The Scottish and UK Governments should make it clear that university principals and academics will not face retribution in terms of future funding if they speak out in the independence debate, the president of the Royal Society has said.
Sir Paul Nurse said some working in Scotland's universities feel inhibited about expressing their views.
He made the comments during a Better Together event in Edinburgh at which he said medical and scientific research would suffer in the event of a Yes vote.
His concerns were endorsed by Sir David Carter, a former Chief Medical Officer in Scotland, who said he feared the general public may take silence from universities as "tacit support" for the Scottish Government.
Both men have made their views public in letters outlining why they believe Scotland's research funding is threatened by independence.
Sir Paul, who co-signed a letter to newspapers with Lord Stern president of the British Academy and Sir John Tooke, president of the Academy of Medical Sciences, told the audience : "Some in our universities feel inhibited about speaking out because of fear of retribution in relation to future funding.
"I do not know if this is correct but I am sure politicians in both Scotland and the rest of the UK will want an open and free debate, as it is so central to the democratic process and coming to the right decision.
"To promote this important debate both the Scottish and UK Governments should endorse a free and open expression of views from academics, and make it clear that there would be no subsequent retribution concerning funding regardless of the views expressed and the final outcome of the referendum.
"This is essential for the democratic process and if the right decisions about this extremely important constitutional issue are to be made."
Sir David said: "My concern is that the general public might take silence on the part of Scottish universities as tacit support for the Scottish Government."
He said he had contacted the principals of the five universities in Scotland with medical schools to ask if they felt "constrained and unable to speak out".
"The answer came back that yes we do feel constrained and unable to speak out, and we would apply that not just to ourselves as principals but to our senior management as well," he said.
Sir David said he had "no doubt" they would be voting against independence.
Meanwhile he said 93.5% of the fellows in Scotland of the Academy of Medical Sciences said they would vote No, with 91% stating a Yes vote would have a "negative or strongly negative effect" on research funding.
Earlier this year Sir David signed an open letter alongside 13 other clinical academics and scientists raising ''grave concerns that the country does not sleepwalk into a situation that jeopardises its present success in the highly-competitive arena of biomedical research''.
He dismissed claims that an independent Scotland would establish a common research area with the rest of the UK.
"The 14 of us thought that would be a very difficult undertaking," he said.
"A lot of what the SNP say is wishful thinking and simply won't happen."
Referring to a recent opinion poll showing 54% support for No and 35% for Yes, he added: "It looks to me as if Scotland is awake after all. People are not that stupid - it will not be all right on the night as the nationalists keep telling us."
Speakers at the event also included Professor Hugh Pennington, Gordon Brown and Sir David Steel.
They also argued that Scotland has done particularly well through its access to UK research funding, stating that this would be put at risk by a Yes vote.
A Scottish Government spokeswoman said: "The Scottish Government has already shown our commitment to research through increased investment since 2007 and we will continue to support research in an independent Scotland providing levels of public investment in university research which enable our universities to remain internationally competitive.
"With independence it will continue to be in the interest of both Scotland and the UK to collaborate as part of a single research area.
"Scotland currently contributes substantially to UK Research Councils' funding through its share of UK tax receipts and, with independence, we will negotiate with the UK Government a fair funding formula for Scotland's contribution."
Professor Bryan MacGregor, a spokesman for Academics for Yes, said: 'The simple truth is that Scotland does well in open competition for funds but poorly where funds are allocated by other means, such as for research council centres and private research and development.
"The Scottish Government is committed to proper funding of research and other benefactors will support quality research wherever it takes place. Charities already raise substantial funds in Scotland."
A spokesman for Education Secretary Michael Russell said: "Academics at universities in Scotland and elsewhere are playing a very active and welcome part in the referendum debate and the fact that there are academic campaigns on either side of the referendum shows how open and vigorous that debate is. For example 60 academics have signed a public statement in support of a Yes vote.
"As the professors themselves say there is no evidence for their concerns and as all academics know funding is determined by the Funding Council which is made up of academics and universities themselves, not by government or politicians.
"With independence we have already guaranteed the continuation of research funding across Scotland's universities and as research becomes increasingly international an independent Scotland with our excellent universities and world leading reputation will be in prime position to capitalise on new opportunities.
"Independence will also ensure that by having access to all of our own resources we can maintain free higher education and not face the continued pressure of Westminster austerity."