The Spiral of Silence
The initial spiral of silence theory was developed between the 1960s and 70s by German researcher Elisabeth Noelle-Neumann in response to novel shifts of public opinion demonstrated during the 1965 German federal election campaign. (link) The two major competing parties were the (already ruling) Christian Democratic Union-Christian Social Union (CDU-CSU) and the Social Democratic Party of Germany (SDP). Despite voter preference surveys indicating the country to be pretty evenly split between the two parties, there was a sudden shift to the favor of the CDU-CSU in just the last few weeks of campaigning, from about 45% voter support for each party to 48% for the CDU-CSU and 39% for the SDP.

Noelle-Neumann theorized that the shift may have been single-handedly instigated by CDU chancellor Ludwig Erhard. He often accompanied Queen Elizabeth II during her visit to Germany in July 1965, and this may have sparked newfound optimism in supporters of the CDU-CSU such that they were more vocal about their political beliefs. Noelle-Neumann further supposed that this vocality from the CDU-CSU may have further led the quieter supporters of the SDP to assume that their political beliefs were not widely held, leading to suppression of those ideas, and an ultimate loss at election. This is the spiral of silence theory- that people are prone to self-censor their opinions on policy if they believe those opinions are not widely held.
The question is, does the internet exacerbate this phenomenon? On platforms like Twitter and Reddit, it's easier than ever for any individual to broadcast their beliefs and engage in discourse around social and political issues. However, the wider possible reach of one's expression of a belief may deter them from doing so, as the amount of criticism in addition to the harshness of said criticism is potentially higher on internet platforms (according to digital dualism). And some 2014 surveys from Pew Research corroborate this notion. Participants were asked to identify how willing they would be to participate in a conversation about government surveillance depending on where the conversation was held and who with. They were least willing to express their opinions over the platforms of Twitter and Facebook by a significant margin.
Shown above: An educational video on the spiral of silence as it relates to social justice
Despite the fact that people are generally less willing to express their political beliefs online, meta-analytic evidence indicates that (as well as we can measure it) instances and effects of the spiral of silence do not differ in significance online and offline.
There's not much room for doubt that the spiral of silence is an observable phenomenon, and it's believable that it interferes with the open discourse. However, it's just not yet clear that the internet exacerbates the discoursal interference of the spiral of silence in any significant way. Presumably, when people don't want to broadcast their political opinions online for many to view, this would track offline as well (as in, people wouldn't want to stand up in front of a group of unknown people and share their opinions either). More research may be needed, though.