With Indian Prime Minister Rajiv Gandhi's arrival this afternoon, a new world leader will be introduced to the West. The Gandhis' event-packed four-day state visit coincides with the beginning of the 18-month-long Festival of India, a nationwide celebration of Indian culture.

Gandhi, who is expected to be accompanied by his wife much of the time, will make the traditional rounds, from the White House to the State Department and to Capitol Hill. He will also visit two museum exhibits, attend a state dinner, appear at four receptions here and in Houston, speak to the National Press Club, confer with four Cabinet secretaries, listen to a Festival inaugural concert and address a joint session of Congress.

He will also meet with a group of Indian physicians, three groups of Indians living in the United States, a group of American scientists and astronomer Carl Sagan.

He probably will not have time to see much of his two children, who are accompanying him and his wife, Sonia. "It's a very tight schedule," said Indian Embassy spokesman Deepak Vohra.

After leaving Washington later in the week, Gandhi will tour the Astronaut Training Facilities and Mission Control Room at the Johnson Space Center in Houston, meet with the mayor of the city and with representatives of high-technology firms.

Throughout all of this, the 40-year-old Gandhi, whose visit is expected to spark Sikh demonstrations here, will be under very tight security. Following the assassination of his mother, Prime Minister Indira Gandhi, by Sikh bodyguards in October 1984 and last month's arrest in New Orleans of a small group of Sikhs on charges of plotting to kill Rajiv Gandhi, Indian and American authorities have been operating with more than the usual secretiveness.

The entire Gandhi family will attend the state arrival ceremony at the White House, but otherwise the embassy is not releasing any information about separate schedules for Sonia Gandhi, their 13-year-old daughter Priyanka and 11-year-old son Rahul. The Gandhis will be staying at the ambassador's residence, instead of at a hotel.

"There are several factors involved," the embassy spokesman said. "Suffice it to say, the prime minister most graciously agreed to stay at the residence."

Originally, Indira Gandhi was scheduled to open the Festival but when her son became prime minister after her death, the trip was upgraded to a state visit.

Sagan, the Cornell University astronomer, along with several others, will present a statement to Gandhi supporting the Five Continent Peace Initiative, a movement to halt the testing, production and deployment of nuclear weapons. Gandhi has been involved in the initiative.

The Indian leader's visit to Houston, says a source close to the prime minister, stems from Gandhi's "own interest in high technology, space, air . . . and shows sort of a 20th-century young man in all ways, the excitement, the promise of space and his curiosity."

And if American press coverage of all of this is inevitable, imagine the Indian interest.

Bettey Bradley, public relations director at the Embassy Row Hotel, says the Indian press corps accompanying Gandhi and artists involved in the festival have taken about 60 rooms.

"If you could see downstairs, you would not believe it," she said. "They took our whole ballroom and turned it into a press room. They have 10 telexes set up. We even had to give them a darkroom. I put a darkroom into what used to be a kitchen."