Eilert Lovborg arrives at the house, having been invited by Tesman via note. When the group compliments him on the success of his book, he produces his new handwritten manuscript - a sequel to the earlier book that presents his predictions for the culture of the future. The subject of the professorship comes up, and Eljert says he doesn't have any plans to compete with Tesman, as what he wants is fame. Tesman is relieved, but Hedda seems more irritated by the news than happy about it.
When Lovborg suggests that he read some of his book that evening, Tesman tries to tell him that he and Brack are off to a party, but is afraid to invite Lovborg because of his alcoholic past. While Tesman and Brack go to enjoy some punch before leaving, Hedda and Lovborg quietly discuss their past, and it becomes clear that Hedda is the "other woman" that Mrs. Elvsted was so afraid of - it was Hedda who threatened to shoot Lovborg with her pistol when their relationship "grew too close." When Lovborg tells Hedda that she should have shot him - that he doesn't understand why she didn't - Hedda replies simply, "The scandal."
Mrs. Elvsted appears and discovers that Brack and Tesman are going out to a drinking party. When Lovborg refuses punch and declines the invitation to the party, Hedda points out to Mrs. Elvsted in front of Lovborg that her concerns were unwarranted - that Lovborg is "a man of principle." Mrs. Elvsted is horrified that Hedda has said this in front of Lovborg, and Lovborg is equally enraged at Mrs. Elvsted's belief that he would suddenly start drinking again the moment he returned to town. Lovborg downs two successive drinks to punish Mrs. Elvsted.
Lovborg then decides to accompany Brack and Tesman to the party and takes his manuscript with him, hoping to read some of it at Brack's house. He promises to return later to take Mrs. Elvsted home, and the three men leave. Mrs. Elvsted is concerned that Lovborg will have a relapse, but Hedda tells her to stay and have tea, and assures her that soon enough Lovborg will return "with vine leaves in his hair."
Every time Tesman leaves the room, isolating Hedda with another man, we learn that she had some kind of relationship with that man in the past. First Brack, and now Lovborg, who arrives at the new Tesman home and quickly reveals that it is Hedda who he has not been able to forget - the woman whom Mrs. Elvsted said threatened to shoot him with pistols.
Hedda, then, is in a strangely untenable position - she has an absent husband, is pregnant with a child, and has two other men (Brack and Lovborg) throwing themselves at her. Perhaps there is a way of working these conflicts out, but Hedda has two character "flaws" that make her feel trapped - she is paralyzed by her fear of scandal, and is simultaneously incapacitated by her fear of getting too close to anybody. Thus the idea of a baby, an emotional relationship with Lovborg (whom she nearly killed when he got too close to her), or a sexual relationship with Brack are all impossible to her - she is both bored by life and unable to take steps to engage with life deeply enough to become excited by it.
When Mrs. Elvsted arrives, Hedda has been presented with the possibility of entertaining Lovborg for the night while the other men are at the party, but instead she sees only an opening to wreak havoc. Having earlier earned Mrs. Elvsted's confidence, she now sets Lovborg against Mrs. Elvsted, induces Lovborg to relapse into drinking after two years of sobriety, and drives him to go to the party with Tesman and Brack, leaving her alone with Mrs. Elvsted - a companion that, we might imagine, is most undesirable to Hedda. For all of her seeming intelligence in the way she strategizes and designs, Hedda nearly always manages to create a situation she didn't quite plan on.
It's important to realize that Hedda isn't a sexual infidel; she does not seem to have consummated her relationship with either Brack or Lovborg. In fact, it's implied that it was Lovborg's proposition of sex that inspired Hedda to bring out her pistols. This begs the question: why is Hedda so threatened by sex? Why does she link sex and "getting too close" to a man? There are of course a variety of theories that might be offered on the matter, but her sexual frigidity is one of the defining aspects of her character.
Hedda also shows a strange penchant for violence and destruction - she shoots off pistols, pinches Mrs. Elvsted's arm and threatens to burn her hair, and encourages Lovborg to drink. Whenever Hedda feels threatened - or even simply bored - her violent streak begins to show itself. This proclivity will, of course, play a crucial role in the play's climax.