly at sorrow and regret, that’s precisely what HBO and the creators of the new drama “The Leftovers” seem to have in mind.

There’s nothing warm or welcoming about it, nor is there meant to be. Where the network’s “True Detective” occasionally broke its dolefulness with the slyest, philosophically artful wink at an audience riveted by its mystery, “The Leftovers” grafts more unhappiness onto unhappiness. Where “Game of Thrones” revels in even its most gruesome developments, it exists safely within the bounds of fantasy, so slay away. “The Leftovers” mainly acts as a means to deliver the worst news about human nature.

Yet, despite the downer language of this review, the show delivers on an exceedingly intriguing premise, with some of the most beguilingly morose performances delivered this year. It’s a strange but good wallow.

Using executive producer and writer Tom Perrotta’s sad and thoughtful novel as a template for a much broader story, “The Leftovers” (premiering June 29) is one of the coldest TV shows I’ve ever seen. It possesses almost no irony, few verbose monologues, a bare minimum of sharp moves, and a style that is conspicuously drab. Watching it produces a numbness that isn’t anything like grief, but more like the tingly approach of a Novocaine local. The tongue can’t help returning to the hurt spot.

Justin Theroux, who until “The Leftovers” has been sorely underutilized as a lead actor, stars as Kevin Garvey, the police chief of Mapleton, N.Y., a small town still coming to grips with a global crisis. Three years earlier, on Oct. 14, one in every 50 or so people randomly vanished in a single instance — a total of 2 percent of global population. They didn’t burn up or float away. They’re just inexplicably gone.

To demonstrate, “The Leftovers” opens on that ordinary day with the scene of a mother trying to run errands and carry on a phone conversation while handling a screaming infant. While she fiddles with her keys in the front seat, her baby’s wails in the car seat behind her suddenly cease. Gone. She gets out of the car and screams in panic; so does a boy across the parking lot who saw his father disappear. On the street, two cars collide — one of them driverless.

You’ve probably seen or imagined something like this if you’ve ever heard or were taught fundamentalist stories of the Christian rapture, when the souls of the faithful are Hoovered up into heaven while the sinners remain for apocalypse. (“The Leftovers” theme sequence references the kitsch paintings seen in free pamphlets — souls leaving buildings, cars, airplanes — this time rendered as Renaissance ceiling work.)

Lots of people are gone, some 6 million Americans. “Poof” becomes a verb — he poofed, she poofed, the rest of us still here did not poof. Celebrities poofed, too, their absence noted during a cable news special on the third anniversary of “the Sudden Departure”: Bonnie Raitt vanished as did Anthony Bourdain (yay?), Condoleezza Rice, Jennifer Lopez, Shaquille O’Neal, Pope Benedict XVI and Gary Busey, among others.

“I get the pope,” a bartender remarks to Chief Garvey. “But Gary [bleepin’] Busey?”

To some degree, I admire how “The Leftovers” is averse to explanations, because that’s the whole point: The people left behind must forever puzzle it out. (Could it happen again? How did it happen? Why did it happen?)

It resists a Hollywood temptation to lavishly depict the Sudden Departure in scenes of chaos and confusion, instead fixating on the lingering psychic wounds of the event. In the four episodes sent to critics, “The Leftovers” also sparingly avoids flashbacks, which is a surprise given that the series is co-created by Damon Lindelof, one of the two men behind ABC’s “Lost,” which used flashback (and flash-forward) as a narrative necessity. Frankly, a few more flashbacks in “The Leftovers’s” first few episodes might better acquaint viewers with what sort of story this show wants to tell, besides a depressing one.

Three years on, we figure out that some Americans viewed the departure as an act of God, flocking to the comforts of belief, while others abandoned faith entirely. Bad people disappeared as well as good people. One woman in Mapleton (Carrie Coon as Nora Durst) has become the town’s emblem for the arbitrary nature of the event: She lost her husband and both of her children. As such, she’s a featured speaker at the town’s Oct. 14 anniversary vigil, where the mayor (Amanda Warren) unveils a sculpture of a woman letting go of a floating baby.

Using Mapleton as a microcosm of society, “The Leftovers” is especially preoccupied with how everyday life changed. This is a world permanently spooked, jangled; the emotional damage cannot be mended. Characters have made drastic life changes, including joining cults — an act of intentional disappearance in response to the Sudden Departure.

Laurie (Amy Brenneman) abandoned her spouse and children to join a group called the Guilty Remnant, a bizarre and irreligious commune whose members take a vow of complete silence, wear only white clothing, smoke cigarettes all day as a symbol of their watchfulness (“Stop wasting your breath” is one of their poster slogans) and silently stalk their neighbors as a living reminder of . . . a reminder of what, exactly?

A young man named Tom dropped out of college after the departure and moved out west to the desert to serve a menacing cult leader who calls himself Holy Wayne (Paterson Joseph). Taking a page straight out of the Rev. Jim Jones’s playbook, Holy Wayne has surrounded himself with paranoid militia fighters and an obedient harem of Asian teenage girls.

“The Leftovers” is intricately imagined, but it also has an off-putting reliance on ambiguity and obfuscation. It almost goes without saying that it’s still difficult to trust Lindelof four years after the miserable wrap-up of “Lost,” a deserted-island saga he co-created that was so burdened with unanswered questions and fuzzy symbology that it became one of modern television’s favorite chew-toys. In promoting “The Leftovers,” Lindelof has described the heated reactions to “Lost’s” finale as a chastening experience, and one that he’s not eager to repeat.

There are telltale Lindelofian touches throughout, including animal metaphors, miraculous acts of coincidence and a pernicious reluctance in characters to explain themselves in a coherent way to other characters. (One is reminded of how the characters of “Lost” could never quite answer direct questions, such as: Where were you last night and what happened?)

The third episode, centered on an Episcopal preacher (Christopher Eccleston as the Rev. Matt Jamison) who has alienated his congregation with his post-departure ravings, is delivered like a sermon: It’s about gambling and greed, with a dramatic tension that builds toward a moment of karma. It’s the first hint of what sort of tapestry that Lindelof and Perrotta hope to weave.

Theroux’s Garvey is a study in heartbreak. Left alone to raise his sullen teenage daughter (Margaret Qualley), he is also haunted by his ineffectualness as a lawman who tries to keep the peace in a community where the meaning of life (and death and whatever’s in-between) has ceased to have any meaning at all. So Garvey drinks too much and flies into rages.

With all that in mind, I’m not turned off by “The Leftovers’s” lack of easy answers. What I do think it desperately needs — since “Lost” is once again on the brain — is a Hurley type of character to lighten some small part of the load that viewers are being asked to shoulder. Perrotta’s best novels (“Election”; “Little Children”) are known for their wicked uses of dark humor, which is entirely absent here.

It’s hard for a viewer to know what to do with all this excess grief, even if it’s quite beautifully offered. People watch television for all sorts of reasons, but I’m not sure they watch it to only feel worse.

The Leftovers (75 minutes) premieres Sunday, June 29 at 10 p.m. on HBO.